Browse Function problems Studdy Solved!

Problem 3201

As a hot bowl of soup is allowed to cool, its temperature $T$ (in degrees Fahrenheit) after $t$ minutes is given by the function $T(t)=65+145 e^{-0.05 t}$ . How long does it take for the soup to cool to $100^{\circ} \mathrm{F}$ ?
The decibel scale for measuring the intensity of sound is a logarithmic scale defined by the formula $\beta=$ $10 \log \left(\frac{1}{10^{-12}}\right)$ , where $\beta$ is the intensity of the sound in decibels $(\mathrm{dB})$ and $/$ is the intensity of the sound in watts per square meter $\left(\mathrm{W} / \mathrm{m}^{2}\right)$ . If the sound of heavy traffic is measured to be 80 dB , what is the sound intensity in $\mathrm{W} / \mathrm{m}^{2}$ ?

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Problem 3202

(1 point)
Use the third-order Taylor polynonial for $e^{x} \sin (3 x)$ at $x=0$ to approximate $e^{\frac{1}{t}} \sin (3 / 8)$ by a rational number. $\mathrm{e}^{\frac{1}{1}} \sin (3 / 8) \approx 27 / 256$
Preview My Answers Submit Answers You have attempted this problem 10 times. Your overall recorded score is $0 \%$ . You have unlimited attempts remaining.

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Problem 3203

Analyze the polynomial function $f(x)=(x+5)^{2}(x-7)^{2}$ using parts (a) through (e). (a) Determine the end behavior of the graph of the function.
The graph of $f$ behaves like $y=$ $\square$ for large values of $|\mathrm{x}|$ . (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 is $\square$ $\square$ . (Simplify your answer. Type an integer or a fraction.) (c) Determine the zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x -axis a
The zero(s) of $f$ islare $\square$ . (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 $f$ $\square$ the $x$ -axis at $x=$ $\square$ . The greater zero is a zero of multiplicity $\square$ , so the (d) Determine the maximum number of turning points on the graph of the function. $\square$ (Type a whole number.) (e) Use the above information to draw a complete graph of the function. Choose the correct graph below. A. B. c. $1500^{4 y}$ 1500 ${ }^{4 y}$ $4500^{4 y}$

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Problem 3204

C. Using two Riemann sums with 4 evenly spaced intervals each, and using the mid-point of each interval, approximate both $\int_{1}^{3} \operatorname{Pr}(x) d x \text { and } \quad \int_{-1}^{1} \operatorname{Pr}(x) d x . \quad \operatorname{Pr}(x)=\frac{1}{\sqrt{2 \pi}} e^{-\frac{x^{2}}{2}}$
Again you can do this by hand (show your calculations) or with Matlab (provide a screen capture of the script and workspace). $\begin{array}{l} \Delta x=\frac{3-1}{4}=0.5 \\ P_{r_{1}}=1+\frac{0.5}{2}=1.25 \\ P_{r_{2}}=1.75 \\ P_{r_{3}}=2.25 \\ P_{r_{4}}=2.75 \\ \Delta x=\frac{1-(-1)}{4}=0.5 \\ P_{r_{1}}=-1+\frac{0.5}{2}=-0.75 \\ P_{r_{2}}=-0.25 \\ P_{r_{3}}=0.25 \\ P_{r_{4}}=0.75 \end{array}$ neight: $\left.\begin{array}{l} \operatorname{Pr}(1.25)=0.183 \\ \operatorname{Pr}(1.75)=0.0863 \\ \operatorname{Pr}(2.25)=0.0317 \\ \operatorname{Pr}(2.75)=0.00909 \end{array}\right\} \begin{array}{c} \text { Added }=0.31009 \\ x \Delta e \\ =0.155 \end{array}$
Height: $\left.\begin{array}{l} \operatorname{Pr}(-0.75)=0.301 \\ \operatorname{Pr}(-0.25)=0.387 \\ \operatorname{Pr}(0.25)=0.387 \\ \operatorname{Pr}(0.75)=0.301 \end{array}\right\} \begin{array}{l} 1.376 \\ x \Delta e \\ =0.688 \end{array}$ D. Is it more likely to observe an outcome of the random event having a value between $[1,3]$ or between $[-1,1]$ ? Justify your answer in one short sentence.

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Problem 3205

The function $h$ is defined by $h(x)=\frac{2+x}{5+2 x}$ .
Find $h(4 x)$ . $h(4 x)=$

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Problem 3206

Problem 1: Multi-species Flocks Ph.D. candidate Jenny Muñez studies multi-species bird flocks in the Colombian Andes. She surveys birds from two species (species 1 and species 2) counting the number of birds every 50 m of elevation gain of along an elevational gradient starting at an altitude of 100 m and ending at 400 m . Her data is given in the following table and plot: \begin{tabular}{c|c|c} \begin{tabular}{c} Elevation \\ $e$ \end{tabular} & \begin{tabular}{c} \#Species 1 \\ $N_{1}(e)$ \end{tabular} & \begin{tabular}{c} \# Species 2 \\ $N_{2}(e)$ \end{tabular} \\ \hline 100 & 2.32 & 0.64 \\ 150 & 30.84 & 7.37 \\ 200 & 15.88 & 13.95 \\ 250 & 7.21 & 14.61 \\ 300 & 3.88 & 18.53 \\ 350 & 1.02 & 17.22 \\ 400 & 1.94 & 18.14 \\ \multicolumn{3}{c}{ $\Delta e=\frac{400-100}{2}=50$ } \end{tabular} A. Use Riemann Sums to approximate the Niche size of species 1 (Blue) and species 2 (Orange) by approximating the following two definite integrals (show your calculations):
Niche Size Species 1: $\quad \int_{100}^{400} N_{1}(e) d e \approx \sum^{b} N_{1}\left(e_{i}\right) \Delta e$ $\Delta e=50$

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Problem 3207

The graphs of $y=f(x), y=g(x)$ and $y=h(x)$ are shown below. Remember that $y=g(x)$ and $y=h(x)$ are transformations of $y=f(x)$ . Write equations for $g(x)$ and $h(x)$ in terms of $f(x)$ . a. b.

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Problem 3208

Graph the function $f(x)=3^{x}+3$ . Give the domain and range.

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Problem 3209

The formula below models the number of calories consumed daily by a person owning $x$ acres of land in a developing country. Estimate the number of acres owned for which average intake is 2250 calories per day. $C(x)=285 \ln (x+1)+1905$
For an average intake of 2250 calories per day, the number of acres of land owned is approximately $\square$ (Round the final answer to the nearest tenth as needed. Round all intermediate values to the nearest thousandth as needed.)

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Problem 3210

Evaluate the line integral, where $C$ is the given curve. $\int_{C} x y z^{2} d s, C$ is the line segment from $(-2,3,0)$ to $(0,4,4)$

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Problem 3211

7. A skier jumps off a ramp from a height of 1 m and follows a parabolic path. Its height $h$ , in metres, after $t$ seconds is $h=-5 t^{2}+20 t+1$ a) Find the maximum height of the skier. $\begin{array}{l} h=-5 t^{2}+20 t+1 \\ h=-5\left(t^{2}-4 t\right)+1 \\ \left.h=-5 f^{2}-4 t+(-2)^{2}-(-2)^{2}\right)+1 \\ h=-5\left(t^{2}-4 t+4-1+1\right. \\ \left.h=-5 t^{2}-4 t+4\right)+20+1 \\ h=-5(t-2)^{2}+21 \end{array}$ $\therefore$ the maximum [3 marsas height of the skies is 21 meters at 2 secons. [1 manks]
The skier is goring fown at 3 seconds becave the skler reaches max height at 2 seconds, 50 the stre would start to descend.

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Problem 3212

Suppose that a company has just purchased a new computer for $\$ 2500$ . The company chooses to depreciate using the straight-line method for 5 years. (a) Write a linear function that expresses the book value V of the computer as a function of its age x . (b) What is the domain of the function found in part (a)? (c) Graph the linear function. (d) What is the book value of the computer after 2 years? (e) When will the computer have a book value of $\$ 500$ ? (a) The linear function is $V(x)=$ $\square$ (Simplify your answer.)

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Problem 3213

Suppose that a company has just purchased a new computer for $\$ 2500$ . The company chooses to depreciate using the straight-line method for 5 years. (a) Write a linear function that expresses the book value V of the computer as a function of its age x . (b) What is the domain of the function found in part (a)? (c) Graph the linear function. (d) What is the book value of the computer after 2 years? (e) When will the computer have a book value of $\$ 500$ ? (b) Choose the correct answer below. A. $[0,2500]$ B. $[0,5]$ C. $(0,5)$ D. $(-\infty, \infty)$ (c) Choose the correct graph below. A. B. C. D.

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Problem 3214

Sketch the graph of the function. $f(x)=\arctan (4 x)$
Compare the graph to the graph of the parent inverse trigonometric function. The graph of $f(x)$ is $\arctan (x)$ with a ---Select--- $\square$ Read It

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Problem 3215

8. The underside of a concrete bridge forms a parabolic arch that is 40 m wide and 16 m tall at its centre. What is the height of the underside of the bridge exactly 5 m from the axis of symmetry? $\therefore$ the helght of the undesside of the bridge 5 m foom Aos is 11 (to the lef) or 21 (to the right).

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Problem 3216

Graph the following function by starting with the graph of $y=x^{2}$ and using transformations (shifting, compressing, stretching, and/or reflection). $f(x)=\frac{2}{3} x^{2}$
Use the graphing tool to graph the function.

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Problem 3217

Determine the quadratic function whose graph is given below.
The quadratic function which describes the given graph is $f(x)=$ $\square$ (Type an expression.)

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Problem 3218

Graph each polynomial function. Give the domain and range.
9. $f(x)=-2 x^{2}+3$
10. $f(x)=-x^{3}+3$

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Problem 3219

Find the derivative of $y=\cos (x)^{\cos (x)}$ . $\frac{d y}{d x}=$ $\square$
Submit answer Next item

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Problem 3220

Sign in What's ne New tab About I Grades fo Mathway Mail 10.4 Hmw CaseStud) PowerPoii https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=35488820\&tags=autosave\#question4909501_14 sudrnit answel
15. [0.19/0.76 Points] DETAILS MY NOTES TANAPMATH7 10.4.057. PREVIOUS ANSWERS PRACTICE ANOTHER
Minimizing Production Costs The total monthly cost (in dollars) incurred by Cannon Precision Instruments for manufacturing $x$ units of the model M1 digital camera is given by the following function. $C(x)=0.002 x^{2}+40 x+32,000$ (a) Find the average cost function $\bar{C}$ . $\bar{C}(x)=$ $\square$ (b) Find the level of production that results in the smallest average production cost. $\square$ units (c) Find the level of production for which the average cost is equal to the marginal cost. $\square$ units (d) Compare the result of part (c) with that of part (b). The number of units resulting in the smallest average production cost is less than the number of units for which the average cost is equal to the marginal cost. The number of units resulting in the smallest average production cost is equal to the number of units for which the average cost is equal to the marginal cost. The number of units resulting in the smallest average production cost is greater than the number of units for which the average cost is equal to the marginal cost. Fantastic job! Need Help? Read It

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Problem 3221

The graph of $h$ is shown above and consists of four linear pieces on the interval $-6 \leq x \leq 6$ . Find a value for the constant $b$ such that the average rate of change of $h(x)$ from $x=1$ to $x=b$ equals the following values.
1. $\mathrm{AROC}=-1$
2. $\mathrm{AROC}=0$
3. AROC $=\frac{1}{5}$
1. $b=$ $\qquad$ 2. $b=$ $\qquad$ 3. $b=$ $\qquad$ $\qquad$

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Problem 3222

The price $p$ (in dollars) and the quantity $x$ sold of a certain product satisfy the demand equation $x=-7 p+700$ . Answer parts (a) through ( g ). (a) Find a model that expresses the revenue $R$ as a function of $p$ . (Remember, $R=x p$ .) $R(p)=-7 p^{2}+700 p$ (Simplify your answer. Use integers or decimals for any numbers in the expression.) (b) What is the domain of R ? Assume that R is nonnegative. A. The domain is $\{p \mid 0 \leq p \leq 100\}$ . (Simplify your answers. Type integers or decimals.) B. The domain is the set of all real numbers. (c) What price $p$ maximizes revenue? $\mathrm{p}=\$ \square$ (Simplify your answer. Type an integer or a decimal.)

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Problem 3223

The price $p$ (in dollars) and the quantity $x$ sold of a certain product satisfy the demand equation $x=-6 p+300$ . Answer parts (a) through ( g ). (a) Find a model that expresses the revenue R as a function of p . (Remember, $\mathrm{R}=\mathrm{xp}$ .) $R(p)=-6 p^{2}+300 p$ (Simplify your answer. Use integers or decimals for any numbers in the expression.) (b) What is the domain of R ? Assume that R is nonnegative. A. The domain is $\{p \mid$ $\square$ $\leq \mathrm{p} \leq$ $\square$ (Simplify your answers. Type integers or decimals.) B. The domain is the set of all real numbers.

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Problem 3224

11. Let $f(x)=3 x+5$ and $g(x)=x^{2}+2$ . Find each of the following. (a) $(f \circ g)(-2)$ (b) $(f \circ g)(x)$ (c) $(g \circ f)(x)$

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Problem 3225

(b) $f(t)=\frac{2 t-4+3 \sqrt{t}}{\sqrt{t}}$

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Problem 3226

Step 4 As we are looking for an absolute maximum, find the derivative of $f(x)$ . $\begin{array}{l} f(x)=3,008 x-2 x^{2} \\ f^{\prime}(x)=1 \end{array}$ Submit Skip (you cannot come back) Need Help? Read It Submit Answer

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Problem 3227

Find the vertex and axis of the graph of the function. $f(x)=2(x-3)^{2}+9$
The vertex is $\square$ (Type an ordered pair.)

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Problem 3228

9. Do not include units in your answer, and use "pi" in your answer. *
Batman is storing fuel for his Batmobile in a tank which has the shape of an inverted cone with a base radius of 2 meters and a height of 4 meters. If fuel is being pumped into the tank at a rate of 2 cubic meters per minute, find the rate at which the fuel level is rising when the fuek is 3 meters deep.

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Problem 3229

Sign in What's new X New tab X Login | Virgir X About | The X 10.5 Hmwk X https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=35488821&tags=autosave #question 5303851_2 M Mathway |A X Submit Answer W10.5 Hmwk- X Mail-Carlsc X The Coconu x + Al
4. [-/1 Points] DETAILS MY NOTES TANAPMATH7 10.5.004.EP. PRACTICE ANOTHER The owner of the Rancho Los Feliz has 3,180 yd of fencing to enclose a rectangular piece of grazing land along the straight portion of a river and then subdivide it by means of a fence running parallel to the sides. No fencing is required along the river. (See the figure below.) x Let x denote the length (in yards) of the sides perpendicular to the river and let y denote the length (in yards) of the side parallel to the river. Assuming that all 3,180 yd of fencing is utilized, write an equation for y in terms of x. y = Write a function A in terms of x that describes the area (in yd2) of the enclosed land. A = Find A'(x). A'(x) = What are the dimensions (in yd) of the largest area that can be enclosed? X = y = yd yd What is this area (in yd²)? vd2

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Problem 3230

A scientist places 23 mg of bacteria in a culture for an experiment and he finds that the mass of the bacteria triples every day. a. The mass of the bacteria in the culture on any given day is what percent of the mass of bacteria in the culture exactly one day prior? \% b. Each day that passes, the mass of bacteria in the culture changes by what percent? \% c. What is the mass of the bacteria in the culture 2 days after the start of the experiment? mg

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Problem 3231

The period, to the nearest tenth, of the function $y=\sin 0.25 x$ , where $x$ is in radians, is

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Problem 3232

Question 13
Use Identities to find the exact value. $\cos \left(\frac{19 \pi}{12}\right)$ (A) $\frac{\sqrt{6}-\sqrt{2}}{4}$ (B) $\sqrt{2}-\sqrt{6}$ (C) $\frac{\sqrt{2}-\sqrt{6}}{4}$ (D) $-\sqrt{6}-\sqrt{2}$

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Problem 3233

$\cos ^{-1}(\sqrt{2} / 2)$

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Problem 3234

(b) Given that $f(x)=x^{2}+|x-4|$ . Determine whether $f$ is differentiable at $x=4$ .

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Problem 3235

Find the slope of the tangent line to the curve $f(x)=\tan ^{-1}(x)$ at $x=\frac{1}{2}$ . $\frac{4}{5}$ $\frac{2}{3}$ $\frac{3}{2}$ $\frac{5}{4}$

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Problem 3236

Ground Level [Ground level will be from the point where the canon was shot out from $\Delta y=0$ ]. 1) Set the cannon to have an initial speed of $20 \mathrm{~m} / \mathrm{s}$ . For which situation do you think the cannon ball will go father: if it is set at a 25-degree angle, or if it is set at a 35-degree angle? (1 pt) Hypothesis: Concluslons: 2) Set the cannon to have an initial speed of $20 \mathrm{~m} / \mathrm{s}$ . For which situation do you think the cannon ball will go father: if it Is set at a 60-degree angle, or if it is set at a 70-degree angle? (1 pt) Hypothesis: Conclusions: 3) Set the cannon to have an initial speed of $15 \mathrm{~m} / \mathrm{s}$ . For which situation do you think the cannon ball will go the highest: If it is set at a 25-degree angle, or if it is set at a 35-degree angle? (1 pt) Hypothesis: Concluslons: 4) Set the cannon to have an initial speed of $15 \mathrm{~m} / \mathrm{s}$ . For which situation do you think the cannon ball will go highest: If It is set at a 60-degree angle, or if it is set at a 70 -degree angle? (1 pt) Hypothesis: Conclusions: 5) Set the cannon to have an initial speed of $25 \mathrm{~m} / \mathrm{s}$ . For which situation do you think the cannon ball will be in the alr for the longest time: if it is set at a 25-degree angle, or If it is set at a 35-degree angle? (1 pt) Hypothes/s: Conclusions: 6) Set the cannon to have an initial speed of $15 \mathrm{~m} / \mathrm{s}$ . For which situation do you think the cannon ball will be in the air for the longest time: if it is set at a 60-degree angle, or If it is set at a 70 -degree angle? (1 pt) Hypothesis: Conclusions:

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Problem 3237

```latex \textbf{Aufgabe:}
Eine Wippe aus Kunststoff hat die abgebildete Form. Obere und untere Berandung können durch Polynome 4. Grades bzw. 2. Grades erfasst werden. Die obere Randkurve läuft horizontal aus. Die Breite der Sitzfläche beträgt 30 cm.
\begin{enumerate} \item[a)] Wie lauten die Gleichungen der Randkurven $f$ und $g$ ? \item[b)] Wie groß ist die Masse der Wippe? (Dichte Kunststoff: $0,7 \, \mathrm{g/cm^3}$ ) \end{enumerate} ```

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Problem 3238

The function $f(x)=4 x^{4}-x^{3}-15 x^{2}+8 x+4$ has at least two rational roots. Use the rational root theorem to find those roots, then proceed to find all complex roots. (Note: roots may be integer, rational, irrational, and/or complex.)

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Problem 3239

1-10, draw a graph of the signed area represented by the d compute it using geometry. $d x$
2. $\int_{-2}^{3}(2 x+4) d x$ +4) $d x$
4. $\int_{-2}^{1} 4 d x$ $-x) d x$
6. $\int_{\pi / 2}^{3 \pi / 2} \sin x d x$ $\overline{5-x^{2}} d x$
8. $\int_{-2}^{3}|x| d x$

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Problem 3240

Find the degree and the leading coefficient for the given polynomial function. $f(x)=-2 x^{2}-5 x$
Answer: Degree: $\square$ Leading Coefficient:

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Problem 3241

Find all real zeros of the polynomial function. $f(x)=x^{3}-8 x^{2}+16 x-8$
Submit multiple zeros by separating them with a comma. For instance, if the zeros are 1,2 , and 3 , then submit your answer as $1,2,3$ .

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Problem 3242

Section 12.6: Problem 1 Previous Problem Problem List Next Problem (1 point) The average cost function for the weekly manufacture of portable gramophones is given by $\bar{C}(x)=750,000 x^{-1}+45+0.045 x$ dollars per gramophone, where $x$ is the number of gramophones manufactured that week. Weekly production is currently 280 gramophones and is increasing at a rate of 60 gramophones per week. What is happening to the average cost?

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Problem 3243

Find the $x$ -and $y$ -intercepts of the quadratic function $f(x)=2 x^{2}+6 x+3$ .Enter just the $x$ or $y$ -coordinate(s) of the intercept(s) separated by commas. For example enter $1,2,5$ if the $x$ -intercepts are at $x=1, x=2, x=5$ .

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Problem 3244

(1 point) The average cost function for the weekly manufacture of portable gramophones is given by $\bar{C}(x)=750,000 x^{-1}+45+0.045 x \text { dollars per gramophone }$ where $x$ is the number of gramophones manufactured that week. Weekly production is currently 280 gramophones and is increasing at a rate of 60 gramophones per week. What is happening to the average cost?
Average cost is changing at (dollars per gramophone) per week

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Problem 3245

The automobile assembly plant you manage has a Cobb-Douglas production function given by $P=30 x^{0.4} y^{0.6}$ where $P$ is the number of automobiles it produces per year, $x$ is the number of employees, and $y$ is the daily operating budget (in dollars). You maintain a constant workforce of 250 workers and wish to increase production in order to meet a demand that is increasing by 300 automobiles per year. The current demand is 7500 automobiles per year. How fast should your daily operating budget be changing?
Daily operating budget should change at dollars per year

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Problem 3246

Find all zeros, real and complex, of the polynomial function. $f(x)=2 x^{3}+6 x^{2}+11 x+7$
Submit multiple zeros by separating them with a comma. For instance, if the zeros are 1,2 , and 3 , then submit your answer as $1,2,3$ .

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Problem 3247

(1 point) The automobile assembly plant you manage has a Cobb-Douglas production function given by $P=30 x^{0.4} y^{0.6},$ where $P$ is the number of automobiles it produces per year, $x$ is the number of employees, and $y$ is the daily operating budget (in dollars). You maintain a constant workforce of 250 workers and wish to increase production in order to meet a demand that is increasing by 300 automobiles per year. The current demand is 7500 automobiles per year. How fast should your daily operating budget be changing?
Daily operating budget should change at dollars per year

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Problem 3248

38. A clarinet is 60.0 cm long. Find the first three harmonic frequencies under the conditions below. Comment on whether the ambient temperature of a concert venue might affect the listener's experience. (9.2) (a) The air temperature is $15.0^{\circ} \mathrm{C}$ . (b) The air temperature is $30.0^{\circ} \mathrm{C}$ .

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Problem 3249

Übung 7 Gegeben sind die Funktionen $f(x)=e^{x}$ und $g(x)=e^{1-x}$ . Diese begrenzen gemeinsam mit der x -Achse und den beiden senkrechten Geraden $\mathrm{x}=-1$ und $\mathrm{x}=1$ ein Flächenstück. Skizzieren Sie dieses und berechnen Sie seinen Flächeninhalt.

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Problem 3250

III. Evaluate each of the following indefinite intiggals. Show $u$ and du if necessary.
1. $\int[\sinh (3 y)-\sin (3 y)] d y$

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Problem 3251

5. Evaluate $\iiint_{G} x^{2} d V$ , where $G$ is bounded by the $x z$ -plane and the hemispheres $y=\sqrt{9-x^{2}-z^{2}}$ and $\mathrm{y}=\sqrt{16-\mathrm{x}^{2}-\mathrm{z}^{2}}$

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Problem 3252

$\text { Q7 : find } \frac{d}{d x}\left(\tan x^{2}+2^{x}\right)$ $\checkmark$ Solution:

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Problem 3253

What is the minimum value of this function?

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Problem 3254

Find $f^{\prime}(x)$ . $\begin{array}{l} f(x)=\left(5 x^{4}+3\right)^{5} \\ f^{\prime}(x)=\square \end{array}$

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Problem 3255

Differentiate. $\begin{array}{c} y=\ln \left[(x+9)^{5}(x+6)^{2}(x+8)^{4}\right] \\ \frac{d}{d x}\left[\ln \left[(x+9)^{5}(x+6)^{2}(x+8)^{4}\right]\right]= \end{array}$

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Problem 3256

Trovare lo sviluppo di Maclaurin di ordine 3 per la funzione $f(x) = \frac{1}{-\sqrt{8} \sin x - 2 \cos x}$ .

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Problem 3257

A
9. Determine the amplitude of the following function. $y=0.5 \sin (x-2)$ A. 0.5 B. 1 C. 2 D. 0
10. Determine the period of the following function. $y=0.5 \sin (x-2)$ A. $180^{\circ}$ B. $360^{\circ}$ C. $720^{\circ}$ D. $1080^{\circ}$
11. Determine the midline of the following function. $y=\cos \frac{1}{3} x+12$ A. $y=12$ B. $y=3$ C. $y=4$ D. $y=0$
12. Determine the midline of the following function. $y=0.5 \sin (x-2)$ A. $y=-2$ B. $y=0.5$ C. $y=0$ D. $y=2$
13. Determine the range of the following function. $\begin{array}{l} y=3 \sin 2\left(x+90^{\circ}\right)-1 \end{array}$ A. $\{y \mid-3 \leq y \leq 3, y \in \mathrm{R}\}$ B. $\{y \mid-2 \leq y \leq 4, y \in R\}$ C. $\{y \mid-4 \leq y \leq 2, y \in R\}$ D. $\{y \mid y \in R\}$ B. 2.6 C. 4.7 D. 5.4

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Problem 3258

2. Which is true about the function $f(x)=\frac{1}{\left|x^{3}\right|}$ ? A. It is an even function. B. It is an odd function. C. It is neither even-nor odd. n It is both even and odd.

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Problem 3259

Find all of the zeros of $t(h)=80 h^{5}-245 h^{3}$ . Show

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Problem 3260

$f(x)=\frac{x^{2}-4 x+3}{x^{3}-x^{2}-6 x}$
4. There is a removable discontinuity at $x=-2$ .
There is an infinite discontinuity at $x=3$ . :. There is a jump discontinuity at $x=0$ . - There is a removable discontinuity at $x=3$ .

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Problem 3261

2. The graph of a sinusoidal function has a maximum at $(4,3)$ followed by a minimum at $(8,1)$ . a) Describe the graph of the function by stating the amplitude, equation of its midline, range, and period. Show your work. ( 2 points -0.5 point for each description) b) Determine the $y$ -value of the function when $x=10$ . Show your work. 2 points

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Problem 3262

Resuelve, en cuentra el limite (1). $f(x)=3 x^{2} \tan x$ (2) $f(x)=\frac{x^{2}-3 x}{2 x}$ (3) $F(x)=\sqrt{2 x^{2}+3}$

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Problem 3263

$\sin ^{-1}\left(-\frac{1}{2}\right)$

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Problem 3264

$\cos ^{-1}\left(-\frac{\sqrt{2}}{2}\right)$

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Problem 3265

$\arccos \frac{1}{2}$

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Problem 3266

Herreverk2024
The table of ordered pairs $(x, y)$ gives an exponential function. Write an equation for the function. \begin{tabular}{|l|l|} \hline 0 & 36 \\ \hline 1 & 6 \\ \hline 2 & 1 \\ \hline \end{tabular}
Try one last time Recheck

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Problem 3267

Differentiate the following function. $\begin{array}{l} y=(\ln x)^{10}+\ln \left(x^{10}\right) \\ \frac{d y}{d x}=10 \end{array}$

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Problem 3268

Imagine a spinner witi every number (in order) Trom I to 20. Wifat are the chances it willand whinin one tone (on either side) of the number l'm thinking of? Imagine a spinner with every number (in order) from 1 to $\mathbf{1 0}$ . What are the chances it will land within two tiles (on either side) of the number l'm thinking of? Imagine a spinner with every number (in order) from 1 to $\mathbf{3 0}$ . What are the chances it will land within three tiles (on either side) of the number l'm thinking of? Imagine a spinner with every number (in order) from 1 to $\mathbf{1 0}$ . What are the chances it will land within four tiles (on either side) of the number l'm thinking of? Imagine a spinner with every number (in order) from 1 to 10 . What are the chances it will land within five tiles (on either side) of the number I'm thinking of? Imagine a spinner with every number (in order) from 1 to $\mathbf{2 0}$ . What are the chances it will land within six tiles (on either side) of the number I'm thinking of? magine a spinner with every number (in order) from 1 to $\mathbf{1 0 0}$ . What are the chances it will land within eighteen tilk (on either side) of the number l'm thinking of?

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Problem 3269

Match the value of $b$ on the left with the shape of the graph of $f(x)=\log _{b} x$ on the right. Graphs on the right may be used more than once. $\begin{array}{l} b=3 \\ b=\frac{5}{2} \\ b=\frac{2}{5} \\ b=0.10 \end{array}$

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Problem 3270

Question 3 Suppose that there are initially 600 rabbits in a population, and that the population changes at a rate of $f(t)=t$ where $t$ is in weeks. How many rabbits will there be after 4 weeks?

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Problem 3271

AA. 12 Compare linear, exponential, and quadratic growth 39 V
Both of these functions grow as $x$ gets larger and larger. Which function eventually exceeds the other? $f(x)=2 x+8 \quad g(x)=2 x^{2}-5$
Submit Work it out

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Problem 3272

1 AA. 12 Compare linear, exponential, and quadratic growth 39 V
Both of these functions grow as $x$ gets larger and larger. Which function eventually exceeds the other? $f(x)=\frac{3}{2} x+6 \quad g(x)=\frac{1}{2} x^{2}-x+6$ Submit

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Problem 3273

bra 1 AA. 12 Compare linear, exponential, and quadratic growth 39 V
Each of these functions grows as $x$ gets larger and larger. Which function eventually exceeds the others? $f(x)=\frac{7}{2} x$ $g(x)=\left(\frac{9}{5}\right)^{x}$ $h(x)=\frac{3}{2} x^{2}$ Subrin

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Problem 3274

6. Determina los factores de la siguiente función (5 puntos) $i^{4}-10 i^{3}+35 i^{2}-50 i+24$ $(i-6)$ $(i+4)$ 7:40 Teams $(i-6)$ $(i+4)$ $(i+8)$ $(i-4)$ $(i+6)$ $(i+3)$ $(i-8)$ $(i-2)$ $(i-1)$ $(i+1)$ $(i+2)$ $(i-3)$

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Problem 3275

Sign in What's new New tab Login / Virgi About / The 10.5 Hmwk https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=35488821\&tags=autosave\#question5097773_4 Mathway Mail Carlse The Coconu $A^{\prime \prime}$
6. [-/1 Points]
DETAILS MY NOTES TANAPMATH7 10.5.010.EP. PRACTICE ANOTHER
Consider the following closed rectangular box that has a square cross section, a capacity of $112 \mathrm{in}^{3}$ , and is constructed using the least amount of material.
Let $x$ denote the length (in inches) of the sides of the box and let $y$ denote the height (in inches) of the box. Utilize the given volume to write an equation for $y$ in terms of $x$ . $y=\square 1$
Write a function $f$ in terms of $x$ that describes the amount of material needed to create the box. $f(x)=$ $\square$ Find $f^{\prime}(x)$ and $f^{\prime \prime}(x)$ . $\begin{array}{c} f^{\prime}(x)=\square \\ f^{\prime \prime}(x)=\square \end{array}$
What are the dimensions of the box if it is constructed using the least amount of material? $\begin{array}{ll} x=\square & \text { in } \\ y=\square & \text { in } \end{array}$

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Problem 3276

Current Attempt in Progress (a) Find an angle $\theta$ , with $0^{\circ}<\theta<360^{\circ}$ , that has the same cosine as $50^{\circ}$ (but is not $50^{\circ}$ ). $\theta=$ $\square$ - (b) Find an angle $\theta$ , with $0^{\circ}<\theta<360^{\circ}$ , that has the same sine as $50^{\circ}$ (but is not $50^{\circ}$ ). $\theta=\boxed{\mathbf{i}}$

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Problem 3277

$\int \frac{\sin x d x}{e^{x}-\sin x-\cos x}$

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Problem 3278

The table below gives selected values for the differentiable and increasing function $f$ and its derivative. If $g(x)=f^{-1}(x)$ , what is the value of $g^{\prime}(-2) ?$ \begin{tabular}{|c|c|c|} \hline $x$ & $f(x)$ & $f^{\prime}(x)$ \\ \hline-2 & -5 & 4 \\ \hline 1 & -2 & 7 \\ \hline 4 & 3 & 3 \\ \hline 6 & 4 & 10 \\ \hline 7 & 6 & 9 \\ \hline \end{tabular}

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Problem 3279

Which of the following is a point on the graph as described by the function $y=(2 x+1)^{2}-4$ ? (1 point) $(-1,-3)$ $(-1,-5)$ $(0,-2)$ $(1,2)$

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Problem 3280

Übung 6 Bestimmen Sie $\mathrm{a}>0$ so, dass die von den Graphen der Funktionen $f$ und $g$ eingeschlossene Fläche den angegebenen Inhalt A hat. a) $f(x)=-x^{2}+2 a^{2}$ $\begin{array}{l} g(x)=x^{2} \\ A=72 \end{array}$ b) $f(x)=x^{2}$ c) $f(x)=x^{2}+1$ $g(x)=a x$ $g(x)=\left(a^{2}+1\right) \cdot x^{2}$ $A=\frac{4}{3}$ $\mathrm{A}=\frac{4}{3}$

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Problem 3281

Which of the following ara the two quartitios whase functional relationship is dascribod in the given graph? (1 point) The two quantities are the average rairtall in inches and the yoars. The two quantilies are inches and monthe of the year. The two quartitics are the $x$ -values and the $y$ -values. The two quantitics are the avsrago rairiall in inches and the month of the yoar.

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Problem 3282

Graph of $f$
9. The graph of $f$ is shown above. Which of the following could be the equation for $f$ ? (A) $f(x)=2 \log _{4}(x)$ (B) $f(x)=-2 \log _{4}(x)$ (C) $f(x)=-2\left(\frac{1}{2}\right)^{x}$ (D) $f(x)=-2(3)^{x}$

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Problem 3283

Determine whether the following statement makes sense or does not make sense, and explain your reasoning The graph of a function is not a straight line, so the slope cannot be used to analyze its rates of change.

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Problem 3284

Given that $v=4 x^{2}+2$ , find $\frac{d}{d x}\left(v^{5}-4 \sin x\right)$ in terms of only $x$ .

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Problem 3285

Which of the following relations represent functions? Select all that apply.
\begin{tabular}{|c|c|c|c|c|c|} \hline $x$ & -2 & -1 & 0 & 1 & 2 \\ \hline $y$ & 3 & 3 & 3 & 3 & 3 \\ \hline \end{tabular}

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Problem 3286

AnE $=$ -
Question The table represents some points on the graph of a linear function f. Which function represents \begin{tabular}{|c|c|c|c|c|} \hline $x$ & -3 & 2 & 5 & 11 \\ \hline $4(1)$ & -30 & 0 & 76 & 24 \\ \hline \end{tabular}
Answer Altempt 1 out of 2 A. $f(x)=26(x-2)$ B. $f(x)=-26(2 x-1)$ C. $f(x)=13(x-2)$ D. $f(x)=-2(26 x-1)$ Submil Answer

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Problem 3287

IM 3 Unit 3 Test (Form A) 115 Name: Abuzir $\qquad$ Online Code: $\qquad$ XPTBGZK
12. Graph the function $h(x)=\frac{2}{x+3}-5$ . Include both asymptotes and two accurate points. (2 points)
13. Multiply: $\frac{x^{2}-2 x-3}{3 x-12}$ and $\frac{x^{2}-16}{x^{2}+6 x+5}$ . Show all work. Circle your final answer. (4 points)
14. Find the quotient. $\frac{9 x^{2}}{3 x^{2}+18 x} \div \frac{1}{x+6}$ . Show all work. Circle your final answer.(3 points)

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Problem 3288

18. The graph of $y=2 \sin b(x-c)+1$ is shown below. Determine a value of $c$ . A. $\frac{2 \pi}{7}$ C. 2 B. $\frac{\pi}{4}$ D. $\frac{2 \pi}{2}$

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Problem 3289

Find the logarithm. $\log (10,000)=$

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Problem 3290

```latex Suppose $f(x) = \frac{x^{2}}{9}$ .
(a) The rectangles in the graph on the left illustrate a left endpoint Riemann sum for $f(x)$ on the interval $2 \leq x \leq 4$ . The value of this left endpoint Riemann sum is $\square$ and it is an $\_\_\_\_\_\_\_\_\_$ .
(b) The rectangles in the graph on the right illustrate a right endpoint Riemann sum for $f(x)$ on the interval $2 \leq x \leq 4$ . The value of this right endpoint Riemann sum is $\square$ and it is an $\_\_\_\_\_\_\_\_\_$ $\square$ the area of the region enclosed by $y = f(x)$ , the $x$ -axis, and the vertical lines $x = 2$ and $x = 4$ .

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Problem 3291

Find the amplitude of the sinusoidal function.
Simplify any fractions. amplitude $=$ $\square$

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Problem 3292

Question
The tables shows the linear relationship between the balance of Bill's bank account and the $n$ umber of days since he was paid. \begin{tabular}{|c|c|c|c|c|} \hline Days & 0 & 4 & 6 & 17 \\ \hline Dollars & 800 & 544 & 46 & 96 \\ \hline \end{tabular}
Answer Attempt 1 out of 2
What was the rate of change of Bill's account balance in dollars per month?

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Problem 3293

Part 1 of 3
Determine the number of cycles the following sine function has in the interval from 0 to $2 \pi$ . Find the amplitude and period of the function $y=-4 \sin 2 \pi \theta$
The given sine function has $\square$ cycle(s). (Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)

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Problem 3294

Question
The table shows the linear relationship between the temperature of Earth's atmosphere and the altitude above sea level. What was the rate of change of the temperature with respect to altitude? \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Altitude \\ $(\mathrm{km})$ \end{tabular} & \begin{tabular}{c} Temperature \\ $\left({ }^{\circ} \mathrm{C}\right)$ \end{tabular} \\ \hline 1 & 8.5 \\ \hline 4 & -11 \\ \hline 5 & -17.5 \\ \hline 7 & -30.5 \\ \hline \end{tabular}

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Problem 3295

Let $f(x)=2 x^{2}+3 x-5$ and $g(x)=x-1$ . Perform the function operation and then find the domain. $(f+g)(x)$ $(f+g)(x)=$ $\square$ (Simplify your answer.)

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Problem 3296

Question
The table shows the linear relationship between the balance of Bob's savings account and the number of months he has been saving. \begin{tabular}{|l|c|c|c|c|} \hline Months & 0 & 3 & 7 & 9 \\ \hline Dollars & 10 & 85 & 185 & 235 \\ \hline \end{tabular}
Answer Attempt 2 out of 2
Find the rate of change of Bob's savings account in dollars and cents per month?

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Problem 3297

\begin{tabular}{|l|c|c|} \hline Slope: \\ $\square-3 / 1$ \\ $\square-1 / 3$ & $x$ & $y$ \\ $\square 3 / 1$ \\ $\square 1 / 3$ & -3 & 5 \\ $Y-1$ Intercept: \\ $\square 5$ & -2 & 2 \\ $\square-4$ & -1 & -1 \\ $\square 2$ & 0 & -4 \\ $\square-7$ & 1 & -7 \\ \hline \end{tabular}

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Problem 3298

A particle in the ocean moves with a wave. The motion of the particle can be modeled by the cosine function. If a 10 in. wave occurs every 6 s , write a function that models the height of the particle in inches $y$ as it moves in seconds $x$ . What is the period of the function?
A function that models the height of the particle is $\square$ (Simplify your answer. Type an equation. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)

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Problem 3299

Graph the function $f(x) = \frac{3}{x-2}$ .

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Problem 3300

Let $f(x)=-2 x-1, h(x)=\frac{x-5}{3}$ . Find $(f \circ h)(3)$ $(f \circ h)(3)=$ $\square$ (Type an integer or a fraction.)

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Function

Problem 3201

Problem 3202

Problem 3203

Problem 3204

Problem 3205

The function hhh is defined by h(x)=2+x5+2xh(x)=\frac{2+x}{5+2 x}h(x)=5+2x2+x​.Find h(4x)h(4 x)h(4x). h(4x)=h(4 x)=h(4x)=

Problem 3206

Problem 3207

The graphs of y=f(x),y=g(x)y=f(x), y=g(x)y=f(x),y=g(x) and y=h(x)y=h(x)y=h(x) are shown below. Remember that y=g(x)y=g(x)y=g(x) and y=h(x)y=h(x)y=h(x) are transformations of y=f(x)y=f(x)y=f(x). Write equations for g(x)g(x)g(x) and h(x)h(x)h(x) in terms of f(x)f(x)f(x). a. b.

Problem 3208

Graph the function f(x)=3x+3f(x)=3^{x}+3f(x)=3x+3. Give the domain and range.

Problem 3209

Problem 3210

Evaluate the line integral, where CCC is the given curve. ∫Cxyz2ds,C\int_{C} x y z^{2} d s, C∫C​xyz2ds,C is the line segment from (−2,3,0)(-2,3,0)(−2,3,0) to (0,4,4)(0,4,4)(0,4,4)

Problem 3211

Problem 3212

Problem 3213

Problem 3214

Sketch the graph of the function. f(x)=arctan⁡(4x)f(x)=\arctan (4 x)f(x)=arctan(4x)Compare the graph to the graph of the parent inverse trigonometric function. The graph of f(x)f(x)f(x) is arctan⁡(x)\arctan (x)arctan(x) with a ---Select--- □\square□ Read It

Problem 3215

Problem 3216

Graph the following function by starting with the graph of y=x2y=x^{2}y=x2 and using transformations (shifting, compressing, stretching, and/or reflection). f(x)=23x2f(x)=\frac{2}{3} x^{2}f(x)=32​x2Use the graphing tool to graph the function.

Problem 3217

Determine the quadratic function whose graph is given below.The quadratic function which describes the given graph is f(x)=f(x)=f(x)= □\square□ (Type an expression.)

Problem 3218

Graph each polynomial function. Give the domain and range.9. f(x)=−2x2+3f(x)=-2 x^{2}+3f(x)=−2x2+310. f(x)=−x3+3f(x)=-x^{3}+3f(x)=−x3+3

Problem 3219

Find the derivative of y=cos⁡(x)cos⁡(x)y=\cos (x)^{\cos (x)}y=cos(x)cos(x). dydx=\frac{d y}{d x}=dxdy​= □\square□Submit answer Next item

Problem 3220

Problem 3221

Problem 3222

Problem 3223

Problem 3224

11. Let f(x)=3x+5f(x)=3 x+5f(x)=3x+5 and g(x)=x2+2g(x)=x^{2}+2g(x)=x2+2. Find each of the following. (a) (f∘g)(−2)(f \circ g)(-2)(f∘g)(−2) (b) (f∘g)(x)(f \circ g)(x)(f∘g)(x) (c) (g∘f)(x)(g \circ f)(x)(g∘f)(x)

Problem 3225

(b) f(t)=2t−4+3ttf(t)=\frac{2 t-4+3 \sqrt{t}}{\sqrt{t}}f(t)=t​2t−4+3t​​

Problem 3226

Step 4 As we are looking for an absolute maximum, find the derivative of f(x)f(x)f(x). f(x)=3,008x−2x2f′(x)=1\begin{array}{l} f(x)=3,008 x-2 x^{2} \\ f^{\prime}(x)=1 \end{array}f(x)=3,008x−2x2f′(x)=1​ Submit Skip (you cannot come back) Need Help? Read It Submit Answer

Problem 3227

Find the vertex and axis of the graph of the function. f(x)=2(x−3)2+9f(x)=2(x-3)^{2}+9f(x)=2(x−3)2+9The vertex is □\square□ (Type an ordered pair.)

Problem 3228

Problem 3229

Problem 3230

Problem 3231

The period, to the nearest tenth, of the function y=sin⁡0.25xy=\sin 0.25 xy=sin0.25x, where xxx is in radians, is

Problem 3232

Problem 3233

cos⁡−1(2/2)\cos ^{-1}(\sqrt{2} / 2)cos−1(2​/2)

Problem 3234

(b) Given that f(x)=x2+∣x−4∣f(x)=x^{2}+|x-4|f(x)=x2+∣x−4∣. Determine whether fff is differentiable at x=4x=4x=4.

Problem 3235

Find the slope of the tangent line to the curve f(x)=tan⁡−1(x)f(x)=\tan ^{-1}(x)f(x)=tan−1(x) at x=12x=\frac{1}{2}x=21​. 45\frac{4}{5}54​ 23\frac{2}{3}32​ 32\frac{3}{2}23​ 54\frac{5}{4}45​

Problem 3236

Problem 3237

Problem 3238

The function f(x)=4x4−x3−15x2+8x+4f(x)=4 x^{4}-x^{3}-15 x^{2}+8 x+4f(x)=4x4−x3−15x2+8x+4 has at least two rational roots. Use the rational root theorem to find those roots, then proceed to find all complex roots. (Note: roots may be integer, rational, irrational, and/or complex.)

Problem 3239

Problem 3240

Find the degree and the leading coefficient for the given polynomial function. f(x)=−2x2−5xf(x)=-2 x^{2}-5 xf(x)=−2x2−5xAnswer: Degree: □\square□ Leading Coefficient:

Problem 3241

Find all real zeros of the polynomial function. f(x)=x3−8x2+16x−8f(x)=x^{3}-8 x^{2}+16 x-8f(x)=x3−8x2+16x−8Submit multiple zeros by separating them with a comma. For instance, if the zeros are 1,2 , and 3 , then submit your answer as 1,2,31,2,31,2,3.

Problem 3242

Problem 3243

Find the xxx-and yyy-intercepts of the quadratic function f(x)=2x2+6x+3f(x)=2 x^{2}+6 x+3f(x)=2x2+6x+3.Enter just the xxx or yyy-coordinate(s) of the intercept(s) separated by commas. For example enter 1,2,51,2,51,2,5 if the xxx-intercepts are at x=1,x=2,x=5x=1, x=2, x=5x=1,x=2,x=5.

Problem 3244

Problem 3245

Problem 3246

Find all zeros, real and complex, of the polynomial function. f(x)=2x3+6x2+11x+7f(x)=2 x^{3}+6 x^{2}+11 x+7f(x)=2x3+6x2+11x+7Submit multiple zeros by separating them with a comma. For instance, if the zeros are 1,2 , and 3 , then submit your answer as 1,2,31,2,31,2,3.

Problem 3247

Problem 3248

Problem 3249

Problem 3250

III. Evaluate each of the following indefinite intiggals. Show uuu and du if necessary.1. ∫[sinh⁡(3y)−sin⁡(3y)]dy\int[\sinh (3 y)-\sin (3 y)] d y∫[sinh(3y)−sin(3y)]dy

Problem 3251

5. Evaluate ∭Gx2dV\iiint_{G} x^{2} d V∭G​x2dV, where GGG is bounded by the xzx zxz-plane and the hemispheres y=9−x2−z2y=\sqrt{9-x^{2}-z^{2}}y=9−x2−z2​ and y=16−x2−z2\mathrm{y}=\sqrt{16-\mathrm{x}^{2}-\mathrm{z}^{2}}y=16−x2−z2​

Problem 3252

Q7 : find ddx(tan⁡x2+2x)\text { Q7 : find } \frac{d}{d x}\left(\tan x^{2}+2^{x}\right) Q7 : find dxd​(tanx2+2x) ✓\checkmark✓ Solution:

Problem 3253

What is the minimum value of this function?

The function $h$ is defined by $h(x)=\frac{2+x}{5+2 x}$ .
Find $h(4 x)$ . $h(4 x)=$

The graphs of $y=f(x), y=g(x)$ and $y=h(x)$ are shown below. Remember that $y=g(x)$ and $y=h(x)$ are transformations of $y=f(x)$ . Write equations for $g(x)$ and $h(x)$ in terms of $f(x)$ . a. b.

Graph the function $f(x)=3^{x}+3$ . Give the domain and range.

Evaluate the line integral, where $C$ is the given curve. $\int_{C} x y z^{2} d s, C$ is the line segment from $(-2,3,0)$ to $(0,4,4)$

Sketch the graph of the function. $f(x)=\arctan (4 x)$
Compare the graph to the graph of the parent inverse trigonometric function. The graph of $f(x)$ is $\arctan (x)$ with a ---Select--- $\square$ Read It

Graph the following function by starting with the graph of $y=x^{2}$ and using transformations (shifting, compressing, stretching, and/or reflection). $f(x)=\frac{2}{3} x^{2}$
Use the graphing tool to graph the function.

Determine the quadratic function whose graph is given below.
The quadratic function which describes the given graph is $f(x)=$ $\square$ (Type an expression.)

Graph each polynomial function. Give the domain and range.
9. $f(x)=-2 x^{2}+3$
10. $f(x)=-x^{3}+3$

Find the derivative of $y=\cos (x)^{\cos (x)}$ . $\frac{d y}{d x}=$ $\square$
Submit answer Next item

11. Let $f(x)=3 x+5$ and $g(x)=x^{2}+2$ . Find each of the following. (a) $(f \circ g)(-2)$ (b) $(f \circ g)(x)$ (c) $(g \circ f)(x)$

(b) $f(t)=\frac{2 t-4+3 \sqrt{t}}{\sqrt{t}}$

Step 4 As we are looking for an absolute maximum, find the derivative of $f(x)$ . $\begin{array}{l} f(x)=3,008 x-2 x^{2} \\ f^{\prime}(x)=1 \end{array}$ Submit Skip (you cannot come back) Need Help? Read It Submit Answer

Find the vertex and axis of the graph of the function. $f(x)=2(x-3)^{2}+9$
The vertex is $\square$ (Type an ordered pair.)

The period, to the nearest tenth, of the function $y=\sin 0.25 x$ , where $x$ is in radians, is

$\cos ^{-1}(\sqrt{2} / 2)$

(b) Given that $f(x)=x^{2}+|x-4|$ . Determine whether $f$ is differentiable at $x=4$ .

Find the slope of the tangent line to the curve $f(x)=\tan ^{-1}(x)$ at $x=\frac{1}{2}$ . $\frac{4}{5}$ $\frac{2}{3}$ $\frac{3}{2}$ $\frac{5}{4}$

The function $f(x)=4 x^{4}-x^{3}-15 x^{2}+8 x+4$ has at least two rational roots. Use the rational root theorem to find those roots, then proceed to find all complex roots. (Note: roots may be integer, rational, irrational, and/or complex.)

Find the degree and the leading coefficient for the given polynomial function. $f(x)=-2 x^{2}-5 x$
Answer: Degree: $\square$ Leading Coefficient:

Find all real zeros of the polynomial function. $f(x)=x^{3}-8 x^{2}+16 x-8$
Submit multiple zeros by separating them with a comma. For instance, if the zeros are 1,2 , and 3 , then submit your answer as $1,2,3$ .

Find the $x$ -and $y$ -intercepts of the quadratic function $f(x)=2 x^{2}+6 x+3$ .Enter just the $x$ or $y$ -coordinate(s) of the intercept(s) separated by commas. For example enter $1,2,5$ if the $x$ -intercepts are at $x=1, x=2, x=5$ .

Find all zeros, real and complex, of the polynomial function. $f(x)=2 x^{3}+6 x^{2}+11 x+7$
Submit multiple zeros by separating them with a comma. For instance, if the zeros are 1,2 , and 3 , then submit your answer as $1,2,3$ .

III. Evaluate each of the following indefinite intiggals. Show $u$ and du if necessary.
1. $\int[\sinh (3 y)-\sin (3 y)] d y$

5. Evaluate $\iiint_{G} x^{2} d V$ , where $G$ is bounded by the $x z$ -plane and the hemispheres $y=\sqrt{9-x^{2}-z^{2}}$ and $\mathrm{y}=\sqrt{16-\mathrm{x}^{2}-\mathrm{z}^{2}}$

$\text { Q7 : find } \frac{d}{d x}\left(\tan x^{2}+2^{x}\right)$ $\checkmark$ Solution:

Find $f^{\prime}(x)$ . $\begin{array}{l} f(x)=\left(5 x^{4}+3\right)^{5} \\ f^{\prime}(x)=\square \end{array}$

Differentiate. $\begin{array}{c} y=\ln \left[(x+9)^{5}(x+6)^{2}(x+8)^{4}\right] \\ \frac{d}{d x}\left[\ln \left[(x+9)^{5}(x+6)^{2}(x+8)^{4}\right]\right]= \end{array}$

Trovare lo sviluppo di Maclaurin di ordine 3 per la funzione $f(x) = \frac{1}{-\sqrt{8} \sin x - 2 \cos x}$ .

2. Which is true about the function $f(x)=\frac{1}{\left|x^{3}\right|}$ ? A. It is an even function. B. It is an odd function. C. It is neither even-nor odd. n It is both even and odd.

Find all of the zeros of $t(h)=80 h^{5}-245 h^{3}$ . Show

$f(x)=\frac{x^{2}-4 x+3}{x^{3}-x^{2}-6 x}$
4. There is a removable discontinuity at $x=-2$ .
There is an infinite discontinuity at $x=3$ . :. There is a jump discontinuity at $x=0$ . - There is a removable discontinuity at $x=3$ .

Resuelve, en cuentra el limite (1). $f(x)=3 x^{2} \tan x$ (2) $f(x)=\frac{x^{2}-3 x}{2 x}$ (3) $F(x)=\sqrt{2 x^{2}+3}$

$\sin ^{-1}\left(-\frac{1}{2}\right)$

$\cos ^{-1}\left(-\frac{\sqrt{2}}{2}\right)$

$\arccos \frac{1}{2}$

Herreverk2024
The table of ordered pairs $(x, y)$ gives an exponential function. Write an equation for the function. \begin{tabular}{|l|l|} \hline 0 & 36 \\ \hline 1 & 6 \\ \hline 2 & 1 \\ \hline \end{tabular}
Try one last time Recheck

Differentiate the following function. $\begin{array}{l} y=(\ln x)^{10}+\ln \left(x^{10}\right) \\ \frac{d y}{d x}=10 \end{array}$

Match the value of $b$ on the left with the shape of the graph of $f(x)=\log _{b} x$ on the right. Graphs on the right may be used more than once. $\begin{array}{l} b=3 \\ b=\frac{5}{2} \\ b=\frac{2}{5} \\ b=0.10 \end{array}$

Question 3 Suppose that there are initially 600 rabbits in a population, and that the population changes at a rate of $f(t)=t$ where $t$ is in weeks. How many rabbits will there be after 4 weeks?

AA. 12 Compare linear, exponential, and quadratic growth 39 V
Both of these functions grow as $x$ gets larger and larger. Which function eventually exceeds the other? $f(x)=2 x+8 \quad g(x)=2 x^{2}-5$
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1 AA. 12 Compare linear, exponential, and quadratic growth 39 V
Both of these functions grow as $x$ gets larger and larger. Which function eventually exceeds the other? $f(x)=\frac{3}{2} x+6 \quad g(x)=\frac{1}{2} x^{2}-x+6$ Submit