Browse Function problems Studdy Solved!

Problem 5401

An athlete releases a shot at $70^{\circ}$ with height $f(x)=-0.05 x^{2}+2.7 x+6.2$ . Find max height and distance.

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Problem 5402

An athlete releases a shot at $40^{\circ}$ , modeled by $f(x)=-0.01 x^{2}+0.8 x+5.3$ . Find the max height and distance.

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Problem 5403

An athlete releases a shot at $70^{\circ}$ with height modeled by $f(x)=-0.05 x^{2}+2.7 x+6.2$ . Find max height and distance.

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Problem 5404

An athlete releases a shot at $30^{\circ}$ with height modeled by $f(x)=-0.01 x^{2}+0.6 x+6.4$ . Find max height and distance.

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Problem 5405

An athlete releases a shot at $35^{\circ}$ with height modeled by $f(x)=-0.01 x^{2}+0.7 x+5.4$ . Find max height and distance.

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Problem 5406

An athlete releases a shot at $35^{\circ}$ , modeled by $f(x)=-0.01 x^{2}+0.7 x+5.4$ . Find its max height and distance from release.

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Problem 5407

Find the equivalent expression for the profit $0.5(200 + 32s)$ and calculate profit for $s = 30$ .

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Problem 5408

An athlete releases a shot at $65^{\circ}$ with height $f(x)=-0.03 x^{2}+2.1 x+6.3$ . Find the max height and distance.

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Problem 5409

An athlete releases a shot at $35^{\circ}$ with height modeled by $f(x)=-0.01 x^{2}+0.7 x+5.8$ . Find max height and distance.

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Problem 5410

An athlete releases a shot at $35^{\circ}$ . Its height is modeled by $f(x)=-0.01 x^{2}+0.7 x+5.8$ . Find max height and distance from release.

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Problem 5411

An athlete releases a shot at $40^{\circ}$ with height modeled by $f(x)=-0.01 x^{2}+0.8 x+5.3$ . Find the max height and distance.

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Problem 5412

An athlete releases a shot modeled by $f(x)=-0.01 x^{2}+0.8 x+5.3$ . Find the max height and distance from release point.

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Problem 5413

An athlete releases a shot at $35^{\circ}$ . The height is modeled by $f(x)=-0.01 x^{2}+0.7 x+5.7$ . Find the max height and distance.

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Problem 5414

An athlete releases a shot at $35^{\circ}$ with height modeled by $f(x)=-0.01 x^{2}+0.7 x+5.7$ . Find max height and distance.

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Problem 5415

An athlete releases a shot at $60^{\circ}$ with height modeled by $f(x)=-0.02 x^{2}+1.7 x+5.7$ . Find max height and distance.

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Problem 5416

An athlete releases a shot at $60^{\circ}$ , modeled by $f(x)=-0.02 x^{2}+1.7 x+6.1$ . Find the max height and distance from release.

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Problem 5417

An athlete releases a shot modeled by $f(x)=-0.02 x^{2}+1.7 x+5.7$ . Find the max height and distance from release.

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Problem 5418

An athlete releases a shot at $40^{\circ}$ with height modeled by $f(x)=-0.01 x^{2}+0.8 x+6.2$ . Find max height and distance.

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Problem 5419

An athlete releases a shot at $70^{\circ}$ , modeled by $f(x)=-0.05 x^{2}+2.7 x+5.7$ . Find its max height and distance from release.

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Problem 5420

A ball is thrown from 6 feet high. Its height is given by $f(x)=-0.4 x^{2}+2.1 x+6$ . Find its max height and distance.

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Problem 5421

A ball is thrown from 8 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+1.4 x+8$ . Find the max height and distance.

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Problem 5422

A ball is thrown from 6 feet high, modeled by $f(x)=-0.1 x^{2}+0.6 x+6$ . Find its max height and distance from release.

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Problem 5423

A local sandwich shop has a weekly cost of \ $565 and a variable cost of \$0.65 per roast beef sandwich. Find the cost function$ C(x) = \square$.

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Problem 5424

Find the weekly profit function $P(x)$ from cost $C(x)=565.00+0.65x$ and revenue $R(x)=-0.001x^2+3x$ .

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Problem 5425

a. Define the weekly cost function $C(x)=575.00+0.65 x$ for roast beef sandwiches sold. b. Use $R(x)=-0.001 x^{2}+3 x$ to find the profit function $P(x)=R(x)-C(x)$ . Simplify your answer.

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Problem 5426

a. Write the cost function $C(x)=565.00+0.65 x$ for $x$ roast beef sandwiches. b. Profit function is $P(x)=-0.001 x^{2}+2.35 x-565.00$ . c. Find $x$ for max profit and state max profit $\$ \square$ when $\square$ sandwiches sold.

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Problem 5427

A sandwich store has a weekly cost of \ $575.00 and \$0.65 per roast beef sandwich. Find profit function$ P(x)$ and max profit.

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Problem 5428

A ball is thrown from 6 feet high. Its height is modeled by $f(x)=-0.3 x^{2}+2.1 x+6$ . Find the max height and distance.

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Problem 5429

For the function $P(x)=-0.74 x^{2}+22 x+75$ , what constraints ensure profits are at least \ $175,000? Options:$ -3.09 \leq x \leq 5.6 $or$ 0 \leq x < 5.6$?

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Problem 5430

Find the maximum height of the ball described by $f(x)=-0.3 x^{2}+2.1 x+6$ and its distance from the throw point.

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Problem 5431

A ball is thrown from 5 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+2.1 x+5$ . Find the max height and distance.

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Problem 5432

A ball is thrown from 8 feet high. Its height is given by $f(x)=-0.2 x^{2}+1.7 x+8$ . Find the max height and distance for parts (a) to (c).

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Problem 5433

A ball is thrown from 6 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+0.6 x+6$ . Find max height and distance.

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Problem 5434

Translate (a) as $x + 19$ and (b) as $19 > x$ .

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Problem 5435

A ball is thrown from 7 feet high, modeled by $f(x)=-0.4 x^{2}+2.7 x+7$ . Find its max height and distance from release.

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Problem 5436

Which point is on the graph of the piecewise function $f(x)$ defined as: $f(x)=-9$ for $x<-6$ , $f(x)=1$ for $x=-6$ , and $f(x)=7x-1$ for $x>-6$ ? Options: $(-6,-9)$ , $(-6,-43)$ , $(1,-6)$ , $(0,-9)$ , $(-5,-36)$ , or None.

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Problem 5437

A ball is thrown from 7 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+0.8 x+7$ . Find the max height and distance.

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Problem 5438

A ball is thrown from 8 feet high. Its height is given by $f(x)=-0.1 x^{2}+0.7 x+8$ . Find its max height and distance from release.

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Problem 5439

A ball is thrown from 6 feet high. Its height is given by $f(x)=-0.1 x^{2}+0.8 x+6$ . Find the max height and distance from release.

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Problem 5440

A ball is thrown from 5 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+1.7 x+5$ . Find max height and distance.

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Problem 5441

An air track glider is attached to a spring. It is pulled back to position A and released from rest. It vibrates back and forth between positions A and E . Position C is the equilibrium position. At what position(s) does it experience a net force of 0 N ?
Tap to select or deselect an answer. Position A only Position C Position E only Position A and E Positions B and D

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Problem 5442

2.2 Gedankenexperiment : l'inégalité s'aggrave avant de s'améliorer (1 point)
Dans un pays riche A , le produit intérieur brut ${ }^{1}$ par habitant est $r=53000$ (dollars US). Dans un pays pauvre B, le $\mathrm{PIB}^{2}$ par habitant est $p=6500$ . Supposons que le PIB du pays A croît de $3 \%$ par année, et qu'un miracle économique dans pays B commence à propulser une croissance de $6 \%$ par année. Pays B va ainsi rattraper pays A. Assumons que ces taux de croissance sont constants ${ }^{3}$ . - Pendant combien d'années croît la différence ${ }^{4}$ de PIB entre pays riche A et pays pauvre B ? - Il doit s'écouler combien d'années que le PIB de pays B dépasse celui de pays A ? (Justifiez vos réponses.)
1. Par les données du Fonds Monétaire International, c'est $\$ 55920$ en moyenne auprès les économies avancées en 2023. [Perspectives de l'économie mondiale : https://www.imf. org/external/datamapper/datasets/WEO]
2. Selon les données du FMI en 2023, c'est US\ $6450 en moyenne parmi les marchés émergents et les économies en développement.<br />3. En vérité, le taux de croissance varie selon les années.<br />4. différence :$ \operatorname{PIB}(A)-\operatorname{PIB}(B)$

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Problem 5443

19. The graph of a cosine function is shown. a) What is the maximum value? the minimum value? b) What is the amplitude? c) What is the vertical translation? d) What is the period? e) What value of $k$ in the formula Period $=\frac{2 \pi}{k}$ will result in the required period? f) Explain why the phase shift can have more than one value. Suggest at least three possible values for the phase shift.

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Problem 5444

\#3 A weight atrached to the end of a long spring hanging above the ground is bouncing up and down As it bounces, its distance from the floor varies sinuscidally with time (assume no friction is present in the spring) A stopwatch is used to measure is height above the foor as a function of time. When the stopvatch reads 0.3 s , the weight first reaches a ligh point $C 0 \mathrm{~cm}$ above the foor. The next low point, at 40 cm above the floor, occurs at 1.8 s . a. Oraw a shetch to dlustrate $d$ , the spring's distance from the foor in centimetres, over the interval $0 \leq 1 \leq 6$ , where $t$ is in secands. Chech Desmos $\begin{array}{l} d(t)=10 \cos \left(\frac{2 \pi}{3}(t-0.3)\right)+50 \end{array}$ c. What is the distance the fioor for the first time?

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Problem 5445

$f(x)=x^{3}-3 x^{2}$ 的根大值点为（） P. 0. B. 2 C. -2 , D. 不有夻 $f(x)=x^{3}-3 x^{2}$ 的最大货点为

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Problem 5446

3LEM 9: THE HAWK PROBLEM A hawk is on top of a tree and spots a fish in the water. The hawks's pathway in metres is measured by time in seconds by the equation: $y=x^{2}-6 x+11$ a) When does the hawk enter the water? b) Explain why this is a problem? c) Sketch a graph

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Problem 5447

Consider the function $f(x)=16 x+81 x^{-1}$ . Give a list of the critical numbers of $f$ and any values for which $f$ is undefined. $x=$ $\square$ Determine the intervals on which $f$ is increasing and decreasing. $f$ is increasing on $\square$ $f$ is decreasing on $\square$ Determine the intervals on which $f$ is concave up and concave down. $f$ is concave up on $\square$ $f$ is concave down on $\square$ Determine the coordinates $(x, y)$ of any inflection points of $f$ . $(x, y)=$ $\square$ No inflection points.

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Problem 5448

2.2 Gedankenexperiment : l'inégalité s'aggrave avant de s'améliorer (1 point)
Dans un pays riche A, le produit intérieur brut ${ }^{5}$ par habitant est $r=58350$ (dollars US). Dans un pays pauvre B, le PIB ${ }^{6}$ par habitant est $p=6650$ . Supposons que le PIB du pays A croît de $a=1.3 \%$ par année, et qu'un miracle économique dans pays B commence à propulser une croissance de $b=4 \%$ par année. Pays B va ainsi rattraper pays A. Assumons que ces taux de croissance sont constants ${ }^{7}$ . - Pendant combien d'années croît la différence ${ }^{8}$ de PIB entre pays riche A et pays pauvre B? - Il doit s'écouler combien d'années que le PIB de pays B dépasse celui de pays A ? (Justifiez vos réponses.)
5. Par les données du Fonds Monétaire International, c'est $\$ 59000$ en moyenne auprès les économies avancées en 2024. [Perspectives de l'économie mondiale : https://www.imf. org/external/datamapper/datasets/WEO]
6. Selon les données du FMI en 2024, c'est US $\$ 650$ en moyenne parmi les marchés émergents et les économies en développement.
7. En vérité, le taux de croissance varie selon les années.
8. diffêrence : $\operatorname{PIB}(A)-\operatorname{PIB}(B)$

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Problem 5449

The graph of a quadratic function with vertex $(1,-4)$ is shown in the figure below. Find the domain and the range.
Write your answers as inequalities, using $x$ or $y$ as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) domain: $\square$ (b) range: $\square$

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Problem 5450

The graph of a quadratic function with vertex $(2,3)$ is shown in the figure below. Find the domain and the range.
Write your answers as inequalities, using $x$ or $y$ as appropriate. Or, you may instead click on "Empty set" or "All reals" as the answer. (a) domain: $\square$ (b) range: $\square$

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Problem 5451

Determine the amplitude of the periodic graph. * 1 po
Determine the period of the periodic graph. * 1 point

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Problem 5452

Video
Find the equation for the least squares regression line of the data described below.
Stem and Leaf Agriculture wants to add a new compound to its bags of sunflower fertilizer. The company produced several bags containing varying amounts of the compound to see how it would affect sunflower growth.
Next, Stem and Leaf collected data on the amount of the compound added to each bag (in grams), $x$ , and the weekly growth of the sunflowers treated with each bag (in centimeters), $y$ . \begin{tabular}{|c|c|} \hline 4) Amount of compound & D) \\ \hline 11 & 13 \\ \hline 22 & 11 \\ \hline 37 & 34 \\ \hline 77 & 28 \\ \hline 80 & 34 \\ \hline \end{tabular}
Round your answers to the nearest thousandth. $y=$ $\square$ $x+$

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Problem 5453

\begin{tabular}{|c|c|} \hline \begin{tabular}{c} Theater revenue, \\ $\boldsymbol{x}$ \\ (in millions of \\ dollars) \end{tabular} & \begin{tabular}{c} Rental revenue, $\boldsymbol{y}$ \\ (in millions of \\ dollars) \end{tabular} \\ \hline 14.5 & 2.3 \\ \hline 36.3 & 11.7 \\ \hline 60.2 & 16.6 \\ \hline 44.3 & 5.7 \\ \hline 67.0 & 10.2 \\ \hline 27.8 & 12.8 \\ \hline 25.5 & 8.3 \\ \hline 12.7 & 10.4 \\ \hline 25.5 & 7.3 \\ \hline 7.3 & 2.4 \\ \hline 49.1 & 15.7 \\ \hline 20.8 & 5.3 \\ \hline 61.9 & 9.8 \\ \hline 30.6 & 5.5 \\ \hline 28.2 & 3.1 \\ \hline \end{tabular} Send data to calculator Send data to Excel
The least-squares regression line for these data has a slope of approximately 0.15 . Answer the following. Carry your intermediate computations to at least four decimal places, and round your answers as specified below. \begin{tabular}{|l|} \hline What is the value of the $y$ -intercept of the least-squares \\ regression line for these data? Round your answer to at least \\ two decimal places. \\ \hline \end{tabular}

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Problem 5454

\begin{tabular}{|c|c|} \hline \begin{tabular}{c} Campaign cost, \\ \begin{tabular}{c} $\boldsymbol{x}$ \\ (in millions of \\ dollars) \end{tabular} \end{tabular} \begin{tabular}{c} Increase in sales, \\ $\boldsymbol{y}$ \\ (percent) \end{tabular} \\ \hline 3.93 & 6.94 \\ \hline 2.08 & 6.78 \\ \hline 3.08 & 6.94 \\ \hline 2.97 & 6.50 \\ \hline 3.36 & 6.55 \\ \hline 1.54 & 6.56 \\ \hline 3.56 & 6.91 \\ \hline 1.35 & 6.41 \\ \hline 1.75 & 6.34 \\ \hline 2.24 & 6.59 \\ \hline 3.80 & 6.78 \\ \hline 2.14 & 6.46 \\ \hline \end{tabular} Send data to calculator Send data to Excel
Figure 1
The value of the sample correlation coefficient $r$ for these data is approximately 0.703 . Answer the following. Carry your intermediate computations to at least four decimal places, and ro \begin{tabular}{|l|l|} \hline \begin{tabular}{l} What is the value of the slope of the least-squares regression \\ line for these data? Round your answer to at least two decimal \\ places. \end{tabular} \\ \hline \begin{tabular}{l} What is the value of the $y$ -intercept of the least-squares \\ regression line for these data? Round your answer to at least \\ two decimal places. \end{tabular} & $\square$ \\ \hline \end{tabular}

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Problem 5455

If $f(x)=6+\frac{3}{x}+\frac{4}{x^{2}}$ , find $f^{\prime}(x)$ .
Find $f^{\prime}(1)$ .

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Problem 5456

Suppose a product's revenue function is given by $R(q)=-3 q^{2}+200 q$ . Find an expression for the marginal revenue function, simplify it, and record your result in the box below. Be sure to use the proper variable in your answer. (Use the preview button to check your syntax before submitting your answer.) $M R(q)=$

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Problem 5457

Question Find $f_{x}, f_{y}, f_{z z}, f_{y y}, f_{y z}$ , and $f_{x y}$ . $f(x, y)=2 x e^{y}+y e^{x}-3 x+y^{2}$

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Problem 5458

During the first couple weeks of a new flu outbreak, the disease spreads according to the equation $I(t)=3900 e^{0.081 t}$ , where $I(t)$ is the number of infected people $t$ days after the outbreak was first identified.
Find the rate at which the infected population is growing after 12 days and select the appropriate units.

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Problem 5459

Tara and Edward each painted their bedrooms. They finished in the same amount of time, even though Edward's bedroom is bigger. They have 4 hours to start painting the basement before dinner is ready. Who will likely paint a larger part of the basement?
Tara Edward

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Problem 5460

Given the piecewise function:
\[ f(x) = \begin{cases} 1, & 0 < x < \frac{3}{2}, \\ -1, & \frac{3}{2} < x < 3 \end{cases}$
with period $l = 3$ .
Find the Fourier series expansion of the function $f(x)$ .
The Fourier series expansion is given by:
$f(x) = \frac{4}{\pi} \sum_{n=0}^{\infty}(-1)^{n} \frac{\cos ((2n+1) \pi x / 3)}{2n+1}.$

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Problem 5461

Which of these statements is true for all exponential functions? a) The sign of the slope of the tangent is always the same for all values of $x$ on the function b) The slope is always positive c) The function changes from increasing to decreasing at the turning point d) The slope is always negative

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Problem 5462

\begin{align} &\text{Given the quadratic function:} \\ &y = -2x^2 - 4x + 3 \\ &\text{Calculate the first and second differences, } \Delta y \text{ and } \Delta^2 y, \text{ for the following values of } x: \\ &x = -3, -2, -1, 0, 1, 2, 3 \end{align}

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Problem 5463

Selected values of the function $f$ are shown in the table below. The function $f$ is continuous on the closed interval $[-3,2]$ and differentiable on the open interval $(-3,2)$ . Determine the validity of the following statement:
There exists a value $c$ in the open interval $(-3,2)$ such that $f^{\prime}(c)=6$ . \begin{tabular}{|c|c|} \hline $x$ & $f(x)$ \\ \hline-3 & -9 \\ \hline-1 & 1 \\ \hline 2 & 4 \\ \hline \end{tabular}
Answer the statement must be true Submit Answer the statement must be false the statement could be either true or false

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Problem 5464

9. Using electronic graphing tools, graph $y=2 \sin (3[x-4])+5$ and $y=2 \csc (4 x-3)-1$ on the same axes. Find all points of intersection of the two functions between $-\pi$ and $\pi$ , with answers to 2 decimal places. Include an image of the graphs in your response. [ 6 marks]

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Problem 5465

(1) $y=\frac{2 x-3}{3 x+4}$

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Problem 5466

10. A given sinusoidal function has a period of 3 , an amplitude of 7 , and a maximum at $(0$ , 2). Represent the function with a sine equation and a cosine equation. [4 marks]

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Problem 5467

$f(x)=x^{2}-1$ y $g(x)=x+3$ . Obtener $(f g)^{\prime}(x)$

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Problem 5468

Find the equation of the linear function containing the Show your w points $(2,-4)$ and $(-1,-7)$ . Submit your answer in slopeintercept form, or $y=m x+b$ .

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Problem 5469

Find the equation of the linear function such that $f(0)=4$ and $f(7)=-5$ . Submit your answer in slopeintercept form, or $y=m x+b$ .

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Problem 5470

Find the equation of the linear function $f(x)$ such that $f(-2)=-6$ and $f(-1)=6$ . Submit your answer in slopeintercept form.

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Problem 5471

12. How many different sinusoidal functions can be written that have a period of $3 \pi$ , an amplitude of 1 , and a minimum at $(2,3)$ ? [1 mark]

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Problem 5472

For the data given in the table, use a calculator to find the Ans equation of the best fit line, and determine the correlation coefficient. Round to three decimal places if necessary. \begin{tabular}{|l|c|c|c|c|c|} \hline $x$ & -9 & -7 & -5 & 1 & 3 \\ \hline $f(x)$ & 8 & 13 & 14 & 30 & 41 \\ \hline \end{tabular} $f(x)=$

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Problem 5473

$\begin{aligned} \text { mit } a \in \mathbb{R} \backslash\{0\} & \text { (das heißt, der Parameter a beinhaltet alle reellen Zahlen } \\ & \text { außer die Zahl Null) }\end{aligned}$
2. Berechnen Sie in Abhängigkeit von a die Schnittpunkte / Berührpunkte mit den Koordinatenachsen und geben Sie diese Punkte an.
3. Berechnen Sie in Abhängigkeit von a die Lage und Art der Extrema und geben sie diese Informationen an.
4. Berechnen Sie in Abhängigkeit von a die Lage und Art der Wendepunkte und geben sie diese Informationen an. Berechnen Sie ebenfalls die Funktion der Wendetangente( $n$ ) und geben Sie die Funktion(en) an. b) Ermitteln Sie die Ortskurve des Wendepunktes. c) Ermitteln Sie die Ortskurven der Extrema.
Für die folgenden Aufgabenteile gilt $\mathbf{a}=-4$ d) Zeichnen Sie den Graphen von $f_{a(x)}$ für $a=-4$

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Problem 5474

If $(f \circ g)(x)=-4 x \cdot(x+1)$ , then find the functions $f(x$ and $g(x)$ . A) $f(x)=x^{2}-1, g(x)=2 x-1$ B) $f(x)=1-x^{2}, g(x)=2 x+1$ C) $f(x)=1-x, g(x)=2 x^{2}+1$ D) $f(x)=2 x+1, g(x)=x^{2}-1$

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Problem 5475

$\lim _{x \rightarrow-\infty} h(x)=\lim _{x \rightarrow-\infty} 1-x-e^{-x}$

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Problem 5476

6) $f(x)=\frac{1}{x^{4}}-\frac{1}{x^{5}}$

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Problem 5477

Molybdenum-99 is a radioactive material. A 100 gram sample decays according to the table below. \begin{tabular}{|c|c|} \hline \begin{tabular}{c} Mass of Molybdenum-99 \\ (g) \end{tabular} & \begin{tabular}{c} Time \\ (h) \end{tabular} \\ \hline 100 & 0 \\ \hline 90 & 10 \\ \hline 35 & 100 \\ \hline 20 & 152 \\ \hline \end{tabular}
The logarithmic regression equation that best shows the time in hours after the Molybdenum starts to decay as a function of mass can be written in the form $y=a+b \mid n x$ .
The time it takes for the Molybdenum-99 to decay to $50 \%$ of its original mass is:
Select one: a. 99 hours b. 67 hours c. 59 hours d. 501 hours

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Problem 5478

2. Der Luftdruck nimmt, wie rechts zu sehen, mit zunehmender Höhe ab. a) Begründen Sie, dass die Abnahme des Luftdrucks nicht gleichmäßig erfolgt. Wo ist die Abnahme am stärksten, wo ist sie am geringsten? b) Ermitteln Sie die durchschnittliche Abnahme zwischen 2 und 4 km Höhe und zwischen 8 und 10 km Höhe näherungsweise.

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Problem 5479

The radius of a Ferris wheel is 260 ft . The entry platform is 30 ft above the ground. As the Ferris wheel rotates, the height above the ground of each individual rider follows a sinusoidal pattern, as shown below.
If the ground level is the reference point, the amplitude and median of the sinusoidal function are respectively,
Select one: a. 260 and 260 b. 520 and 260 c. 260 and 290 d. 230 and 290

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Problem 5480

$\int\left(\frac{2 x}{x^{2}+1}+\frac{1}{x^{2}+1}-\frac{2}{x-1}+\frac{1}{(x-1)^{2}}\right)$

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Problem 5481

7. $\int \frac{\operatorname{arctg} x}{x^{2}+1} d x$

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Problem 5482

ب) ليكن الاقتران $f(x)=2 x^{2}-6 x+4 \quad$ معطى لديك : فجد نقاط نقاطع الاقتران مع محاور الإحاثيات، ثم جد راس القطع المكافئ.

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Problem 5483

ج) مادة مشعة نضمحل حسب النموذج الأسي $x(t)=x_{0} e^{-k t}, k>0$ فإذا كانت فترة نصف الحيا 1780 سنة، بَعْدَ كم سنة يبتبقى ثُلثُ المادة الأصلية ؟

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Problem 5484

Express the function $h(x)=\frac{1}{x+9}$ in the form $f \circ g$ . If $g(x)=(x+9)$ , find the function $f(x)$ . Your answer is $f(x)=$ $\square$

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Problem 5485

Given that $f(x)=4 x+5$ and $g(x)=5-x^{2}$ , calculate (a) $f(g(0))=$ $\square$ (b) $g(f(0))=$ $\square$ Question Help: Video 1 Video 2

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Problem 5486

Let $f(x)=\sqrt{30-x}$ and $g(x)=x^{2}-x$ . Then the domain of $f \circ g$ is equal to

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Problem 5487

13. A company manufactures and sells a product. The revenue, in dollars, from selling $x$ units is given by the equation: $R(x)=-2 x^{2}+40 x$
Find the number of units that must be sold to achieve a revenue of $\$ 200$ .

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Problem 5488

If X is a discrete random variable. With the following CDF: $F(x)=\left\{\begin{array}{lc} 0, & x<2 \\ 0.2 & 2 \leq x<5 \\ 0.5 & 5 \leq x<7 \\ 0.8 & 7 \leq x<9 \\ 1 & 9 \leq x \end{array}\right.$
Select one: a. 0 b. 1 c. 0.2 a. 0.5 e 0.3

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Problem 5489

$\begin{array}{l} \text { خارجي إذا ق (س) = س+ لـر ي س ، وكان متوسط تغير الاقتران ق (س) في [1، } \end{array}$ $\begin{array}{l} \text { ه一 } \end{array}$

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Problem 5490

Math210 Sheet 2 1) Use integration by parts or American method to evaluate: a) $\int x^{3} \cdot e^{x} d x$

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Problem 5491

1) Use integration by parts or American method to evaluate: b) $\int x^{3} \cdot \ln x d x$

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Problem 5492

$\int x \ln x d x$

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Problem 5493

Exercice 4 : Soit $P \in \mathbb{K}[X]$ non constant. On pose $Q=P(X+1)-P(X)$ . Montrer que $\operatorname{dcg}(Q)=\operatorname{dog}(P)-1$ . Indication : commencer par le cas où $P=X^{n}, n \geq 1$ .

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Problem 5494

Question 18 (1 point) $\checkmark$ Saved
Fit a quadratic curve $y=a x^{2}+b x+c$ that best fits the given data: \begin{tabular}{|l|l|l|l|l|l|} \hline $x$ & 10 & 12 & 15 & 23 & 20 \\ \hline $y$ & 14 & 17 & 23 & 25 & 21 \\ \hline \end{tabular}
For this question, you need to write the Pyithon code and execute it to find the solution $y=6.1 x^{2}+2 x-4.71$ $y=-0.07 x^{2}+3.01 x-8.73$ $y=0.7 x^{2}+4 x+6.73$ $y=-4.71 x^{2}+x+5.5$

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Problem 5495

Evaluate. Assume $u>0$ when $\ln 4$ appears $\int x^{11} e^{x^{12}} d x$

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Problem 5496

For the function $f(x)=2 x^{3}-5 x^{2}+7 x+1$ , find $f^{\prime \prime}(x)$ . Then find $f^{\prime \prime}(0)$ and $f^{\prime \prime}(7)$
To find $f^{\prime \prime}(x)$ , first find $f^{\prime}(x)$ . $f^{\prime}(x)=$

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Problem 5497

Find the limit. Use I'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. $\lim _{t \rightarrow 0} \frac{e^{5 t}-1}{\sin (t)}$ Need Help? Read It Watch It

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Problem 5498

11. What is $\sin ^{-1}\left(\frac{1}{2}\right)$ ? a. $\frac{\pi}{6}$ b. $\frac{\pi}{4}$ C. $\frac{\pi}{3}$ d. $\frac{\pi}{2}$

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Problem 5499

2) $\lim _{x \rightarrow 0} \frac{(x+3)^{2}-9}{x}$

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Problem 5500

For the following exercises, find the horizontal and vertical asymptotes.
271. $f(x)=x-\frac{9}{x}$
272. $f(x)=\frac{1}{1-x^{2}}$
273. $f(x)=\frac{x^{3}}{4-x^{2}}$
274. $f(x)=\frac{x^{2}+3}{x^{2}+1}$
275. $f(x)=\sin (x) \sin (2 x)$
276. $f(x)=\cos x+\cos (3 x)+\cos (5 x)$
277. $f(x)=\frac{x \sin (x)}{x^{2}-1}$
278. $f(x)=\frac{x}{\sin (x)}$
279. $f(x)=\frac{1}{x^{3}+x^{2}}$
280. $f(x)=\frac{1}{x-1}-2 x$

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Function

Problem 5401

An athlete releases a shot at 70∘70^{\circ}70∘ with height f(x)=−0.05x2+2.7x+6.2f(x)=-0.05 x^{2}+2.7 x+6.2f(x)=−0.05x2+2.7x+6.2. Find max height and distance.

Problem 5402

An athlete releases a shot at 40∘40^{\circ}40∘, modeled by f(x)=−0.01x2+0.8x+5.3f(x)=-0.01 x^{2}+0.8 x+5.3f(x)=−0.01x2+0.8x+5.3. Find the max height and distance.

Problem 5403

An athlete releases a shot at 70∘70^{\circ}70∘ with height modeled by f(x)=−0.05x2+2.7x+6.2f(x)=-0.05 x^{2}+2.7 x+6.2f(x)=−0.05x2+2.7x+6.2. Find max height and distance.

Problem 5404

An athlete releases a shot at 30∘30^{\circ}30∘ with height modeled by f(x)=−0.01x2+0.6x+6.4f(x)=-0.01 x^{2}+0.6 x+6.4f(x)=−0.01x2+0.6x+6.4. Find max height and distance.

Problem 5405

An athlete releases a shot at 35∘35^{\circ}35∘ with height modeled by f(x)=−0.01x2+0.7x+5.4f(x)=-0.01 x^{2}+0.7 x+5.4f(x)=−0.01x2+0.7x+5.4. Find max height and distance.

Problem 5406

An athlete releases a shot at 35∘35^{\circ}35∘, modeled by f(x)=−0.01x2+0.7x+5.4f(x)=-0.01 x^{2}+0.7 x+5.4f(x)=−0.01x2+0.7x+5.4. Find its max height and distance from release.

Problem 5407

Find the equivalent expression for the profit 0.5(200+32s)0.5(200 + 32s)0.5(200+32s) and calculate profit for s=30s = 30s=30.

Problem 5408

An athlete releases a shot at 65∘65^{\circ}65∘ with height f(x)=−0.03x2+2.1x+6.3f(x)=-0.03 x^{2}+2.1 x+6.3f(x)=−0.03x2+2.1x+6.3. Find the max height and distance.

Problem 5409

An athlete releases a shot at 35∘35^{\circ}35∘ with height modeled by f(x)=−0.01x2+0.7x+5.8f(x)=-0.01 x^{2}+0.7 x+5.8f(x)=−0.01x2+0.7x+5.8. Find max height and distance.

Problem 5410

An athlete releases a shot at 35∘35^{\circ}35∘. Its height is modeled by f(x)=−0.01x2+0.7x+5.8f(x)=-0.01 x^{2}+0.7 x+5.8f(x)=−0.01x2+0.7x+5.8. Find max height and distance from release.

Problem 5411

An athlete releases a shot at 40∘40^{\circ}40∘ with height modeled by f(x)=−0.01x2+0.8x+5.3f(x)=-0.01 x^{2}+0.8 x+5.3f(x)=−0.01x2+0.8x+5.3. Find the max height and distance.

Problem 5412

An athlete releases a shot modeled by f(x)=−0.01x2+0.8x+5.3f(x)=-0.01 x^{2}+0.8 x+5.3f(x)=−0.01x2+0.8x+5.3. Find the max height and distance from release point.

Problem 5413

An athlete releases a shot at 35∘35^{\circ}35∘. The height is modeled by f(x)=−0.01x2+0.7x+5.7f(x)=-0.01 x^{2}+0.7 x+5.7f(x)=−0.01x2+0.7x+5.7. Find the max height and distance.

Problem 5414

An athlete releases a shot at 35∘35^{\circ}35∘ with height modeled by f(x)=−0.01x2+0.7x+5.7f(x)=-0.01 x^{2}+0.7 x+5.7f(x)=−0.01x2+0.7x+5.7. Find max height and distance.

Problem 5415

An athlete releases a shot at 60∘60^{\circ}60∘ with height modeled by f(x)=−0.02x2+1.7x+5.7f(x)=-0.02 x^{2}+1.7 x+5.7f(x)=−0.02x2+1.7x+5.7. Find max height and distance.

Problem 5416

An athlete releases a shot at 60∘60^{\circ}60∘, modeled by f(x)=−0.02x2+1.7x+6.1f(x)=-0.02 x^{2}+1.7 x+6.1f(x)=−0.02x2+1.7x+6.1. Find the max height and distance from release.

Problem 5417

An athlete releases a shot modeled by f(x)=−0.02x2+1.7x+5.7f(x)=-0.02 x^{2}+1.7 x+5.7f(x)=−0.02x2+1.7x+5.7. Find the max height and distance from release.

Problem 5418

An athlete releases a shot at 40∘40^{\circ}40∘ with height modeled by f(x)=−0.01x2+0.8x+6.2f(x)=-0.01 x^{2}+0.8 x+6.2f(x)=−0.01x2+0.8x+6.2. Find max height and distance.

Problem 5419

An athlete releases a shot at 70∘70^{\circ}70∘, modeled by f(x)=−0.05x2+2.7x+5.7f(x)=-0.05 x^{2}+2.7 x+5.7f(x)=−0.05x2+2.7x+5.7. Find its max height and distance from release.

Problem 5420

A ball is thrown from 6 feet high. Its height is given by f(x)=−0.4x2+2.1x+6f(x)=-0.4 x^{2}+2.1 x+6f(x)=−0.4x2+2.1x+6. Find its max height and distance.

Problem 5421

A ball is thrown from 8 feet high. Its height is modeled by f(x)=−0.2x2+1.4x+8f(x)=-0.2 x^{2}+1.4 x+8f(x)=−0.2x2+1.4x+8. Find the max height and distance.

Problem 5422

A ball is thrown from 6 feet high, modeled by f(x)=−0.1x2+0.6x+6f(x)=-0.1 x^{2}+0.6 x+6f(x)=−0.1x2+0.6x+6. Find its max height and distance from release.

Problem 5423

A local sandwich shop has a weekly cost of \565andavariablecostof$0.65perroastbeefsandwich.Findthecostfunction565 and a variable cost of \$0.65 per roast beef sandwich. Find the cost function 565andavariablecostof$0.65perroastbeefsandwich.FindthecostfunctionC(x) = \square$.

Problem 5424

Find the weekly profit function P(x)P(x)P(x) from cost C(x)=565.00+0.65xC(x)=565.00+0.65xC(x)=565.00+0.65x and revenue R(x)=−0.001x2+3xR(x)=-0.001x^2+3xR(x)=−0.001x2+3x.

Problem 5425

a. Define the weekly cost function C(x)=575.00+0.65xC(x)=575.00+0.65 xC(x)=575.00+0.65x for roast beef sandwiches sold. b. Use R(x)=−0.001x2+3xR(x)=-0.001 x^{2}+3 xR(x)=−0.001x2+3x to find the profit function P(x)=R(x)−C(x)P(x)=R(x)-C(x)P(x)=R(x)−C(x). Simplify your answer.

Problem 5426

Problem 5427

A sandwich store has a weekly cost of \575.00and$0.65perroastbeefsandwich.Findprofitfunction575.00 and \$0.65 per roast beef sandwich. Find profit function 575.00and$0.65perroastbeefsandwich.FindprofitfunctionP(x)$ and max profit.

Problem 5428

A ball is thrown from 6 feet high. Its height is modeled by f(x)=−0.3x2+2.1x+6f(x)=-0.3 x^{2}+2.1 x+6f(x)=−0.3x2+2.1x+6. Find the max height and distance.

Problem 5429

For the function P(x)=−0.74x2+22x+75P(x)=-0.74 x^{2}+22 x+75P(x)=−0.74x2+22x+75, what constraints ensure profits are at least \175,000?Options:175,000? Options: 175,000?Options:-3.09 \leq x \leq 5.6or or or0 \leq x < 5.6$?

Problem 5430

Find the maximum height of the ball described by f(x)=−0.3x2+2.1x+6f(x)=-0.3 x^{2}+2.1 x+6f(x)=−0.3x2+2.1x+6 and its distance from the throw point.

Problem 5431

A ball is thrown from 5 feet high. Its height is modeled by f(x)=−0.2x2+2.1x+5f(x)=-0.2 x^{2}+2.1 x+5f(x)=−0.2x2+2.1x+5. Find the max height and distance.

Problem 5432

A ball is thrown from 8 feet high. Its height is given by f(x)=−0.2x2+1.7x+8f(x)=-0.2 x^{2}+1.7 x+8f(x)=−0.2x2+1.7x+8. Find the max height and distance for parts (a) to (c).

Problem 5433

A ball is thrown from 6 feet high. Its height is modeled by f(x)=−0.1x2+0.6x+6f(x)=-0.1 x^{2}+0.6 x+6f(x)=−0.1x2+0.6x+6. Find max height and distance.

Problem 5434

Translate (a) as x+19x + 19x+19 and (b) as 19>x19 > x19>x.

Problem 5435

A ball is thrown from 7 feet high, modeled by f(x)=−0.4x2+2.7x+7f(x)=-0.4 x^{2}+2.7 x+7f(x)=−0.4x2+2.7x+7. Find its max height and distance from release.

Problem 5436

Problem 5437

A ball is thrown from 7 feet high. Its height is modeled by f(x)=−0.1x2+0.8x+7f(x)=-0.1 x^{2}+0.8 x+7f(x)=−0.1x2+0.8x+7. Find the max height and distance.

Problem 5438

A ball is thrown from 8 feet high. Its height is given by f(x)=−0.1x2+0.7x+8f(x)=-0.1 x^{2}+0.7 x+8f(x)=−0.1x2+0.7x+8. Find its max height and distance from release.

Problem 5439

A ball is thrown from 6 feet high. Its height is given by f(x)=−0.1x2+0.8x+6f(x)=-0.1 x^{2}+0.8 x+6f(x)=−0.1x2+0.8x+6. Find the max height and distance from release.

Problem 5440

A ball is thrown from 5 feet high. Its height is modeled by f(x)=−0.2x2+1.7x+5f(x)=-0.2 x^{2}+1.7 x+5f(x)=−0.2x2+1.7x+5. Find max height and distance.

Problem 5441

An athlete releases a shot at $70^{\circ}$ with height $f(x)=-0.05 x^{2}+2.7 x+6.2$ . Find max height and distance.

An athlete releases a shot at $40^{\circ}$ , modeled by $f(x)=-0.01 x^{2}+0.8 x+5.3$ . Find the max height and distance.

An athlete releases a shot at $70^{\circ}$ with height modeled by $f(x)=-0.05 x^{2}+2.7 x+6.2$ . Find max height and distance.

An athlete releases a shot at $30^{\circ}$ with height modeled by $f(x)=-0.01 x^{2}+0.6 x+6.4$ . Find max height and distance.

An athlete releases a shot at $35^{\circ}$ with height modeled by $f(x)=-0.01 x^{2}+0.7 x+5.4$ . Find max height and distance.

An athlete releases a shot at $35^{\circ}$ , modeled by $f(x)=-0.01 x^{2}+0.7 x+5.4$ . Find its max height and distance from release.

Find the equivalent expression for the profit $0.5(200 + 32s)$ and calculate profit for $s = 30$ .

An athlete releases a shot at $65^{\circ}$ with height $f(x)=-0.03 x^{2}+2.1 x+6.3$ . Find the max height and distance.

An athlete releases a shot at $35^{\circ}$ with height modeled by $f(x)=-0.01 x^{2}+0.7 x+5.8$ . Find max height and distance.

An athlete releases a shot at $35^{\circ}$ . Its height is modeled by $f(x)=-0.01 x^{2}+0.7 x+5.8$ . Find max height and distance from release.

An athlete releases a shot at $40^{\circ}$ with height modeled by $f(x)=-0.01 x^{2}+0.8 x+5.3$ . Find the max height and distance.

An athlete releases a shot modeled by $f(x)=-0.01 x^{2}+0.8 x+5.3$ . Find the max height and distance from release point.

An athlete releases a shot at $35^{\circ}$ . The height is modeled by $f(x)=-0.01 x^{2}+0.7 x+5.7$ . Find the max height and distance.

An athlete releases a shot at $35^{\circ}$ with height modeled by $f(x)=-0.01 x^{2}+0.7 x+5.7$ . Find max height and distance.

An athlete releases a shot at $60^{\circ}$ with height modeled by $f(x)=-0.02 x^{2}+1.7 x+5.7$ . Find max height and distance.

An athlete releases a shot at $60^{\circ}$ , modeled by $f(x)=-0.02 x^{2}+1.7 x+6.1$ . Find the max height and distance from release.

An athlete releases a shot modeled by $f(x)=-0.02 x^{2}+1.7 x+5.7$ . Find the max height and distance from release.

An athlete releases a shot at $40^{\circ}$ with height modeled by $f(x)=-0.01 x^{2}+0.8 x+6.2$ . Find max height and distance.

An athlete releases a shot at $70^{\circ}$ , modeled by $f(x)=-0.05 x^{2}+2.7 x+5.7$ . Find its max height and distance from release.

A ball is thrown from 6 feet high. Its height is given by $f(x)=-0.4 x^{2}+2.1 x+6$ . Find its max height and distance.

A ball is thrown from 8 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+1.4 x+8$ . Find the max height and distance.

A ball is thrown from 6 feet high, modeled by $f(x)=-0.1 x^{2}+0.6 x+6$ . Find its max height and distance from release.

A local sandwich shop has a weekly cost of \ $565 and a variable cost of \$0.65 per roast beef sandwich. Find the cost function$ C(x) = \square$.

Find the weekly profit function $P(x)$ from cost $C(x)=565.00+0.65x$ and revenue $R(x)=-0.001x^2+3x$ .

a. Define the weekly cost function $C(x)=575.00+0.65 x$ for roast beef sandwiches sold. b. Use $R(x)=-0.001 x^{2}+3 x$ to find the profit function $P(x)=R(x)-C(x)$ . Simplify your answer.

A sandwich store has a weekly cost of \ $575.00 and \$0.65 per roast beef sandwich. Find profit function$ P(x)$ and max profit.

A ball is thrown from 6 feet high. Its height is modeled by $f(x)=-0.3 x^{2}+2.1 x+6$ . Find the max height and distance.

For the function $P(x)=-0.74 x^{2}+22 x+75$ , what constraints ensure profits are at least \ $175,000? Options:$ -3.09 \leq x \leq 5.6 $or$ 0 \leq x < 5.6$?

Find the maximum height of the ball described by $f(x)=-0.3 x^{2}+2.1 x+6$ and its distance from the throw point.

A ball is thrown from 5 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+2.1 x+5$ . Find the max height and distance.

A ball is thrown from 8 feet high. Its height is given by $f(x)=-0.2 x^{2}+1.7 x+8$ . Find the max height and distance for parts (a) to (c).

A ball is thrown from 6 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+0.6 x+6$ . Find max height and distance.

Translate (a) as $x + 19$ and (b) as $19 > x$ .

A ball is thrown from 7 feet high, modeled by $f(x)=-0.4 x^{2}+2.7 x+7$ . Find its max height and distance from release.

A ball is thrown from 7 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+0.8 x+7$ . Find the max height and distance.

A ball is thrown from 8 feet high. Its height is given by $f(x)=-0.1 x^{2}+0.7 x+8$ . Find its max height and distance from release.

A ball is thrown from 6 feet high. Its height is given by $f(x)=-0.1 x^{2}+0.8 x+6$ . Find the max height and distance from release.

A ball is thrown from 5 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+1.7 x+5$ . Find max height and distance.

$f(x)=x^{3}-3 x^{2}$ 的根大值点为（） P. 0. B. 2 C. -2 , D. 不有夻 $f(x)=x^{3}-3 x^{2}$ 的最大货点为

3LEM 9: THE HAWK PROBLEM A hawk is on top of a tree and spots a fish in the water. The hawks's pathway in metres is measured by time in seconds by the equation: $y=x^{2}-6 x+11$ a) When does the hawk enter the water? b) Explain why this is a problem? c) Sketch a graph

Determine the amplitude of the periodic graph. * 1 po
Determine the period of the periodic graph. * 1 point

If $f(x)=6+\frac{3}{x}+\frac{4}{x^{2}}$ , find $f^{\prime}(x)$ .
Find $f^{\prime}(1)$ .

Question Find $f_{x}, f_{y}, f_{z z}, f_{y y}, f_{y z}$ , and $f_{x y}$ . $f(x, y)=2 x e^{y}+y e^{x}-3 x+y^{2}$

Tara and Edward each painted their bedrooms. They finished in the same amount of time, even though Edward's bedroom is bigger. They have 4 hours to start painting the basement before dinner is ready. Who will likely paint a larger part of the basement?
Tara Edward

\begin{align} &\text{Given the quadratic function:} \\ &y = -2x^2 - 4x + 3 \\ &\text{Calculate the first and second differences, } \Delta y \text{ and } \Delta^2 y, \text{ for the following values of } x: \\ &x = -3, -2, -1, 0, 1, 2, 3 \end{align}

(1) $y=\frac{2 x-3}{3 x+4}$

10. A given sinusoidal function has a period of 3 , an amplitude of 7 , and a maximum at $(0$ , 2). Represent the function with a sine equation and a cosine equation. [4 marks]

$f(x)=x^{2}-1$ y $g(x)=x+3$ . Obtener $(f g)^{\prime}(x)$

Find the equation of the linear function containing the Show your w points $(2,-4)$ and $(-1,-7)$ . Submit your answer in slopeintercept form, or $y=m x+b$ .

Find the equation of the linear function such that $f(0)=4$ and $f(7)=-5$ . Submit your answer in slopeintercept form, or $y=m x+b$ .

Find the equation of the linear function $f(x)$ such that $f(-2)=-6$ and $f(-1)=6$ . Submit your answer in slopeintercept form.

12. How many different sinusoidal functions can be written that have a period of $3 \pi$ , an amplitude of 1 , and a minimum at $(2,3)$ ? [1 mark]