Browse Function problems Studdy Solved!

Problem 6201

Select and graph the function that represents continuous data. Function A: $f(x)=2 x-5$ , where the domain is $\{x \in R\}$ unction B: $h(x)=3 x+4$ , where the domain is $\{-2,-1,0,1,2\}$ nded Response he graph shows soil temperature over 3 days at different depth

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Problem 6202

5.
Describe the domain for the following function. Write your answer in interval notation. $f(x)=\frac{1}{x-7}-\frac{\sqrt{x+2}}{x-6}$

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Problem 6203

\begin{tabular}{|c||c|c|c|c|c|c|c|} \hline \begin{tabular}{c} $t$ \\ (in seconds) \end{tabular} & 0.1 & 0.5 & 0.9 & 1.5 & 1.9 & 2.3 & 2.6 \\ \hline \begin{tabular}{c} $H(t)$ \\ (in meters) \end{tabular} & 1.4 & 5.7 & 8.4 & 9.6 & 8.4 & 5.6 & 2.5 \\ \hline \end{tabular}
1. Justin Tucker, the kicker for the Baltimore Ravens, is considered one of the greatest kickers in NFL history. On a recent kickoff, the height of the ball, in meters, was measured for selected times. This data is shown in the table above. a) Based on this situation and the data presented in the table, would a linear, quadratic, or cubic function be most appropriate to model this data? Give a reason for your answer. b) Find the appropriate regression function to model these data. c) Using the model found in part $b$ , what is the predicted height of the football, in meters, at tine $t=1.3$ seconds?

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Problem 6204

A cleaning company charges $\$ 120$ for each office it cleans. The fixed monthly cost of $\$ 490$ for the company includes telephone service and the depreciation on cleaning equipment and a van. The variable cost is $\$ 50$ per office and includes labor, gasoline, and cleaning supplies. (a) Write a linear cost function representing the cost $C(x)$ (in $\$$ ) to clean $x$ offices per month. (b) Write a linear revenue function representing the revenue $R(x)$ (in $\$$ ) for cleaning $x$ offices per month. (c) Determine the number of offices to be cleaned per month for the company to break even. (d) If 10 offices are cleaned, will the company make money or lose money?
Part 1 of 4 (a) The linear cost function representing the cost is $C(x)=490+50 x$ .
Part: $1 / 4$
Part 2 of 4 (b) The linear revenue function representing the revenue is $R(x)=\square$ . Skip Part Check Save For Later Submit earch

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Problem 6205

Find a quadratic function $f(x)=a x^{2}+b x+c$ whose vertex is $(4,5)$ and whose $y$ -intercept is $(0,21)$ .

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Problem 6206

Analyze the polynomial function $f(x)=-4(x+4)(x-3)^{3}$ using parts (a) through (h) below. (a) Determine the end behavior of the graph of the function.
The graph of $f$ behaves like $y=$ $\square$ for large values of $|x|$ . (b) Find the $x$ -and $y$ -intercepts of the graph of the function.
The $x$ -intercept(s) is/are $\square$ . (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)
The $y$ -intercept(s) is/are $\square$ 1. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.) (c) Determine the real zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept.
The real zero(s) of $f$ is/are $\square$ (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed. Type each answer only once.)
The lesser zero is a zero of multiplicity $\square$ , so the graph of $f(1)$ $\qquad$ the $x$ -axis at $x=$ $\qquad$ . The greater zero is a zero of multiplicity $\square$ so the graph off (2) $\qquad$ the $x$ -axis at $x=$ $\square$ . (d) Use a graphing utility to graph the function. The graphs are shown in the viewing window $X_{\min }=-10, X_{\max }=10, X_{s d l}=1$ , $Y_{\min }=-2100, Y_{\max }=2100 Y_{\text {scl }}=210$ . Choose the correct graph below. A. B. c. D.

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Problem 6207

Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.) $f(x, y)=6 x^{2}+2 x y+3 y^{2}$ a. $\nabla f(x, y)=6 y \mathbf{i}-12 x \mathrm{j}$ b. $\nabla f(x, y)=12 x i+6 y \mathbf{j}$ c. $\nabla f(x, y)=6 y \mathbf{i}+12 x \mathbf{j}$ d. $\nabla f(x, y)=(6 x+2 y) \mathbf{i}+(12 y+2 x) \mathbf{j}$ e. $\nabla f(x, y)=(12 x+2 y) \mathbf{i}+(6 y+2 x) \mathbf{j}$

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Problem 6208

Select the correct choice that completes the sentence below. The vertical line through the vertex of a parabola that opens upward or downward is the $\square$ of the parabola. The two halves of the parabola are $\square$ images of each other across this line. Clear all Final chest

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Problem 6209

Find the slope of the line passing through the given points. $(-4,4),(-6,10)$
The slope of the line is $\square$ 16 (Type an integer or a simplified fraction.)

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Problem 6210

2. Estimate the affordable monthly mortgage payment, the affordable mortgage amount, and the affordable home purchase price for the following situation (Figure 9.1.4 Mortgage Affordability Calculation).
Monthly gross income, \$4,167 Down payment to be made-15 percent of purchase price
Other debt (monthly payment), \$500 Monthly Property Taxes and Home Insurance, \$200 30-year loan at 8 percent a. Affordable monthly mortgage payment b. Affordable mortgage amount c. Affordable home purchase

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Problem 6211

The Second Gate As you move through the first gate, you can see another gate not far in front of you. You approach the second gate and your computer reads: "There are 2 values for which the below function does not exist. The passcode is the limit of $g(x)$ as $x$ approaches the smaller of these two values." $g(x)=\frac{x+5}{x^{2}-25}$
Your computer also reminds you to type "infinity" for $\infty$ , "-infinity" for $-\infty$ , and "NA" if the limit does. not exist. What do you enter for your computer to translate? $a^{b}$ $\sin (a)$ $\infty$ $\alpha$ 而 $\square$
Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team. $\square$ $\square$ 4 15 D Equation Editor Editor $\underline{A} \cdot \boldsymbol{A} \cdot \underline{I}_{x}$ B $I \underline{u} \quad \mathcal{S} x_{2} x^{2}$

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Problem 6212

Given the function shown in the graph below, state the domain and range of the function using interval notation:
Domain: $\square$ Range: $\square$

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Problem 6213

bicyclist traveling at $12 \mathrm{ft} / \mathrm{sec}$ uts on the brakes to slow down at constant rate, coming to a stop n 7 seconds. The figure shows the relocity of the bike during braking. velocity ( $\mathrm{ft} / \mathrm{sec}$ ) a) What are the values of $a$ and $b$ in the figure? $\begin{array}{l} a=\square \\ b=\square \end{array}$ b) How far does the bike travel while braking?
The distance traveled while braking is $\square$ feet. Textbook and Media

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Problem 6214

Current Attempt in Progress The velocity of a car is $f(t)=4 t$ meters $/ \mathrm{sec}$ . Use a graph of $f(t)$ to find the exact distance traveled by the car, in meters, from $t=0$ to $t=6$ seconds.
The distance traveled by the car is $\square$ meters. eTextbook and Media

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Problem 6215

Given the function shown in the graph below, state the domain and range of the function using interval notation:
Domain: $\square$ Range: $\square$

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Problem 6216

Given the function shown in the graph below, state the domain and range of the function using interval notation:
Domain: $\square$
Range: $\square$ $(-2,2)$ 6

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Problem 6217

decreasing when the diameter is 70 cm . (Note the answer is a positive number) 重

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Problem 6218

Find a formula for the exponential function shown in the graph. Use the variables $x$ and $f(x)$ or $x$ and $y$ .
If necessary, round any parameters of the function to four decimal places: Formula: $\square$

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Problem 6219

Suppose that $F^{\prime}(x)=f(x)$ and $F(0)=3, F(2)=7$ . a. What is the area under $y=f(x)$ over $[0,2]$ if $f(x) \geq 0$ ? b. What is the graphical interpretation of $F(2)-F(0)$ if $f(x)$ takes on both positive and negative values?

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Problem 6220

Find the percentage rate of change of $f$ at the given value of $x$ . $f(x)=\sqrt{2 x^{2}+23} ; x=1$ $\square$ percent per unit change in $x$ Need Help? Read It

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Problem 6221

The total revenue and total cost functions for the production and sale of $x$ TV s are given as $\left(x(x)=160 x-0.5 x^{2}\right.$ and $C(x)=3240+14 x$ (A) Find the value of $x$ where the graph of $R(x)$ has a horizontal tangent line. $x$ values is 160 (B) Find the profit function in terms of $x$ . $P(x)=-0.5 x^{2}+146 x-3240$ (c) Find the value of $x$ where the graph of $P(x)$ has a horizontal tangent line. x vallues $=146$ (1) ist all the $x$ values of the break-even point(s).
If there are no break-even points, enter NONE List of $x$ values =

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Problem 6222

11. What is the maximum value of the function $y=2 \cos \frac{2 \pi}{3}(x-7)-8$ ? [8.7] A. 2 B. -6 C. -5 D. -10

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Problem 6223

Consider the graph shown below. y 200 150 100 8. 4 2 50 50 100 150 -200 2 X 6 8 -250 If the complete graph of the function is shown, estimate the absolute maximum and absolute minimum. absolute maximum (x, y) = absolute minimum (x, y) =

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Problem 6224

The points $(-3,-4)$ and $(-5,-9)$ are a maximum and minimum, respectively, of a periodic function $f(x)$ , which has period 9 . What is the amplitude of the function? The amplitude is $\square$ 2.5 $\square$ What is an equation for the midline? The midline is $y=$ $\square$ $-6.5$
Which of the following points must lie on the graph of the function $y=f(x)$ ? Select all that are correct. $(31,-12)$ $(-50,-9)$ $(22,-4)$ $(31,-9)$ $(24,-4)$ $(-48,-1)$ None of the above

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Problem 6225

Determine the domain and range of the quadratic function. (Enter your answers using interval notation.) $f(x)=-3(x+2)^{2}-6$ domain $\square$ range $\square$

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Problem 6226

Question 10
Find the present value of a continuous income stream $F(t)=30+8 t$ , where $t$ is in years and $F$ is in thousands of dollars per year, for 5 years, if money can earn $2.1 \%$ annual interest, compounded continuously.
Present value $=$ $\square$ thousand dollars.

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Problem 6227

Function $A$ and Function $B$ are linear functions.
Function A
Function B \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 3 & 2 \\ \hline 6 & 3 \\ \hline 9 & 4 \\ \hline \end{tabular}

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Problem 6228

Edgar accumulated $\$ 6,000$ in credit card debt. If the interest rate is $30 \%$ per year, and he does not make any payments for 3 years, how much will he owe (in dollars) on this debt in 3 years by each method of compounding? (Simplify your answers completely. Round your answers to the nearest cent.) (a) compound quarterly \\square $(b) compound monthly \$$ \square $(c) compound continuously \$$ \square$

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Problem 6229

The vertex of a parabola is always located midway between the focus and the directrix. True False

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Problem 6230

20. Write an equation that represents the sine function graphed below. [8.7]

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Problem 6231

Given that $\log (2) \approx 0.3010$ , find the value of the logarithm. $\log (\sqrt{2})$ $\square$ Need Help? Watch it

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Problem 6232

Growth of a Fruit Fly Population On the basis of data collected during an experiment, a biologist found that the growth of a fruit fly population (Drosophila) with a limited food supply could be approximated by $N(t)=\frac{600}{1+24 e^{-0.23 t}}$ where $t$ denotes the number of days since the beginning of the experiment. (a) What was the initial fruit fly population in the experiment? $\square$ flies (b) What was the population of the fruit fly colony on the $t=17$ day? (Round your answer to the nearest integer.)" $\square$ flies

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Problem 6233

21. Determine the exact values of the six trigonometric ratios for $585^{\circ}$ . [8.1] [2 marks]

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Problem 6234

L steps for full marks as required. Correct answer with NO work shown = NO ma
1. Determine the exact values of the six trigonometric ratios for $585^{\circ}$ . [8.1] [2 marks]

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Problem 6235

The function $f(x)=2 x^{3}-33 x^{2}+168 x-10$ has two critical numbers.
Give the two critical numbers as a commaseparated list. $x=$ $\square$

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Problem 6236

An artifact originally had 16 grams of carbon-14 present. The decay model $A=16 e^{-0.000121 t}$ describes the amount of carbon-14 present after $t$ years. Use the model to determine how many grams of carbon-14 will be present in 8969 years.
The amount of carbon-14 present in 8969 years will be approximately $\square$ grams. (Round to the nearest whole number.)

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Problem 6237

Evaluate the definite integral $\int_{0}^{\pi} 10 \sin (x) d x$

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Problem 6238

If $f(x)=\int_{0}^{x}\left(16-t^{2}\right) e^{t^{3}} d t$ for all $x$ , then find the largest open interval on which $f$ is increasing. Answer (in interval notation): $\square$

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Problem 6239

HW\#6 Part 2 of 2 points Points: 0.5 of 1 Save
The following function is one-to-one. Find the inverse of the function and graph the function and its inverse on the same set of axes. $\begin{array}{r} f(x)=2 x+3 \\ f^{-1}(x)=\frac{x-3}{2} \end{array}$ (Type a simplified fraction.) Use the graphing tool to graph the function and its inverse. View an example Get more help - Clear all

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Problem 6240

The function $f(x)=\frac{1}{x+4}-3$ is a rational function. a. Use transformations of $y=\frac{1}{x}$ or $y=\frac{1}{x^{2}}$ to sketch the graph. b. Find all $x$ -intercepts or state that the function has no $x$ -intercepts. c. Find the $y$ -intercept or state that the function does not have a $y$ -intercept. d. Find the equation(s) of all vertical asymptotes. e. Find the equation(s) of all horizontal asymptotes.

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Problem 6241

Find the definite integral. (Use symbolic notation and fractions where needed.) $\int_{-\pi / 4}^{\pi / 2} \cos (x) d x=$ $\square$

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Problem 6242

8987.19 8987.19 incorrect
The answer above is NOT correct.
A retail store estimates that weekly sales $s$ and weekly advertising costs $x$ (both in dollars) are related by $s=50000-440000 e^{-0.0003 x}$
The current weekly advertising costs are 2000 dollars and these costs are increasing at the rate of 300 dollars per week. Find the current rate of change of sales.
Rate of change of sales $=$ $\square$ 8987.1

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Problem 6243

Question 3 of 32 Find the area under the graph of $f(x)=\frac{5}{\sqrt{1-x^{2}}}$ from 0 to $\frac{1}{\sqrt{2}}$ .

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Problem 6244

(b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of $1 \mathrm{~m} / \mathrm{s}$ , how fast is the area of the spill increasing when the radius is 30 m ? $\square$ $\mathrm{m}^{2} / \mathrm{s}$
Viowing Saved Work Revert to Last Response

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Problem 6245

Given: $y=\log _{5} x$ a. Rewrite to exponential form. $\square$ b. Which of the following graphs represents the equation

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Problem 6246

Consider the function.(If an answer does not exist, enter DNE.) $f(x)=(x-4)^{2}(x-8)^{2}$ (a) Determine intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation.) increasing $\square$ decreasing $\square$ (b) Determine the local minima and maxima of $f$ . (Enter your answers as comma-separated lists.) locations of local minima $\quad x=$ $\square$ locations of local maxima $\quad x=$ $\square$ (c) Determine intervals where $f$ is concave up or concave down. (Enter your answers using interval notation.) concave up $\square$ concave down $\square$ (d) Determine the locations of inflection points of $f$ . Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. (Enter your answers as a comma-separated list.) $x=$ $\square$

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Problem 6247

Without graphing, find the vertex, $f(x)=-\frac{2}{3}(x+8)^{2}+4$
What is the vertex? $\square$

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Problem 6248

Without graphing, find the vertex, the axis of symmetry, and $f(x)=-\frac{2}{3}(x+8)^{2}+4$
What is the vertex? $(-8,4)$ (Type an ordered pair.) What is the equation of the axis of symmetry? $\square$

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Problem 6249

Schoof Hame I Microsoft 365 Teams and Channels / General / M 14 of 23 Next ? Cl ถ B $<$ Marbleslides: Parabolas nirban khunkhun
Use your own advice from the last screen. Did it help? c $y=2(x-2)^{2}+4$
Verify \#4 « samen 1212024

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Problem 6250

$\begin{aligned} &\text{Given the cost function } C(x) = 60,000 + 60x, \\ &\text{and the price function } p = 200 - \frac{x}{50}, \quad 0 \leq x \leq 10,000, \\ &\text{solve the following:} \\ &\text{(A) Find the maximum revenue.} \\ &\text{(B) Find the maximum profit, the production level that will realize the maximum profit,} \\ &\text{and the price the company should charge for each television set.} \\ &\text{(C) If the government decides to tax the company \$5 for each set it produces,} \\ &\text{how many sets should the company manufacture each month to maximize its profit?} \\ &\text{What is the maximum profit? What should the company charge for each set?} \end{aligned}$

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Problem 6251

Using a Pattern to Form an Equation
The table shows a representation of the number of miles a car drives over time. \begin{tabular}{|c|c|} \hline Hours, $\boldsymbol{x}$ & Miles, $\boldsymbol{y}$ \\ \hline 3 & 195 \\ \hline 4 & 260 \\ \hline 5 & 325 \\ \hline 6 & 390 \\ \hline \end{tabular}
Pattern: Each $x$ value is multiplied by 65 to get eachy value.
What is the equation for this situation? $\square$ Which could NOT be a point on this table? $\square$

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Problem 6252

Follow the link Least Squares Line. This will direct you to a spreadsheet download that may be useful for checking your work for the exercise. Astronomer Edwin Hubble postulated a relationship between the distance between Earth and the velocity at which a galaxy appears to be traveling away from Earth. The following table shows observations of seven galaxies. Distance is measured in megaparsecs ( 1 Mpc is approximately 3,260 light-years), and velocity is measured in kilometers per second. \begin{tabular}{|c|c|} \hline Distance (Mpc) & Velocity (km/s) \\ \hline 51.8 & 4,560 \\ \hline 12.2 & 1,184 \\ \hline 27.1 & 1,736 \\ \hline 46.2 & 3,807 \\ \hline 58.2 & 5,168 \\ \hline 46.2 & 3,807 \\ \hline 29.1 & 1,714 \\ \hline \end{tabular} (a) Find the equation of linear regression line for the data where distance is the independent variable, $x$ , and velocity is the dependent variable. (Round your numerical answers to two decimal places.) $\hat{y}=\square$ (b) Using the equation from part (a), estimate the velocity (in kilometers per second) at which a galaxy 130 Mpc from Earth is traveling. (Round your answer to the nearest whole number.) $\qquad$ $\mathrm{km} / \mathrm{s}$

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Problem 6253

12.3 Performing Linear Regressions with Technology
1. An economist is trying to understand whether there is a strong link between CEO pay ration and corporate revenue. The economist gathers data, including the CEO pay ratio and the corporate revenue for 10 companies for a particular year. The pay ratio data is reported by the companies themselves and represents the ratio of CEO compensation to the median employee salary. The data has been reproduced in the table below. Corporate Revenue (million \$) \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|} \hline CEO & 286 & 944 & 321 & 268 & 183 & 309 & 132 & 264 & 236 & 259 \\ \hline Revenue & 21,973 & 29,846 & 38,507 & 18,912 & 25,947 & 97,023 & 35,888 & 59,131 & 60,579 & 27,242 \\ \hline \end{tabular} a) What is the equation of the line of best fit? b) What is "r "and determine if it is a strong, moderate, or weak correlation.

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Problem 6254

Find the derivative of the function. $\begin{array}{r} f(x)=\ln (9 x) \\ f^{\prime}(x)=\square \end{array}$ Need Help? Watch It

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Problem 6255

Find the derivative of the function. $\begin{array}{l} f(x)=\ln (\sqrt{x}+5) \\ f^{\prime}(x)=\square \end{array}$

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Problem 6256

Solve a Consumers' or Producers' Surplus Problem.
The price-supply equation for some commodity is given by $p=S(x)=14+1.8 x$ and the equilibrium point is $(23,55.4)$ Find the producers' surplus.
The surplus is $\square$ (Your answer must begin with \$.)

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Problem 6257

Find the derivative of the function. $\begin{array}{l} f(x)=\ln \left(2 x^{2}-5 x+8\right) \\ f^{\prime}(x)=\square \end{array}$

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Problem 6258

Solve a Consumers' or Producers' Surplus Problem.
A cordless leaf blower has a price-demand equation given by $p=D(x)=5749.8-2.1 x^{2}$ dollars, which gives the price per leaf blower when $x$ leaf blowers are demanded. The price-supply equation for the leaf blower is given by $p=S(x)=2.1 x^{2}$ dollars, which gives the price per leaf blower when $x$ leaf blowers are supplied. Find the consumers' surplus and the producers' surplus.
The consumers' surplus is $\square$ ( Your answer must begin with \$.)
The producers' surplus is $\square$ (Your answer must begin with \$.)

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Problem 6259

Find a function $F$ such that $\mathbf{F} = \nabla f$ , where $\mathbf{F}(x, y) = \langle 2x, 4y \rangle$ , and $C$ is the arc of the parabola $x = y^2$ from $(4, -2)$ to $(1, 1)$ .

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Problem 6260

3. [-/2 Points]
DETAILS MY NOTES
MARSVECTORCALC6 3.4.012. PRACTICE ANOTHER
Use the method of Lagrange multipliers to find the absolute maximum and minimum values of $f(x, y)=x^{2}+y^{2}-x-y+5$ on the unit disc, namely, $D=\left\{(x, y) \mid x^{2}+y^{2} \leq 1\right\}$ . maximum $\square$ $\square$ minimum
Additional Materials eBook

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Problem 6261

54.Дараах функцийн уламжлалыг үржвэрийн уламжлалын дүрмээр ол. Хэрэв боломжтой бол нийлбэр функц болгоод, уламжлалыг ол. Гарсан хариунуудыг жиш. a) $y=x^{2}(x-3)$ б) $y=\sqrt{x}\left(x^{2}+3 x\right)$ в) $y=\sin 2 x \cos 4 x$ г) $y=\cos 3 x \cos x$ д) $y=\sin 4 x \sin 6 x$ e) $y=\sin 2 x \cos x$ 109

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Problem 6262

4. [-/4 Points] DETAILS MY NOTES MARSVECTORCALC6 3.4.015.
Find the extrema of $f(x, y)=4 x+2 y$ , subject to the constraint $2 x^{2}+3 y^{2}=189$ . maximum $\square$ at $(x, y)=($ $\square$ ) minimum $\square$ at $(x, y)=($ $\square$ )
Additional Materials $\square$ eBook

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Problem 6263

Determine whether the function given by the table is linear, exponential, or neither. If the function is linear, find a linear function that models the data; if it is exponential, find an exponential function that models the data. \begin{tabular}{|rr|} \hline $x$ & $f(x)$ \\ \hline-1 & $\frac{1}{8}$ \\ 0 & 1 \\ 1 & 8 \\ 2 & 64 \\ 3 & 512 \\ \hline \end{tabular}
Select the correct choice below and fill in any answer boxes within your choice. A. The function is linear. A linear function that models the data is $f(x)=$ $\square$ (Simplify your answer.) B. The function is exponential. An exponential function that models the data is $f(x)=$ $\square$ $\square$ . (Simplify your answer.) C. The function is neither linear nor exponential.

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Problem 6264

Find the extrema of $f$ subject to the stated constraint. $f(x, y, z)=x-y+z$ , subject to $x^{2}+y^{2}+z^{2}=7$ maximum $\quad(x, y, z)=(\square)$ minimum $\quad(x, y, z)=(\square)$
Additional Materials eBook

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Problem 6265

Find the derivative of the function. $\begin{array}{l} f(x)=7 x^{2} \ln (6 x) \\ f^{\prime}(x)=\square \end{array}$ Need Help? Watch It

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Problem 6266

The half-life of the radioactive element unobtanium-41 is 20 seconds. If 176 grams of unobtanium-41 are initially present, how many grams are present after 20 seconds? 40 seconds? 60 seconds? 80 seconds? 100 seconds? The amount left after 20 seconds is grams.

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Problem 6267

Elasticity of Demand The demand function for a certain brand of backpacks is $p=53 \ln \left(\frac{53}{x}\right) \quad(0<x \leq 53)$ where $p$ is the unit price in dollars and $x$ is the quantity (in hundreds) demanded per month. (a) Find the elasticity of demand $E(p)$ . $E(p)=$ $\square$
Determine the range of prices corresponding to inelastic, unitary, and elastic demand. Demand is inelastic if $\square$ , unitary if $\square$ --Select-, and elastic if $\square$ -Select--. (b) If the unit price is increased slightly from $\$ 53$ , will the revenue increase or decrease? The revenue will increase. The revenue will decrease. The revenue will remain constant.

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Problem 6268

A bottle of ginger ale initially has a temperature of $72^{\circ} \mathrm{F}$ . It is left to cool in a refrigerator that has a temperature of $34^{\circ} \mathrm{F}$ . After 10 minutes the temperature of the ginger ale is $62^{\circ} \mathrm{F}$ . Complete parts a through c. a. Use Newton's Law of Cooling, $\mathrm{T}=\mathrm{C}+\left(\mathrm{T}_{0}-\mathrm{C}\right) e^{\mathrm{kt}}$ , to find a model for the temperature of the ginger ale, T , after t minutes. $\mathrm{T}=\square+\square \mathrm{e}^{\square}$ (Simplify your answer. Use integers or decimals for any numbers in the equation. Round to four decimal places as needed.)

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Problem 6269

A bottle of ginger ale initially has a temperature of $72^{\circ} \mathrm{F}$ . It is left to cool in a refrigerator that has a temperature of $34^{\circ} \mathrm{F}$ . After 10 minutes the temperature of the ginger ale is $62^{\circ} \mathrm{F}$ . Complete parts a through c. a. Use Newton's Law of Cooling, $\mathrm{T}=\mathrm{C}+\left(\mathrm{T}_{0}-\mathrm{C}\right) e^{k t}$ , to find a model for the temperature of the ginger ale, T , after t minutes. $T=34+(38) e^{-0.0305 t}$ (Simplify your answer. Use integers or decimals for any numbers in the equation. Round to four decimal places as needed) b. What is the temperature of the ginger ale after 15 minutes? $\square^{\circ} \mathrm{F}$ (Round to nearest degree as needed.)

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Problem 6270

A bottle of ginger ale initially has a temperature of $72^{\circ} \mathrm{F}$ . It is left to cool in a refrigerator that has a temperature of $34^{\circ} \mathrm{F}$ . After 10 minutes the temperature of the ginger ale is $62^{\circ} \mathrm{F}$ . Complete parts a through c. a. Use Newton's Law of Cooling, $\mathrm{T}=\mathrm{C}+\left(\mathrm{T}_{0}-\mathrm{C}\right) e^{\mathrm{kt}}$ , to find a model for the temperature of the ginger ale, T , after t minutes. $T=34+(38) e^{-0.0305 t}$ (Simplify your answer. Use integers or decimals for any numbers in the equation. Round to four decimal places as needed.) b. What is the temperature of the ginger ale after 15 minutes? $58^{\circ} \mathrm{F}$ (Round to nearest degree as needed.) c. When will the temperature of the ginger ale be $52^{\circ} \mathrm{F}$ ? $\square$ minute(s) (Round to nearest minute as needed.)

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Problem 6271

A bottle of seltzer water initially has a temperature of $79^{\circ} \mathrm{F}$ . It is left to cool in a refrigerator that has a temperature of $40^{\circ} \mathrm{F}$ . After 10 minutes the temperature of the seltzer water is $66^{\circ} \mathrm{F}$ . Complete parts a through C . a. Use Newton's Law of Cooling, $\mathrm{T}=\mathrm{C}+\left(\mathrm{T}_{0}-\mathrm{C}\right) e^{\mathrm{kt}}$ , to find a model for the temperature of the seltzer water, T , after t minutes. $T=40+(39) e^{-0.0405 t}$ (Simplify your answer. Use integers or decimals for any numbers in the equation. Round to four decimal places as needed.) b. What is the temperature of the seltzer water after 15 minutes? $\square$ ${ }^{\circ} \mathrm{F}$ (Round to nearest degree as needed.)

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Problem 6272

A bottle of seltzer water initially has a temperature of $79^{\circ} \mathrm{F}$ . It is left to cool in a refrigerator that has a temperature of $40^{\circ} \mathrm{F}$ . After 10 minutes the temperature of the seltzer water is $66^{\circ} \mathrm{F}$ . Complete parts a through c . a. Use Newton's Law of Cooling, $T=C+\left(T_{0}-C\right) e^{k t}$ , to find a model for the temperature of the seltzer water, $T$ , after $t$ minutes. $T=40+(39) e^{-0.0405 t}$ (Simplify your answer. Use integers or decimals for any numbers in the equation. Round to four decimal places as needed) b. What is the temperature of the seltzer water after 15 minutes? $61^{\circ} \mathrm{F}$ (Round to nearest degree as needed.) c. When will the temperature of the seltzer water be $49^{\circ} \mathrm{F}$ ? $\square$ minute(s) (Round to nearest minute as needed.)

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Problem 6273

3. State the domain and range of each function. Explain your thinking. a. $f(x)=-3 \sqrt{2 x+8}-1$ [4 marks] b. $g(x)=-5 \cos (9[x-80 \pi])+3[3$ marks] c. $-2 \log _{3}\left(x^{2}-5\right)+1$ [4 marks]

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Problem 6274

As you walk through Gate 4 , you realize that Gate 5 is nowhere to be found. In front of you lies an expansive desert as far as you can see. You look at your map and see that there is an alert for this area. The warning states that this desert is almost entirely quicksand, with only one path safely through the desert. That path is defined by a piecewise function but requires that some parameters be determined before your computer can generate the plot. Thinking back on what you learned in calculus, you realize that your path will need to be continuous. You just need to tell your computer what the parameters below should be in order to create this continuous path. What parameters do you give your computer? $f(x)=\left\{\begin{array}{cc} 4, & x \leq-2 \\ -4 x+A, & -2<x \leq-1 \\ B x+7, & -1<x \leq 0 \\ -x+C, & 0<x \leq 1 \\ D x+4, & 1<x \leq 2 \\ 8, & h^{x>2} \end{array}\right.$ \begin{tabular}{|c|c|c|c|} \hline A & B & C & D \\ \hline Number & Number & Number & Number \\ \hline \end{tabular}
Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team.

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Problem 6275

35. Do this problem on a worksheet. Both car A and car B leave school when a clock reads zero. Car A travels at a constant $75 \mathrm{~km} / \mathrm{h}$ , and car B travels at a constant $85 \mathrm{~km} / \mathrm{h}$ . a. Draw a position-time graph showing the motion of both cars. b. How far are the two cars from school when the clock reads 2.0 h ? Calculate the distances using the equation for motion and show them on your graph. c. Both cars passed a gas station 120 km from the school. When did each car pass the gas station? Calculate the times and show them on your graph.

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Problem 6276

MY NOTES TANAP
Find the derivative of the function. $\begin{array}{l} g(t)=\sqrt[3]{9-2 t^{3}} \\ g^{\prime}(t)=\square \end{array}$

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Problem 6277

Find the local minimum value of the function $f(x) = x \ln(2x)$ .

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Problem 6278

Calculate the producers' surplus for the supply equation at the indicated unit price $\bar{p}$ . HINT [See Example 2.] (Round your answer to the nearest cent.) $\begin{array}{l} \quad p=110+e^{0.01 q} ; \bar{p}=150 \\ \$ 10842.89 \times \end{array}$

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Problem 6279

The following question is taken from a Practice SAT test on the NonCalculator section.
The graph of $y=2 x^{2}+10 x+12$ is shown. If the graph crosses the $y$ -axis at the point $(0, k)$ , what is the value of $k$ ? 12 2 10 6

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Problem 6280

Consider the function $m(x)=24 x^{5}-360 x^{4}+1400 x^{3}-5 .$
Differentiate $m$ and use the derivative to determine each of the following.
The intervals on which $m$ is increasing. $m$ increases on: $\square$ The intervals on which $m$ is decreasing. $m$ decreases on: $\square$ The value(s) of $x$ at which $m$ has a relative maximum. If there are more than one solutions, separate them by a comma. Use exact values. $m$ has local maximum(s) at $x=$ $\square$ The value(s) of $x$ at which $m$ has a relative minimum. If there are more than one solutions, separate them by a comma. Use exact values. $m$ has local minimum(s) at $x=$ $\square$

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Problem 6281

The Fifth Gate After traversing your continuous path, you finally arrive at Gate 5. Your computer reads the gate's directions to you. "The passcode for this gate is the number found by first entering $m^{\prime}(-1)$ and then entering $n^{\prime}(7)$ using the definitions below." What values do you provide to your computer? $\begin{array}{l} f(x)=\left(x^{8}-2 x\right) \\ g(x)=\left(x^{2}+6 x-90\right) \\ h(x)=2 x-13 \\ m(x)=f(x) \cdot g(x) \\ n(x)=\frac{g(x)}{h(x)} \end{array}$ $m^{\prime}(-1)=$ \begin{tabular}{l|c|c|c|c|c} \hline $a$ & $\frac{a}{b}$ & $\sqrt{a}$ & $|a|$ & $\pi$ & $\sin (a)$ \\ \hline \end{tabular} $n^{\prime}(7)=$

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Problem 6282

5 Bestimmen Sie die Halbwerts- bzw. die Verdopplungszeit für den Bestand $f(t)$ ( $t$ in $s$ ). a) $f(t)=17 \cdot e^{0,3 t}$ b) $f(t)=50 \cdot e^{-0,25 t}$ c) $f(t)=56 \cdot e^{-0,001 t}$ d) $f(t)=506 \cdot e^{\ln (4) \cdot t}$

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Problem 6283

5. $\frac{d}{d x} \csc 6 x$

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Problem 6284

63. Pollution Pollution from a factory is entering a lake. The rate of concentration of the pollutant at time $l$ is given by $P^{\prime}(t)=140 t^{5 / 2}$ where $t$ is the number of years since the factory started introducing pollutants into the lake. Ecologists estimate that the lake can accept a total level of pollution of 4850 units before all the fish life in the lake ends. Can the factory operate for 4 years without killing all the fish in the lake?

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Problem 6285

8 Abiturprüfung 2011 (Bayern), Analysis, Aufgabengruppe I, Teil 1, Aufgabe 3 Die Anzahl der auf der Erde lebenden Menschen wuchs von 6,1 Milliarden zu Beginn des Jahres 2000 auf 6,9 Milliarden zu Beginn des Jahres 2010. Dieses Wachstum lässt sich näherungsweise durch eine Exponentialfunktion mit einem Term der Form $N(x)=N_{0} \cdot e^{k \cdot(x-2000)}$ beschreiben, wobei $\mathrm{N}(\mathrm{x})$ die Anzahl der Menschen zu Beginn des Jahres $x$ ist. Bestimmen Sie $N_{0}$ und $k$ .

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Problem 6286

Die Anzahl der auf der Erde lebenden Menschen wuchs von 6,1 Milliarden zu Beginn des Jahres 2000 auf 6,9 Milliarden zu Beginn des Jahres 2010. Dieses Wachstum lässt sich näherungsweise durch eine Exponentialfunktion mit einem Term der Form $N(x)=N_{0} \cdot e^{k \cdot(x-2000)}$ beschreiben, wobei N(x) die Anzahl der Menschen zu Beginn des Jahres $x$ ist. Bestimmen Sie $N_{0}$ und $k$ .

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Problem 6287

Given the function $g(x)=8 x^{3}+24 x^{2}-360 x$ , find the first derivative, $g^{\prime}(x)$ . $g^{\prime}(x)=$ $\square$ Notice that $g^{\prime}(x)=0$ when $x=3$ , that is, $g^{\prime}(3)=0$ 。
Now, we want to know whether there is a local minimum or local maximum at $x=3$ , so we will use the second derivative test.
Find the second derivative, $g^{\prime \prime}(x)$ . $g^{\prime \prime}(x)=$ $\square$ Evaluate $g^{\prime \prime}(3)$ . $g^{\prime \prime}(3)=$ $\square$ Based on the sign of this number, does this mean the graph of $g(x)$ is concave up or concave down at $x=3$ ? concave down concave up
Based on the concavity of $g(x)$ at $x=3$ , does this mean that there is a local minimum or local

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Problem 6288

11 Bei dem Reaktorunfall in Tschernobyl am 26. April 1986 wurde u.a. radioaktives Cäsium-137 freigesetzt. Cäsium-137 zerfällt exponentiell mit einer Halbwertszeit von ca. 30 Jahren. Über der damaligen Bundesrepublik Deutschland hatten sich nach Angaben der Gesellschaft für Strahlenund Umweltforschung etwa 230 Gramm radioaktives Cäsium-137 abgelagert, ein Großteil davon in Bayern. a) Beschreiben Sie den Zerfall dieser Menge Cäsium-137 durch eine Funktion $f: t \mapsto b \cdot e^{k t}$ ( $t$ in Jahren und $f(t)$ in Gramm). b) Geben Sie die Bedeutung des Faktors b im Sachzusammenhang an und berechnen Sie den prozentualen Anteil, um den die Masse des Cäsium-137 jedes Jahr abnimmt. c) Berechnen Sie, nach welcher Zeit weniger als ein Gramm des Cäsium-137 übrig ist. d) Bestimmen Sie die Funktion der Wachstumsgeschwindigkeit für die gegebene Menge Cäsi-um-137. Berechnen Sie die Wachstumsgeschwindigkeit zu Beginn und zum heutigen Zeitpunkt. Beschreiben Sie die Werte im Sachzusammenhang.

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Problem 6289

Consider the function.(If an answer does not exist, enter DNE.) $f(x)=(x-4)^{2}(x-8)^{2}$ (a) Determine intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation.) increasing $\square$ decreasing $\square$ (b) Determine the local minima and maxima of $f$ . (Enter your answers as comma-separated lists.) locations of local minima $\quad x=$ $\square$ locations of local maxima $\quad x=$ $\square$ (c) Determine intervals where $f$ is concave up or concave down. (Enter your answers using interval notation.) concave up $\square$ concave down $\square$ (d) Determine the locations of inflection points of $f$ . Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. (Enter your answers as a comma-separated list.) $x=$ $\square$

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Problem 6290

Consider the function.(If an answer does not exist, enter DNE.) $f(x)=(x-4)^{2}(x-8)^{2}$ (a) Determine intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation.) increasing $\square$ decreasing $\square$ (b) Determine the local minima and maxima of $f$ . (Enter your answers as comma-separated lists.) locations of local minima $\quad x=$ $\square$ locations of local maxima $\quad x=$ $\square$ (c) Determine intervals where $f$ is concave up or concave down. (Enter your answers using interval notation.) concave up $\square$ concave down $\square$ (d) Determine the locations of inflection points of $f$ . Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. (Enter your answers as a comma-separated list.) $x=\square$

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Problem 6291

86 FUNCTIONS (Chapter 3) 11 Suppose $f(x)=\sqrt{1-x}$ and $g(x)=x^{2}$ . Find: a $(f \circ g)(x)$ b the domain and range of $(f \circ g)(x)$ .

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Problem 6292

Consider the function. (If an answer does not exist, enter DNE.) $f(x)=(x-4)^{2}(x-8)^{2}$ (a) Determine intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation.) increasing $\quad(4,6) \cup(8, \infty)$ decreasing $\quad(-\infty, 4) \cup(6,8)$ (b) Determine the local minima and maxima of $f$ . (Enter your answers as comma-separated lists.) locations of local minima $\quad x=$ $\square$ $\square$ locations of local maxima $\quad x=$ $\square$ (c) Determine intervals where $f$ is concave up or concave down. (Enter your answers using interval notation.) concave up $\quad(-\infty, 4.84) \cup(7.16, \infty)$ concave down (4.84,7.16) (d) Determine the locations of inflection points of $f$ . Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. (Enter your answers as a comma-separated list.) $x=4.84,7.16$

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Problem 6293

ANSWERS
12. $\sin 51.9^{\circ}=$ .997 $\cos 51.9^{\circ} \approx$ $\qquad$ $\tan 51.9^{\circ}=$ $\qquad$ $\csc 51.9^{\circ}=$ $\qquad$ $\sec 51.9^{\circ}=$ $\qquad$ $\cot 51.9^{\circ}=$ $\qquad$
13. $B=$ $\qquad$ $a \approx$ $\qquad$ $c=$ $\qquad$
14. $\qquad$
15. $\qquad$
16. $\sin \theta=$ $\qquad$ $\tan \theta=$ $\qquad$ $\csc \theta=$ $\qquad$ $\sec \theta=$ $\qquad$ $\cot \theta=$ $\qquad$
17. $\qquad$
18. $\qquad$
19. Find the length of an are of a circle, given a central angle of $\frac{5 \pi}{3}$ and a radius of 6 m .
18. Convert $\frac{5 \pi}{9}$ to degree measure.
12. Given that $\sin 38.1^{\circ} \approx 0.6170, \cos 38.1^{\circ} \approx 0.7869$ , and $\tan 38.1^{\circ}=0.7841$ , find the six trigonometric function values for $51.9^{\circ}$ . Round to four decimal places.
13. Solve the right triangle with $A=14.2^{\circ}$ and $b=9.5$ . Standard lettering has been used.
14. Find a positive angle and a negative angle coterminal with a $103^{\circ}$ angle.
15. Find the complement of $\frac{3 \pi}{10}$ .
16. Given that $\cos \theta=-51 \sqrt{89}$ and that the terminal side is in quadrant I, find the other five trigonometric function values.
17. Convert $150^{\circ}$ to radian measure in terms of $\pi$ .

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Problem 6294

If $g(x)=\sqrt[3]{x-20}$ , find $g(12)$ $g(12)=$

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Problem 6295

Consider the function. (If an answer does not exist, enter DNE.) $f(x)=(x-4)^{2}(x-8)^{2}$ (a) Determine intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation.) increasing $\quad(4,6) \cup(8, \infty)$ decreasing $\quad(-\infty, 4) \cup(6,8)$ (b) Determine the local minima and maxima of $f$ . (Enter your answers as comma-separated lists.) locations of local minima $\quad x=$ $\square$ $\square$ locations of local maxima $\quad x=$ $\square$ (c) Determine intervals where $f$ is concave up or concave down. (Enter your answers using interval notation.) concave up $\quad(-\infty, 4.84) \cup(7.16, \infty)$ concave down (4.84,7.16) (d) Determine the locations of inflection points of $f$ . Sketch the curve, then use a calculator to compare your answer. If you cannot determine the exact answer analytically, use a calculator. (Enter your answers as a comma-separated list.) $x=4.84,7.16$

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Problem 6296

Consider the function. (If an answer does not exist, enter DNE.) $f(x)=\sin (x)+\sin ^{3}(x) \text { over }-\pi<x<\pi$ (a) Determine intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation.) increasing $\square$ decreasing $\square$ (b) Determine local minima and maxima of $f$ . (Enter your answers as comma-separated lists.) locations of local minima $\quad x=$ $\square$ locations of local maxima $\quad x=$ $\square$

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Problem 6297

Analyze the graph of $f^{\prime}$ , then list all inflection points and intervals where $f$ is concave up and concave down. (Enter your answer for inflection points as a comma-separated list. Enter your answers for concavity using interval notation. If an answer does not exist, enter DNE.) locations of inflection points $\quad x=$ $\square$ concave up $\square$ concave down $\square$

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Problem 6298

Analyze the graph of $f^{\prime}$ , then list all intervals where $f$ is increasing or decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing $-2,0$ U 2,3 decreasing $-2,2$

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Problem 6299

```latex \text{Flüssigkeiten bei einem Produktionsprozess} \\ \text{In einem Produktionsprozess werden Flüssigkeiten erhitzt und anschließend abgekühlt. Der Temperaturverlauf kann gezielt gesteuert werden, sodass er sich für den gesamten Erhitzungs- bzw. Abkühlungsvorgang für } t \geq 0 \text{ durch eine der in } \mathbb{R} \text{ definierten Funktionen } f_{k} \text{ mit } f_{k}(t)=23+20 \cdot t \cdot e^{-\frac{1}{10} \cdot k \cdot t}, \text{ wobei } k \text{ eine positive, reelle Zahl sein soll, beschreiben lässt. Dabei ist } t \text{ die seit Beginn des Vorgangs vergangene Zeit in Minuten und } f_{k}(t) \text{ die Temperatur in } { }^{\circ} C. \\ \text{a) Die in Abbildung 1 dargestellten Graphen } A, B \text{ und } C \text{ gehören jeweils zu einem der Werte } k=0,5 ; k=2 \text{ und } k=5. \text{ Ordnen Sie jedem dieser Werte den zugehörigen Graphen zu.} \\ \text{b) Begründen Sie, dass der in Abbildung 1 dargestellte Graph } D \text{ nicht zu einer der Funktionen } f_{k} \text{ gehören kann.} \\ \text{c) Zeigen Sie, dass gilt} \\ f_{k}^{\prime}(t)=20 \cdot e^{-\frac{1}{10} \cdot k \cdot t} \cdot\left(1-\frac{1}{10} \cdot k \cdot t\right) \\ \text{d) Ermitteln Sie denjenigen Wert von } k, \text{ für den die Flüssigkeit im Modell eine Höchsttemperatur von } 123^{\circ} \mathrm{C} \text{ erreicht.} \\ \text{e) Ermitteln Sie die Koordinaten des Wendepunktes des Graphen von } f_{10}. \text{ Interpretieren Sie anschließend die Bedeutung der x-Koordinate dieses Wendepunkts des Graphen von } f_{10} \text{ im Sachzusammenhang.} ```

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Problem 6300

How many years are required for an investment to double in value if it is appreciating at the rate of $11 \%$ compounded continuously?
At 11\% compounded continuously, the investment doubles in $\square$ years. (Round to one decimal place as needed.)

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Function

Problem 6201

Problem 6202

5.Describe the domain for the following function. Write your answer in interval notation. f(x)=1x−7−x+2x−6f(x)=\frac{1}{x-7}-\frac{\sqrt{x+2}}{x-6}f(x)=x−71​−x−6x+2​​

Problem 6203

Problem 6204

Problem 6205

Find a quadratic function f(x)=ax2+bx+cf(x)=a x^{2}+b x+cf(x)=ax2+bx+c whose vertex is (4,5)(4,5)(4,5) and whose yyy-intercept is (0,21)(0,21)(0,21).

Problem 6206

Problem 6207

Problem 6208

Select the correct choice that completes the sentence below. The vertical line through the vertex of a parabola that opens upward or downward is the □\square□ of the parabola. The two halves of the parabola are □\square□ images of each other across this line. Clear all Final chest

Problem 6209

Find the slope of the line passing through the given points. (−4,4),(−6,10)(-4,4),(-6,10)(−4,4),(−6,10)The slope of the line is □\square□ 16 (Type an integer or a simplified fraction.)

Problem 6210

Problem 6211

Problem 6212

Given the function shown in the graph below, state the domain and range of the function using interval notation:Domain: □\square□ Range: □\square□

Problem 6213

Problem 6214

Problem 6215

Given the function shown in the graph below, state the domain and range of the function using interval notation:Domain: □\square□ Range: □\square□

Problem 6216

Given the function shown in the graph below, state the domain and range of the function using interval notation:Domain: □\square□Range: □\square□ (−2,2)(-2,2)(−2,2) 6

Problem 6217

decreasing when the diameter is 70 cm . (Note the answer is a positive number) 重

Problem 6218

Find a formula for the exponential function shown in the graph. Use the variables xxx and f(x)f(x)f(x) or xxx and yyy.If necessary, round any parameters of the function to four decimal places: Formula: □\square□

Problem 6219

Problem 6220

Find the percentage rate of change of fff at the given value of xxx. f(x)=2x2+23;x=1f(x)=\sqrt{2 x^{2}+23} ; x=1f(x)=2x2+23​;x=1 □\square□ percent per unit change in xxx Need Help? Read It

Problem 6221

Problem 6222

11. What is the maximum value of the function y=2cos⁡2π3(x−7)−8y=2 \cos \frac{2 \pi}{3}(x-7)-8y=2cos32π​(x−7)−8 ? [8.7] A. 2 B. -6 C. -5 D. -10

Problem 6223

Consider the graph shown below. y 200 150 100 8. 4 2 50 50 100 150 -200 2 X 6 8 -250 If the complete graph of the function is shown, estimate the absolute maximum and absolute minimum. absolute maximum (x, y) = absolute minimum (x, y) =

Problem 6224

Problem 6225

Determine the domain and range of the quadratic function. (Enter your answers using interval notation.) f(x)=−3(x+2)2−6f(x)=-3(x+2)^{2}-6f(x)=−3(x+2)2−6 domain □\square□ range □\square□

Problem 6226

Problem 6227

Function AAA and Function BBB are linear functions.Function AFunction B \begin{tabular}{|c|c|} \hlinexxx & yyy \\ \hline 3 & 2 \\ \hline 6 & 3 \\ \hline 9 & 4 \\ \hline \end{tabular}

Problem 6228

Problem 6229

The vertex of a parabola is always located midway between the focus and the directrix. True False

Problem 6230

20. Write an equation that represents the sine function graphed below. [8.7]

Problem 6231

Given that log⁡(2)≈0.3010\log (2) \approx 0.3010log(2)≈0.3010, find the value of the logarithm. log⁡(2)\log (\sqrt{2})log(2​) □\square□ Need Help? Watch it

Problem 6232

Problem 6233

21. Determine the exact values of the six trigonometric ratios for 585∘585^{\circ}585∘. [8.1] [2 marks]

Problem 6234

L steps for full marks as required. Correct answer with NO work shown = NO ma1. Determine the exact values of the six trigonometric ratios for 585∘585^{\circ}585∘. [8.1] [2 marks]

Problem 6235

The function f(x)=2x3−33x2+168x−10f(x)=2 x^{3}-33 x^{2}+168 x-10f(x)=2x3−33x2+168x−10 has two critical numbers.Give the two critical numbers as a commaseparated list. x=x=x= □\square□

Problem 6236

Problem 6237

Evaluate the definite integral ∫0π10sin⁡(x)dx\int_{0}^{\pi} 10 \sin (x) d x∫0π​10sin(x)dx

Problem 6238

If f(x)=∫0x(16−t2)et3dtf(x)=\int_{0}^{x}\left(16-t^{2}\right) e^{t^{3}} d tf(x)=∫0x​(16−t2)et3dt for all xxx, then find the largest open interval on which fff is increasing. Answer (in interval notation): □\square□

Problem 6239

Problem 6240

Problem 6241

Find the definite integral. (Use symbolic notation and fractions where needed.) ∫−π/4π/2cos⁡(x)dx=\int_{-\pi / 4}^{\pi / 2} \cos (x) d x=∫−π/4π/2​cos(x)dx= □\square□

Problem 6242

Problem 6243

Question 3 of 32 Find the area under the graph of f(x)=51−x2f(x)=\frac{5}{\sqrt{1-x^{2}}}f(x)=1−x2​5​ from 0 to 12\frac{1}{\sqrt{2}}2​1​.

Problem 6244

Problem 6245

Given: y=log⁡5xy=\log _{5} xy=log5​x a. Rewrite to exponential form. □\square□ b. Which of the following graphs represents the equation

Problem 6246

Problem 6247

Without graphing, find the vertex, f(x)=−23(x+8)2+4f(x)=-\frac{2}{3}(x+8)^{2}+4f(x)=−32​(x+8)2+4What is the vertex? □\square□

Problem 6248

Without graphing, find the vertex, the axis of symmetry, and f(x)=−23(x+8)2+4f(x)=-\frac{2}{3}(x+8)^{2}+4f(x)=−32​(x+8)2+4What is the vertex? (−8,4)(-8,4)(−8,4) (Type an ordered pair.) What is the equation of the axis of symmetry? □\square□

Problem 6249

Schoof Hame I Microsoft 365 Teams and Channels / General / M 14 of 23 Next ? Cl ถ B <<< Marbleslides: Parabolas nirban khunkhunUse your own advice from the last screen. Did it help? c y=2(x−2)2+4y=2(x-2)^{2}+4y=2(x−2)2+4Verify \#4 « samen 1212024

Problem 6250

Problem 6251

5.
Describe the domain for the following function. Write your answer in interval notation. $f(x)=\frac{1}{x-7}-\frac{\sqrt{x+2}}{x-6}$

Find a quadratic function $f(x)=a x^{2}+b x+c$ whose vertex is $(4,5)$ and whose $y$ -intercept is $(0,21)$ .

Select the correct choice that completes the sentence below. The vertical line through the vertex of a parabola that opens upward or downward is the $\square$ of the parabola. The two halves of the parabola are $\square$ images of each other across this line. Clear all Final chest

Find the slope of the line passing through the given points. $(-4,4),(-6,10)$
The slope of the line is $\square$ 16 (Type an integer or a simplified fraction.)

Given the function shown in the graph below, state the domain and range of the function using interval notation:
Domain: $\square$ Range: $\square$

Given the function shown in the graph below, state the domain and range of the function using interval notation:
Domain: $\square$ Range: $\square$

Given the function shown in the graph below, state the domain and range of the function using interval notation:
Domain: $\square$
Range: $\square$ $(-2,2)$ 6

Find a formula for the exponential function shown in the graph. Use the variables $x$ and $f(x)$ or $x$ and $y$ .
If necessary, round any parameters of the function to four decimal places: Formula: $\square$

Find the percentage rate of change of $f$ at the given value of $x$ . $f(x)=\sqrt{2 x^{2}+23} ; x=1$ $\square$ percent per unit change in $x$ Need Help? Read It

11. What is the maximum value of the function $y=2 \cos \frac{2 \pi}{3}(x-7)-8$ ? [8.7] A. 2 B. -6 C. -5 D. -10

Determine the domain and range of the quadratic function. (Enter your answers using interval notation.) $f(x)=-3(x+2)^{2}-6$ domain $\square$ range $\square$

Function $A$ and Function $B$ are linear functions.
Function A
Function B \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 3 & 2 \\ \hline 6 & 3 \\ \hline 9 & 4 \\ \hline \end{tabular}

Given that $\log (2) \approx 0.3010$ , find the value of the logarithm. $\log (\sqrt{2})$ $\square$ Need Help? Watch it

21. Determine the exact values of the six trigonometric ratios for $585^{\circ}$ . [8.1] [2 marks]

L steps for full marks as required. Correct answer with NO work shown = NO ma
1. Determine the exact values of the six trigonometric ratios for $585^{\circ}$ . [8.1] [2 marks]

The function $f(x)=2 x^{3}-33 x^{2}+168 x-10$ has two critical numbers.
Give the two critical numbers as a commaseparated list. $x=$ $\square$

Evaluate the definite integral $\int_{0}^{\pi} 10 \sin (x) d x$

If $f(x)=\int_{0}^{x}\left(16-t^{2}\right) e^{t^{3}} d t$ for all $x$ , then find the largest open interval on which $f$ is increasing. Answer (in interval notation): $\square$

Find the definite integral. (Use symbolic notation and fractions where needed.) $\int_{-\pi / 4}^{\pi / 2} \cos (x) d x=$ $\square$

Question 3 of 32 Find the area under the graph of $f(x)=\frac{5}{\sqrt{1-x^{2}}}$ from 0 to $\frac{1}{\sqrt{2}}$ .

Given: $y=\log _{5} x$ a. Rewrite to exponential form. $\square$ b. Which of the following graphs represents the equation

Without graphing, find the vertex, $f(x)=-\frac{2}{3}(x+8)^{2}+4$
What is the vertex? $\square$

Without graphing, find the vertex, the axis of symmetry, and $f(x)=-\frac{2}{3}(x+8)^{2}+4$
What is the vertex? $(-8,4)$ (Type an ordered pair.) What is the equation of the axis of symmetry? $\square$

Schoof Hame I Microsoft 365 Teams and Channels / General / M 14 of 23 Next ? Cl ถ B $<$ Marbleslides: Parabolas nirban khunkhun
Use your own advice from the last screen. Did it help? c $y=2(x-2)^{2}+4$
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Find the derivative of the function. $\begin{array}{r} f(x)=\ln (9 x) \\ f^{\prime}(x)=\square \end{array}$ Need Help? Watch It

Find the derivative of the function. $\begin{array}{l} f(x)=\ln (\sqrt{x}+5) \\ f^{\prime}(x)=\square \end{array}$

Solve a Consumers' or Producers' Surplus Problem.
The price-supply equation for some commodity is given by $p=S(x)=14+1.8 x$ and the equilibrium point is $(23,55.4)$ Find the producers' surplus.
The surplus is $\square$ (Your answer must begin with \$.)

Find the derivative of the function. $\begin{array}{l} f(x)=\ln \left(2 x^{2}-5 x+8\right) \\ f^{\prime}(x)=\square \end{array}$

Find a function $F$ such that $\mathbf{F} = \nabla f$ , where $\mathbf{F}(x, y) = \langle 2x, 4y \rangle$ , and $C$ is the arc of the parabola $x = y^2$ from $(4, -2)$ to $(1, 1)$ .

Find the derivative of the function. $\begin{array}{l} f(x)=7 x^{2} \ln (6 x) \\ f^{\prime}(x)=\square \end{array}$ Need Help? Watch It