Function

Problem 3301

One cycle of the graph of a trigonometric function of the form y=Asin(Bx)y=A \boldsymbol{\operatorname { s i n }}(B x) or y=Acos(Bx)y=A \boldsymbol{\operatorname { c o s }}(B x) is given. Determine the equation of the function represented by the following graph.
What function of the form y=Asin(Bx)y=A \sin (B x) or y=Acos(Bx),B>0y=A \cos (B x), B>0 is represented by the given graph? \square (bse integers or fractions for any numbers in the equation.)

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Problem 3302

What is the range of the function y=4exy=4 e^{x} ? all real numbers greater than 0 all real numbers less than 0 all real numbers less than 4 all real numbers greater than 4

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Problem 3303

For the function f(x)=x2+2x31f(x)=x^{2}+2 x-31, find f(14)f(-14)
The value of the function is \square (Type an integer or a simplifie

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Problem 3304

Evaluate y=ln(x2)y=\ln (x-2) for the following values of xx. Round to the nearest thousandth. x=3,y=x=3, y= \square x=4,yx=4, y \approx \square x=6,yx=6, y \approx \square

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Problem 3305

2. The graph of a linear function 9 passes through the points (7,4)(-7,-4) and (7,6)(7,6).
What are the slope and yy-intercept of the graph of gg ?
4. The slope is 75\frac{7}{5} and the yy-intercept is -1 . B. The slope is 75\frac{7}{5} and the yy-intercept is 1 . C. The slope is 57\frac{5}{7} and the yy-intercept is -1 . D. The slope is 57\frac{5}{7} and the yy-intercept is 1 .
3. Which ordered pair is in the solution set of y35x6y \leq \frac{3}{5} x-6 ? A. (5,4)(5,-4) B. (2,5)(-2,-5) C. (9,1)(9,1) D. (8,3)(-8,3)

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Problem 3306

Given f(x)=x2+3x+11f(x)=-x^{2}+3 x+11, find f(1)f(-1)

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Problem 3307

Find 04(5x4+2)dx\int_{0}^{4}\left(5 x^{4}+2\right) d x

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Problem 3308

9) Graph the following; your curve may go off of the graph: f(x)=3ex+12f(x)=3 e^{x+1}-2

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Problem 3309

Remaining Tim
A very small car (apparently a VW Beetle) is driving back and forth along the xx-axis with velocity given by the function v(t)=3t218t+24v(t)=3 t^{2}-18 t+24. At time t=1t=1 second, the car's postion is x(1)=20 cmx(1)=20 \mathrm{~cm}. (a) Give an expression for the acceleration of the car at any time tt. a(t)=a(t)= aba^{b} ab\frac{a}{b} a\sqrt{a} a|a| π\pi sin(a)\sin (a)

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Problem 3310

One cycle of the graph of a trigonometric function of the form y=Asin(Bx)y=A \sin (B x) or y=Acos(Bx)y=A \cos (B x) is given. Determine the equation of the function represented by the following graph
What function of the form y=Asin(Bx)y=A \sin (B x) or y=Acos(Bx),B>0y=A \cos (B x), B>0 is represented by the given graph? \square (Use integers or fractions lor any numbers in the equation)

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Problem 3311

What is the range of the function y=4exy=4 e^{x} ? all real numbers greater than 0 all real numbers less than 0 all real numbers less than 4 all real numbers greater than 4

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Problem 3312

Consider the quadratic function written below in intercept form. f(x)=(x2)(x4)f(x)=(x-2)(x-4)
Which of the following represents the vertex of the quadratic function? (A) (4,0)(4,0) (B) (3,1)(3,-1) (C) (2,4)(2,4) (D) (2,0)(2,0) (E) (3,0)(3,0)

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Problem 3313

x2;f(x)=x43x3+2x2+8x16x-2 ; f(x)=x^{4}-3 x^{3}+2 x^{2}+8 x-16

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Problem 3314

Diana has 440 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width W of the rectangle. (b) For what value of W is the area largest? (c) What is the maximum area? (a) A(W)=A(W)= \square

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Problem 3315

Farmer has 5,000 meters of fencing, and wants to enclose a rectangular plot that borders on a river. If Farmer does not fence the side along the river, what is the largest area that can be enclosed?
The largest area that can be enclosed is \square \square

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Problem 3316

tank of water was drained at a constant rate. The table shows the number of gallons of water left rained for two amounts of time. \begin{tabular}{|c|c|} \hline Draining Time (minutes) & Water in Tank (gallons) \\ \hline 10 & 450 \\ \hline 30 & 330 \\ \hline \end{tabular}
Part A What is the rate at which the water was drained from the tank? A 11 gallons of water per minute (B) 6 gallons of water per minute (C) 45 gallons of water per minute
D 120 gallons of water per minute

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Problem 3317

On the coordinate grid, the graph of y=x13+3y=\sqrt[3]{x-1}+3 is shown. It is a translation of y=x3y=\sqrt[3]{x}.
What is the domain of the graphed functi {x1<x<5}\{x \mid 1<x<5\} {y1<y<5}\{y \mid 1<y<5\} {xx\{x \mid x is a real number }\} {yy\{y \mid y is a real number }\} Save and Exit Next

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Problem 3318

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. 12) Zeros of 3,1,4-3,-1,4 and P(2)=5P(2)=5

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Problem 3319

How are the domain and range of the function y=14cos[3(x2π3)]+2y=\frac{1}{4} \cos \left[3\left(x-\frac{2 \pi}{3}\right)\right]+2 related to the domain and range of the parent function y=cosxy=\cos x ? Explain your reasoning
Choose the correct answer below. A. The domain is the same, and the range is narrower and higher. The endpoints of the range are moved 4 times closer to the xx-axis because of the vertical compression and then increased by because of the vertical shift. The horizontal compression and horizontal shift have no effect on the domain because it is infinitely wide (all real numbers) for both functions. B. The domain is the same, and the range is higher. The endpoints of range are increased by 2 because of the vertical shift. The vertical compression has no effect on the range, The horizontal compression and horizontal shift have no effect on the domain because it is infinitely wide (all real numbers) for both functions. c.
The range is the same, and the domain is shifted to the right. The endpoints of the domain are increased by 2π3\frac{2 \pi}{3} because of the horizontal shift. The horizontal compression has no effect on th domain. The vertical compression and vertical shift have no effect on the range because it is infinitely wide (all real numbers) for both functions. - D. The range is the same, and the domain is narrower and to the right. The endpoints of the domain are moved 3 times closer to the yy-axis because of the horizontal compression and then increased by 2πn\frac{2 \pi}{n} because of the horizontal shift. The vertical compression and vertical shift have no effect on the range because it is infinitely wide (all real numbers) for both functions.

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Problem 3320

The accompanying graph shows a sinusoidal function. Complete parts a) through c) below. a) What is the period of this function?
The period is \square

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Problem 3321

11.) f(x)=3x1(x+3)(x1)f(x)=\frac{3 x-1}{(x+3)(x-1)} Find the Domain of the function Algebraically

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Problem 3322

A relation in xx and yy is given. Determine if the relation defines yy as a one-to-one function of xx. The relation defines yy as a one-to-one function of xx. The relation does not define yy as a one-to-one function of xx.

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Problem 3323

1. Функції f,g:[1,)Rf, g:[1, \infty) \rightarrow \mathbb{R} \in невід'ємними і такими, що інтеграли 1f(x)dx\int_{1}^{\infty} f(x) d x та 1g(x)dx\int_{1}^{\infty} g(x) d x \in розбіжними. Що можна сказати про збіжність інтеграла 1max{f(x),g(x)}dx\int_{1}^{\infty} \max \{f(x), g(x)\} d x ?

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Problem 3324

6. A quadratic function of the form y=x2+bx+cy=x^{2}+b x+c is shown graphed. (a) What are the xx-intercepts of this parabola? (b) Based on your answer to part (a), write the equation of this quadratic function first in factored form and then in trinomial form.

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Problem 3325

he second derivative of the function. f(x)=113x4f(x)=\frac{1}{13 x-4}

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Problem 3326

What is the current in a wire of radius R=3.61 mmR=3.61 \mathrm{~mm} if the magnitude of the current density is given by (a)Ja=J0r/R(a) J_{a}=J_{0} r / R and (b)Jb=J0(1r/R)(b) J_{b}=J_{0}(1-r / R) in which rr is the radial distance and J0=4.03×104 A/m2J_{0}=4.03 \times 10^{4} \mathrm{~A} / \mathrm{m}^{2} ? (c) Which function maximizes the current density near the wire's surface? (a) Number i Units \square (b) Number i \square Units \square

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Problem 3327

Dilate FGH\triangle F G H by a scale factor of 4 with the center of diliation at the origin.
How can you use the coordinates of point FF to find the coordinates of point FF^{\prime \prime} ?
Multiply each coordinate by 4 .
What are the coordinates of point FF^{\prime} ? Point F:(,)F^{\prime}:(\square, \square) \begin{tabular}{|c|c|c|c|} \hline \multicolumn{4}{|c|}{\cdots} \\ \hline x\mathbf{x} & 8\mathbf{8} & 9 & x\boldsymbol{x} \\ \hline 4 & 5 & 6 & - \\ \hline 1 & 2 & 3 & - \\ \hline 0 & & (1(-1 & \\ \hline \end{tabular}

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Problem 3328

Find the following antiderivatives:
1. 6+sec2(x)dx=+C\int 6+\sec ^{2}(x) d x=\square+C.
2. 7x23x2dx=+C\int \frac{7 x^{2}-3}{x^{2}} d x=\square+C.

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Problem 3329

The quadratic function y=18x26y=\frac{1}{8} x^{2}-6 has a vertex at (h,k)(h, k) and focal length of c\boldsymbol{c}^{\prime}.
What are the values for h,kh, k, and cc^{\prime} ? h=k=c=\begin{array}{l} h=\square \\ k=\square \\ c^{\prime}=\square \end{array}
The focal point for y=18x26y=\frac{1}{8} x^{2}-6 is at (0,p)(0, p). What is the value of pp ? p=p=\square

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Problem 3330

7. Students who completed a class participated in a year-long study to see how much content from the class they retained over the following year. At the end of the class, students completed an initial test to determine the group's content knowledge. At that time (t=0)(t=0), the group of students achieved a score of 75 out of 100 points. For the next 12 months, the group was evaluated at the end of each month to track their retention of the content. After 3 months (t=3)(t=3), the group's score was 70.84 points. The group's score can be modeled by the function RR given by R(t)=a+bln(t+1)R(t)=a+b \ln (t+1), where R(t)R(t) is the score, in points, for month tt, and tt is the number of months since the initial test. (A) (i) Use the given data to write two equations that can be used to find the values for constants aa and bb in the expression for R(t)R(t). (ii) Find the values for aa and bb. (B) (i) Use the given data to find the average rate of change of the scores, in points per month, from t=0t=0 to t=3t=3 months. Express your answer as a decimal approximation. Show the computations that lead to your answer. (ii) Interpret the meaning of your answer from (i) in the context of the problem. (iii) Consider the average rates of change of RR from t=3t=3 to t=pt=p months, where p>3p>3. Are these average rates of change less than or greater than the average rate of change from t=0t=0 to t=3t=3 months found in (i)? Explain your reasoning.
The leaders of the study decide to use model RR to make predictions about the group's score beyond 12 months ( 1 year). For a given year, model RR is an appropriate model if the group's predicted score at the end of the year is at least 1 point lower than the group's predicted score at the end of the previous year. Based on this information, for how many years is model RR an appropriate model? Give a reason for you answer. (Note: The end of a year occurs every 12 months from the initial evaluation-- t=12,t=24t=12, t=24,

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Problem 3331

Use logarithmic differentiation to find the derivative. y=x2+3x2+45y=\sqrt[5]{\frac{x^{2}+3}{x^{2}+4}}

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Problem 3332

10. Find all holes of the following function. Write your answer as a coordinate point in simplest form. If no hole exists, write 'none'. f(x)=2x2+12x2x217x+36f(x)=\frac{2 x^{2}+12 x}{2 x^{2}-17 x+36}

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Problem 3333

* Consider the function f(x)=x((x21)2+12)f(x)=x\left(\left(x^{2}-1\right)^{2}+\frac{1}{2}\right) - Find the transition points. - Find the intervals where the function is increasing / decreasing and concave down. - Find the local minima and maxima. - Find the horizontal and vertical asymptotes, if there are any. - Sketch the graph.

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Problem 3334

5. Determine if the function below has a horizontal or a slant asymptote, and explain why. 510x+25x25x+2\frac{5-10 x+25 x^{2}}{-5 x+2}
The function has a (slant / horizontal) asymptote because the degree of the numerator is (greater than/equal to/ less than) the degree of the denominator.
As xx approaches infinity (positive or negative), the value f approaches

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Problem 3335

Show all work! A correct answer with no work is worth 1 point. You must show all your work to receive credit. I cannot see what is in your head or what is on your calculator; I can only see what is on the paper you turn in. You must follow the directions of the problem to receive full credit.
12. If the daily marginal cost for a product is MC=e3x+15\overline{M C}=e^{3 x}+15, with fixed costs amounting to $500\$ 500, find the total cost function for each day. Do not use your calculator to find/simplify your answer.

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Problem 3336

* Consider the function f(x)=x((x21)2+12)f(x)=x\left(\left(x^{2}-1\right)^{2}+\frac{1}{2}\right) - Find the transition points.

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Problem 3337

3. Determine if the function below has a horizontal or a slant asymptote, and explain why. 3+2x33x+4x25x21+4x3\frac{-3+2 x^{3}-3 x+4 x^{2}}{5 x^{2}-1+4 x^{3}}
The function has a (slant / horizontal) as ymptote because the degree of the numerator is (greater than/equal to/ less than) the degree of the denominator.
Asymptote: \qquad

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Problem 3338

Suppose that the population of wolves is initially 800 , and that the rate of change of the population is given by r(t)r(t), where tt is in years. What is the meaning of 610r(t)dt\int_{6}^{10} r(t) d t The rate of change of the number of wolves in year 10 The change in the number of wolves from year 6 to year 10 Thê rate of change of the number of wolves in year 6 The difference in the growth rate r(t)r(t) between year 6 and year 10 . The total number of wolves after 10 years.

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Problem 3339

g(x)=5x47g(x)=-\frac{5 \sqrt[4]{x}}{7}
Step 1 of 2 : Identify the general shape of the graph of this function. Answer Keypad Keyboard Shortcuts

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Problem 3340

Score: 6/10
Find the exact value of sin135\sin 135^{\circ}
Answer

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Problem 3341

Use a calculator to evaluate arcsin( 0.55 ) to 4 decimal places in radian

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Problem 3342

Question 2
Plot the function f(x)=2xx25f(x)=\frac{2 x}{x^{2}-5}. How many inflection points does this function have? 0 2 1 3

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Problem 3343

Question 3 1 pts
Factor the following function: x4+3x315x219x+30x^{4}+3 x^{3}-15 x^{2}-19 x+30. How many real-valued roots does this polynomial have? 3 1 2 4

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Problem 3344

Question 4 1 pts
Consider the function f(x)=x37x2xx35x2f(x)=\frac{x^{3}-7 x^{2}-x}{x^{3}-5 x^{2}}. How many horizontal asymptote(s) are there? (e.g. if you get a horizontal asymptote at y=5y=-5 and y=3y=3, then the answer should be " 2 ".) 0 2 3 1

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Problem 3345

Use a calculator to evaluate tan1(51)\tan ^{-1}(51) to 2 decimal places in degrees. If necessary, use 3.1416 as an approximation to pi.

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Problem 3346

The function f(t)={3 if 0<t10 if 1<t42 it t>4f(t)=\left\{\begin{array}{cc} 3 & \text { if } 0<t \leq 1 \\ 0 & \text { if } 1<t \leq 4 \\ 2 & \text { it } t>4 \end{array}\right. can bewritten as a sum of unit step functions f(t)=a+bu(tc)+du(te)f(t)=a+b u(t-c)+d u(t-e) wherea= \square , b=b= \square , c=c= \square , d= \square , ande = \square

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Problem 3347

Question 5
What is the value of limx0+12+e1x\lim _{x \rightarrow 0^{+}} \frac{1}{2+e^{-\frac{1}{x}}}.Your answer should be in decimal form rounded to one decimal place.

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Problem 3348

```latex \text{Predict the ball's rebound height after each successive bounce if its starting height is 200 cm. Create a table with these predicted heights.}
\begin{tabular}{|c|c|} \hline \text{Bounce} & \text{Height (cm)} \\ \hline 1 & 166.4 \\ \hline 2 & 138.445 \\ \hline 3 & \\ \hline 4 & \\ \hline 5 & \\ \hline 6 & \\ \hline \end{tabular}
\text{If the ball was left to bounce uninterrupted how high ................} ```
\text{The user took a picture with their phone and the text was extracted above. The user then had a dialogue with an AI Assistant to help clarify the instructions.}
\text{Dialogue Transcript:}
\text{Hello! It looks like you have a question about predicting the rebound height of a ball. The information you've provided shows the ball starts at a height of 200 cm and gives the rebound heights for the first two bounces. However, there is missing information, and it seems the table is incomplete.}
\text{To help you further, I need to know:} \begin{enumerate} \item \text{The rebound ratio or the percentage of the height retained after each bounce.} \item \text{How many bounces you would like to calculate the height for.} \end{enumerate}
\text{Once you provide this information, I can assist you in completing the table with the predicted heights for each bounce. Looking forward to your response!}
\text{Extracted text from attached image:} \begin{tabular}{|c|c|} \hline \text{Drop Height (cm)} & \text{Rebound Height (cm)} \\ \hline 150 & 124 \\ 70 & 59 \\ 120 & 100 \\ 100 & 83 \\ 110 & 92 \\ 40 & 33 \\ \hline \end{tabular}

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Problem 3349

Let C(q)C(q) represent the cost, R(q)R(q) the revenue, and π(q)\pi(q) the total profit, in dollars, of producing qq items. (a) If C(50)=76C^{\prime}(50)=76 and R(50)=84R^{\prime}(50)=84, approximately how much profit is earned by the 51st 51^{\text {st }} item?
The profit earned from the 51st 51^{\text {st }} item will be approximately $\$ \square . (b) If C(90)=71C^{\prime}(90)=71 and R(90)=66R^{\prime}(90)=66, approximately how much profit is earned by the 91st 91^{\text {st }} item?
The profit earned from the 91st 91^{\text {st }} item will be approximately $\$ \square . (c) If π(q)\pi(q) is a maximum when q=78q=78, how do you think C(78)C^{\prime}(78) and R(78)R^{\prime}(78) compare? C(78)C^{\prime}(78) \square R(78)R^{\prime}(78)

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Problem 3350

Question 11
Find the critical numbers of the following function f(x)=14x453x3+x2+8xf(x)=\frac{1}{4} x^{4}-\frac{5}{3} x^{3}+x^{2}+8 x. How many critical numbers does this function have? 1 4 2 3

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Problem 3351

Question 12 1 pts
Consider the function f(x)=excosxf(x)=e^{x} \cos x. Using a linear approximation of this function centered at the point x=2x=2, estimate f(x)f(x) at x=2x=2. (round to one decimal place) \square

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Problem 3352

2. Differentiate the following function. (Do not simplify your a) [8pts] f(x)=cos(2x)tan(3x)ex23xf(x)=\cos (2 x) \tan (3 x)-e^{x^{2}-3 x}

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Problem 3353

3. In a linear programming problem, the function to be maximized or minimized is called the \qquad objective function linear programming corner points feasible points

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Problem 3354

The answer above is NOT correct. Find the area between the curves: y=x313x2+40xy=x^{3}-13 x^{2}+40 x and y=x3+13x240xy=-x^{3}+13 x^{2}-40 x \square

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Problem 3355

Consider the region bounded by the line y=2y=2, the curve y=x3y=\sqrt[3]{x} and the yy-axis. Setup an integral with respect to xx that gives the area of the region. Area =abf(x)dx=\int_{a}^{b} f(x) d x where f(x)=23f(x)=2-3 sqrt (x)(x) \square a=a= 0 \square b=b= \square 8
Setup an integral with respect to yy that gives the area of the region. Area =cdg(y)dy=\int_{c}^{d} g(y) d y where g(y)=y3g(y)=y^{\wedge} 3 \square , c=0c=0 \square , d=d= \square 2
Evaluate either (or both) of these integrals to find the area of the region.
Area == \square 4

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Problem 3356

The rational function r(x)=x2+3x10(x+1)(x3)(x+5)r(x)=\frac{x^{2}+3 x-10}{(x+1)(x-3)(x+5)} has a hole at x=\mathrm{x}= \qquad .
Type your answer...
3 Numeric 1 point Refer to the last problem. What is the yy-coordinate of the hole? Must be within 1%1 \%.

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Problem 3357

Consider the rational function r(x)=2x3x21r(x)=\frac{2 x-3}{x^{2}-1}. The horizontal asymptote is y=\mathrm{y}= \square type your answer... \square type your answer... and x=x= \square type your answer... (Enter the VA's in increasing order).

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Problem 3358

The following table shows the total sales, in thousands, since a new game was brought to market. \begin{tabular}{c|c|c|c|c|c|c|c|c} \hline Month & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 \\ \hline Sales & 0 & 2.2 & 5.4 & 9.5 & 19.1 & 27.2 & 32.9 & 35.4 \\ \hline \end{tabular} (a) Plot this data and determine the point of diminishing returns.
Enter the closest value in the table.
The point of diminishing returns occurs \square i \square months after the game is introduced. (b) Predict total possible sales of this game, using the point of diminishing returns from the table.
Total sales \approx i \square

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Problem 3359

Question 4 (4 point) True or False: The graph of the following function would be narrower than the quadratic parent function: f(x)=2x2f(x)=2 x^{2} True False

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Problem 3360

Consider the function f(x)=excosxf(x)=e^{x} \cos x. Using a linear approximation of this function centered point x=2x=2, estimate f(x)f(x) at x=2x=2. (round to one decimal place) Not saved

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Problem 3361

For the function f(x)f(x) shown below, determine limx2+f(x)\lim _{x \rightarrow-2^{+}} f(x).

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Problem 3362

apply properties of exponents in order to write each exponential function in the form f(t)=abtf(t)=a \cdot b^{t}. By what percent does the function change each time tt increases by one unit? a) f(t)=312tf(t)=3^{1-2 t} b) f(t)=(1.2)4t+3f(t)=(1.2)^{4 t+3}

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Problem 3363

Find the vertical asymptotes (VA) and horizontal asymptotes (HA) of the function f(x)=2xx27x+10 f(x) = \frac{2x}{x^2 - 7x + 10} .

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Problem 3364

Find the most general antiderivative of the function. (Check your answer by differentiation. Use CC for the constant of the antiderivative.) f(t)=2t4+7ttF(t)=\begin{array}{l} f(t)=\frac{2 t-4+7 \sqrt{t}}{\sqrt{t}} \\ F(t)=\square \end{array}

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Problem 3365

Find the vertical asymptotes (VA) and horizontal asymptotes (HA) of the rational function y=x2+4x+32x2+5x7 y = \frac{x^2 + 4x + 3}{2x^2 + 5x - 7} .

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Problem 3366

4- Write a Python program that takes a student's grade as input and checks if they passed or failed. Assume the passing grade is 50 .

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Problem 3367

ln(1+j)\ln (-1+j)

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Problem 3368

Use the sum or difference formula for cosine to find the exact value for cos(105)\cos \left(105^{\circ}\right) cos(105)=\cos \left(105^{\circ}\right)=

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Problem 3369

Oil is leaking out of a ruptured tanker at the rate of r(t)=30e0.04tr(t)=30 e^{-0.04 t} thousand liters per minute. A. At what rate, in thousands of liters per minute, is the oil leaking out at t=0t=0 ? rate == \square thousand liters/min at t=60t=60 ? rate == \square thousand liters/min B. How many thousands of liters leak out during the first hour? Number of liters = \square thousand liters

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Problem 3370

5. (15 pts) Sketch the graph of the following function. Include the following: f(x)=(x2x)exf(x)=\left(x^{2}-x\right) e^{-x} a. Domain: \qquad b. Vertical Asymptote: \qquad c. Intervals Increasing: \qquad d. Intervals Decreasing: \qquad e. Local Extrema: \qquad f. Inflection Points: \qquad g. Intervals Concave Up: \qquad h. Intervals Concave Down: \qquad

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Problem 3371

Use the table of xx - and yy-values below to determine the slope of the least-square m=0.744m=-0.744 m=127.917m=127.917 m=0.881m=-0.881

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Problem 3372

Find the coordinates of the maximum point. y=4lnx+4xy=\frac{4 \ln x+4}{\sqrt{x}}
The maximum point is \square (Type an ordered pair. Type your answer using exponential notation.)

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Problem 3373

Find the derivative of the function f(x)=(5x5)2(4x2+1)3 f(x) = (5x - 5)^2(4x^2 + 1)^3 .

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Problem 3374

Use a compound angle formula to determine the exact value of tanπ12\tan \frac{\pi}{12}

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Problem 3375

A linear function is given. Complete parts (a)-(d). h(x)=4x+2h(x)=4 x+2 (a) Determine the slope and yy-intercept of the function.
The slope is \square (Type an integer or a simplified fraction.)

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Problem 3376

Let g(x)=3+1.8xg(x)=3+1.8 x and f(x)=3(1.8)xf(x)=3(1.8)^{x}. Explore the rates of change (constant? average?) for the linear function gg and the exponential function ff. a. Determine the value of the ratios Δg(x)Δx\frac{\Delta g(x)}{\Delta x} and Δf(x)Δx\frac{\Delta f(x)}{\Delta x} over the following intervals of xx : a. From x=0x=0 to x=1.5x=1.5. Δg(x)Δx=Δf(x)Δx=\begin{array}{l} \frac{\Delta g(x)}{\Delta x}=\square \\ \frac{\Delta f(x)}{\Delta x}=\square \end{array} b. From x=1.5x=1.5 to x=3x=3. Δg(x)Δx=Δf(x)Δx=\begin{array}{l} \frac{\Delta g(x)}{\Delta x}=\square \\ \frac{\Delta f(x)}{\Delta x}=\square \end{array} c. From x=3x=3 to x=5x=5. Δg(x)Δx=Δf(x)Δx=\begin{array}{l} \frac{\Delta g(x)}{\Delta x}=\square \\ \frac{\Delta f(x)}{\Delta x}=\square \end{array} b. Do the functions gg and ff have constant rates of change? Yes for gg and not for ff because, for any change in xx, the ratio Δg(x)Δx\frac{\Delta g(x)}{\Delta x} is constant and the ratio Δf(x)Δx\frac{\Delta f(x)}{\Delta x} is not constant. No, because, for any change in xx, the ratios Δg(x)Δx\frac{\Delta g(x)}{\Delta x} and Δf(x)Δx\frac{\Delta f(x)}{\Delta x} are not constant. Yes, because, for any change in xx, the ratios Δg(x)Δx\frac{\Delta g(x)}{\Delta x} and Δf(x)Δx\frac{\Delta f(x)}{\Delta x} are constant Yes for ff and no for gg because, for any change in xx, the ratio Δf(x)Δx\frac{\Delta f(x)}{\Delta x} is constant and the

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Problem 3377

A linear function is given. Complete parts (a)-(d). h(x)=4x+2h(x)=4 x+2 (a) Determine the slope and yy-intercept of the function.
The slope is 4 . (Type an integer or a simplified fraction.) The yy-intercept is (Type an integer or a simplified fraction.)

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Problem 3378

A linear function is given. Complete parts (a)-(d). h(x)=4x+2h(x)=4 x+2 (a) Determine the slope and yy-intercept of the function.
The slope is 4 . (Type an integer or a simplified fraction.) The yy-intercept is 2 . (Type an integer or a simplified fraction.) (b) Use the slope and yy-intercept to graph the linear function.
Use the graphing tool to graph the function. Use the slope and y-intercept when drawing the line. \square (c) Determine the average rate of change of the function.
The average rate of change is \square

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Problem 3379

A linear function is given. Complete parts (a)-(d). h(x)=12x6h(x)=\frac{1}{2} x-6 (a) Determine the slope and yy-intercept of the function.
The slope is \square (Type an integer or a simplified fraction.)

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Problem 3380

A linear function is given. Complete parts (a)-(d). h(x)=12x6h(x)=\frac{1}{2} x-6 (a) Determine the slope and yy-intercept of the function.
The slope is 12\frac{1}{2}. (Type an integer or a simplified fraction.) The yy-intercept is \square . (Type an integer or a simplified fraction.)

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Problem 3381

A linear function is given. Complete parts (a)-(d). h(x)=12x6h(x)=\frac{1}{2} x-6
The slope is 12\frac{1}{2}. (Type an integer or a simplified fraction.) The yy-intercept is -6 . (Type an integer or a simplified fraction.) (b) Use the slope and yy-intercept to graph the linear function.
Use the graphing tool to graph the function. Use the slope and yy-intercept when drawing the line. \square (c) Determine the average rate of change of the function.
The average rate of change is 12\frac{1}{2}. (Type an integer or a fraction.) (d) Determine whether the linear function is increasing, decreasing, or constant. Choose the correct answer below. A. decreasing B. constant C. increasing

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Problem 3382

Determine whether the given function is linear or nonlinear. If it is linear, determine the slope. \begin{tabular}{|rr|} \hline x\mathbf{x} & y=f(x)\mathbf{y = f}(\mathbf{x}) \\ \hline 0 & -4 \\ 1 & 2 \\ 2 & 4 \\ 3 & 5 \\ 4 & 3 \\ \hline \end{tabular}
Is the function a linear function? Yes No

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Problem 3383

I) Soit la fonction g définie par g(x)=1x3x2+x2g(x)=\frac{1-x^{3}}{x^{2}+x-2} et soit (Cg)\left(\mathrm{C}_{\mathrm{g}}\right) sa courbe dans un repère du 1) Déterminer le domaine DgD_{g} de la fonction gg. 2) a) Calculer : limx+g(x)\lim _{x \rightarrow+\infty} g(x) et limx+g(x)x\lim _{x \rightarrow+\infty} \frac{g(x)}{x}. b) Calculer : limx(2)g(x)\lim _{x \rightarrow(-2)^{-}} g(x) et limx(2)+g(x)\lim _{x \rightarrow(-2)^{+}} g(x). Interpréter graphiquement les résultats obtenus. 3) a) Montre que g est prolongeable par continuité en 1 . Définir son prolongement h par continuité en 1 .

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Problem 3384

Differentiate. y=ln[e6x(x5+4)(x8+3x)]ddx[ln[e6x(x5+4)(x8+3x)]]=\begin{array}{c} y=\ln \left[e^{6 x}\left(x^{5}+4\right)\left(x^{8}+3 x\right)\right] \\ \frac{d}{d x}\left[\ln \left[e^{6 x}\left(x^{5}+4\right)\left(x^{8}+3 x\right)\right]\right]= \end{array}

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Problem 3385

Suppose that f(x)=6x1f(x)=6 x-1 and g(x)=3x+8g(x)=-3 x+8 (a) Solve f(x)=0f(x)=0. (b) Solve f(x)>0f(x)>0. (c) Solve f(x)=g(x)f(x)=g(x). (d) Solve f(x)g(x)f(x) \leq g(x). (e) Graph y=f(x)y=f(x) and y=g(x)y=g(x) and find the point that represents the solution to the equation f(x)=g(x)f(x)=g(x). (a) For what value of xx does f(x)=0f(x)=0 ? x=x=\square (Type an integer or a simplified fraction.)

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Problem 3386

Suppose that f(x)=6x1f(x)=6 x-1 and g(x)=3x+8g(x)=-3 x+8 (a) Solve f(x)=0f(x)=0. (b) Solve f(x)>0f(x)>0. (c) Solve f(x)=g(x)f(x)=g(x). (d) Solve f(x)g(x)f(x) \leq g(x). (e) Graph y=f(x)y=f(x) and y=g(x)y=g(x) and find the point that represents the solution to the equation f(x)=g(x)f(x)=g(x). (a) For what value of xx does f(x)=0f(x)=0 ? x=16x=\frac{1}{6} (Type an integer or a simplified fraction.) (b) For which values of x is f(x)>0\mathrm{f}(\mathrm{x})>0 ? (16,)\left(\frac{1}{6}, \infty\right) (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) (c) For what value of xx does f(x)=g(x)f(x)=g(x) ? x=1x=1 (Type an integer or a simplified fraction.) (d) For which values of xx is f(x)g(x)f(x) \leq g(x) ? \square (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

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Problem 3387

7. f(x)=2x2f(x)=-2 x^{2} yy-inter =0=0

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Problem 3388

Shape of a parabola. The support pillars are 400 feet apart and 150\mathbf{1 5 0} feet high above the bridge deck. a. If the cable, at its lowest, is 30 feet above the bridge at its midpoint determine the quadratic function in vertex form that represents the shape of the ca p=200p=200
Assume the origin is on the bridge deck directly below the vertex. =30=30 -0 y=31000y=\frac{3}{1000} 150=a(0200)2+30150=a(0-200)^{2}+30 x=150x=150 150=40000+30150=40000+30 12C2=10000=0.4.312 C^{2}=\frac{10000}{}=0.4 .3 b. How high is the cable 50 feet away (horizontally) from either tower?

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Problem 3389

Graw Hill K-12 S. Clever I Portal Classes XtraMath Home Justin and Hailey Bi. 28 Middle School M... All Bookmarks 6.4.1 \#6
A quadratic function has the complex roots (1+3i)(1+3 i) and (13i)(1-3 i). What is the quadratic function in standard form?
Edit View Insert Format Tools Table
12pt \vee Paragraph \vee \quad \vdots

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Problem 3390

Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about three-fourths the amount found in living human beings. The amount of carbon-14 present in animal bones after tt years is given by y=y0e0.0001216ty=y_{0} e^{-0.0001216 t}, where y0y_{0} is the amount of carbon-14 present in living human beings. About how long ago did the Egyptian die?
About \square yr ago the Egyptian had died. (Round to the nearest integer as needed.)

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Problem 3391

Question 8
Use the identity AAf(x)dx=A0f(x)dx+0Af(x)dx\int_{-A}^{A} f(x) d x=\int_{-A}^{0} f(x) d x+\int_{0}^{A} f(x) d x to compute the integral. ππ9sin(t)25+t2dt=\int_{-\pi}^{\pi} \frac{9 \sin (t)}{25+t^{2}} d t= \square Hint: sin(t)=sin(t)\sin (-t)=-\sin (t). Submit Question

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Problem 3392

Find the shaded region in the graph.
The area of the shaded region is \square . (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Type an exact answer in terms of π\pi.)

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Problem 3393

Decide whether the following statement is true or false. If the discriminant b24ac=0b^{2}-4 a c=0, the graph of f(x)=ax2+bx+c,a0f(x)=a x^{2}+b x+c, a \neq 0, will touch the xx-axis at its vertex.
Choose the correct answer below. True False

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Problem 3394

\begin{tabular}{|l|c|c|} \hline Time Line & Price(dollars) & Average rate of change \\ \hline 1970 & $0.20\$ 0.20 & XXXXXXXXXXXXXX X X X X X X X X X X X X \\ \hline 1980 & $0.50\$ 0.50 & 0.03 \\ \hline 2003 & $2.00\$ 2.00 & 0.0652 \\ \hline 2009 & $2.25\$ 2.25 & 0.0417 \\ \hline 2013 & $2.50\$ 2.50 & 0.0625 \\ \hline 2015 & $2.75\$ 2.75 & 0.125 \\ \hline \end{tabular}
Do these values suggest a linear trend? Explain. The average rates of change do not suggest a linear because their is no direct relation independent variable (time in years) and the dependent variable (cost in dollars).
Step 5: Linear Modeling (6 pts)
Assuming that the trend is linear, generate a linear model. To make the calculation easier, rescale the time values for 2009 through 2015 in the above table.
Let 2009 be the year 0 . \begin{tabular}{|c|c|} \hline t & P ( dollars) \\ \hline 0 & \\ \hline & \\ \hline & \\ \hline \end{tabular}

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Problem 3395

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

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Problem 3396

Out-of-pocket spending in a country for health care increased between 2004 and 2009. The function f(x)=2581e0.0359x\mathrm{f}(\mathrm{x})=2581 e^{0.0359 x} models average annual expenditures per household, in dollars. In this model, xx represents the year, where x=0x=0 corresponds to 2004. (a) Estimate out-of-pocket household spending on health care in 2009. (b) Determine the year when spending reached $2793\$ 2793 per household. (a) The total expenditures per household in the year 2009 were approximately $\$ \square (Round to the nearest dollar as needed.)

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Problem 3397

A sample of 9 grams of radioactive material is placed in a vault. Let P(t)P(t) be the amount remaining after tt years, and let P(t)P(t) satisfy the differential equation P(t)=0.032P(t)P^{\prime}(t)=-0.032 P(t). Answer parts (a)(a) through (g)(g). (a) Find the formula for P(t)\mathrm{P}(\mathrm{t}). P(t)=9e0.032tP(t)=9 e^{-0.032 t} (Type an expression using tt as the variable.) (b) What is P(0)P(0) ? P(0)=P(0)= \square

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Problem 3398

Part 2 of 5 Points: 0 of 1
The monthly revenue RR achieved by selling xx wristwatches is figured to be R(x)=75x0.2x2R(x)=75 x-0.2 x^{2}. The monthly cost CC of selling xx wristwatches is C(x)=30x+1700C(x)=30 x+1700. (a) How many wristwatches must the firm sell to maximize revenue? What is the maximum revenue? (b) Profit is given as P(x)=R(x)C(x)\mathrm{P}(\mathrm{x})=\mathrm{R}(\mathrm{x})-\mathrm{C}(\mathrm{x}). What is the profit function? (c) How many wristwatches must the firm sell to maximize profit? What is the maximum profit? (d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue. (a) The firm must sell 188 wristwatches to maximize revenue. (Round to the nearest integer as needed.) The maximum revenue is $7,031.20\$ 7,031.20^{\circ}. (Round to two decimal places as needed.) (b) The profit function is P(x)=\mathrm{P}(\mathrm{x})= \square (Type an expression usinglx as the variable.)

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Problem 3399

The monthly revenue RR achieved by selling xx wristwatches is figured to be R(x)=75x0.2x2R(x)=75 x-0.2 x^{2}. The monthly cost CC of selling xx wristwatches is C(x)=30x+1700C(x)=30 x+1700. (a) How many wristwatches must the firm sell to maximize revenue? What is the maximum revenue? (b) Profit is given as P(x)=R(x)C(x)\mathrm{P}(\mathrm{x})=\mathrm{R}(\mathrm{x})-\mathrm{C}(\mathrm{x}). What is the profit function? (c) How many wristwatches must the firm sell to maximize profit? What is the maximum profit? (d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue. (a) The firm must sell 188 wristwatches to maximize revenue. (Round to the nearest integer as needed.) The maximum revenue is $7,031.20\$ 7,031.20^{\top}. (Round to two decimal places as needed.) (b) The profit function is P(x)=45x0.2x21700P(x)=45 x-0.2 x^{2}-1700. (Type an expression using xx as the variable.) (c) The firm must sell \square wristwatches to maximize profit. (Round to the nearest integer as needed.) The maximum profit is $\$ \square. (Round to two decimal places as needed.)

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Problem 3400

The monthly revenue RR achieved by selling xx wristwatches is figured to be R(x)=75x0.2x2R(x)=75 x-0.2 x^{2}. The monthly cost CC of selling xx wristwatches is C(x)=30x+1700C(x)=30 x+1700. (a) How many wristwatches must the firm sell to maximize revenue? What is the maximum revenue? (b) Profit is given as P(x)=R(x)C(x)P(x)=R(x)-C(x). What is the profit function? (c) How many wristwatches must the firm sell to maximize profit? What is the maximum profit? (d) Provide a reasonable explanation as to why the answers found in parts (a) and (c) differ. Explain why a quadratic function is a reasonable model for revenue. (a) The firm must sell 188 wristwatches to maximize revenue. (Round to the nearest integer as needed.) The maximum revenue is $7,031.20\$ 7,031.20^{\circ}. (Round to two decimal places as needed.) (b) The profit function is P(x)=45x0.2x21700\mathrm{P}(\mathrm{x})=45 \mathrm{x}-0.2 \mathrm{x}^{2}-1700. (Type an expression using xx as the variable.) (c) The firm must sell 113 wristwatches to maximize profit. (Round to the nearest integer as needed.) The maximum profit is $831.20\$ 831.20. (Round to two decimal places as needed.) (d) Why do the answer found in part (a) and part (c) differ? Choose the correct answer below. A. The parts differ because part (a) uses the revenue function which is equal to the sum of the profit function and the cost function. B. The parts differ because part (c) uses the profit function which is equal to the product of the revenue function and the cost function. C. The parts differ because part (c) uses the revenue function which is equal to the sum of the profit function and the cost function. D. The parts differ because part (a) uses the profit function which is equal to the difference of the revenue function and the cost function.

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