Browse Function problems Studdy Solved!

Problem 5501

integrate $\cos x$

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Problem 5502

differentiats $\cos ^{x}$

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Problem 5503

differentiate $\cos (x) .$

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Problem 5504

Evaluate the exponential function for the indicated value of $x$ . $h(x)=-\frac{1}{2}\left(\frac{1}{2}\right)^{x}+7 \text { for } x=-8$ $\square$
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Problem 5505

7. The population of a town, $P(t)$ , is modelled by the function $P(t)=6 t^{2}+110 t+3000$ , where $t$ is time in years. Note: $t=0$ represents the year 2000. a) When will the population reach 6000 ? b) What will the population be in 2030?

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Problem 5506

Karen buys apples from the local orchard. The table below shows the relationship between the cost $C$ (in dollars) and the weight $W$ (in kilograms) of the apples purchased. \begin{tabular}{|c|c|c|c|c|} \hline Weight & 0 & 1 & 2 & 3 \\ \hline \begin{tabular}{c} (kilograms) \end{tabular} & 0 cost \\ (dollars) \end{tabular} (a) For the information in the table, write an equation to represent the relationship between $C$ and $W$ . (b) Choose the correct statement to represent this relationship.
Apples cost 1 dollar per 4 kilograms.
Apples cost 4 dollars per kilogram.
Apples cost 1 dollar per kilogram. $\square$ Apples cost 12 dollars per kilogram. Explanation Check

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Problem 5507

Let $y=\ln \left(x^{2}+y^{2}\right)$ . Determine the derivative $y^{\prime}$ at the point $\left(\sqrt{e^{3}-9}, 3\right)$ . $y^{\prime}\left(\sqrt{e^{3}-9}\right)=$

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Problem 5508

Le graphique $v(t)$ d'un corps en mouvement est donné par la figure ci-dessous. The graph $v(t)$ of a moving body is given by the figure below.
Quelle est l'accélération à linstant $t=3$ s? What is the acceleration at time $\mathrm{t}=3 \mathrm{~s}$ ?
Select one or more: $4 \mathrm{~m} / \mathrm{s}^{2}$ $-2 \mathrm{~m} / \mathrm{s}^{2}$ $-4 \mathrm{~m} / \mathrm{s}^{2}$ $2 \mathrm{~m} / \mathrm{s}^{2}$ $0 \mathrm{~m} / \mathrm{s}^{2}$

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Problem 5509

La représentation de $x(t)$ pour un point en mouvement rectiligne uniforme selon l'axe x'x est donnée par: La représentation de $\mathrm{x}(\mathrm{t})$ pour un point en mouvement rectiligne uniforme le long de l'axe $\mathrm{x}^{\prime} \mathrm{x}$ est donnée par: Sélectionnez une option:

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Problem 5510

Evaluating and Solving Exonential Functions Since 1993, the number of fish in Lake Beckett has been decreasing at a rate of 1.1\% per year. In 1993, the population of fish was estimated to be 136 million. Use this information to answer the following: a) Write the exponential function $P(t)$ for this scenario where $P(t)$ is the fish population in millions $t$ years after 1993.
Exponential Function: $P(t)=$ $\square$ b) Determine the number of fish in Lake Beckett in 1998. Round your answer to two decimal places.
The population of fish in Lake Beckett in 1998 will be $\square$ million fish. c) Determine in what year the population of fish will be half the amount it was in 1993. Round your answer to the nearest year.
The population of fish in Lake Beckett will be half of what it was in 1993 in the year $\square$ Question Help: Video Submit Question

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Problem 5511

The functions $g$ and $t$ are defined for $x \in \mathbb{R}$ as follows: $\begin{array}{l} g: x \rightarrow 4x - 5 \\ t: x \rightarrow x^2 - 5x + 1 \end{array}$ (a) Find $t(6)$
(b) Show that $t(g(x)) = 16x^2 - 60x + 51$

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Problem 5512

1. A boat tied up at a dock bobs up and down with passing waves. The vertical distance between its high point and its low point is 1.8 m and the cycle is repeated every 4 seconds. The boat starts at its maximum of 3.4 m . Determine a sinusoidal equation to model the vertical position, in metres, of the boat versus time, in seconds.

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Problem 5513

If we perform the appropriate (i.e. helpful) $u$ -sub for $\int x^{2} \sin \left(x^{3}\right) \mathrm{dx}$ , what does the new integral look like in terms of $u$ right after performing the substitution? $\int x^{2} \sin \left(u^{3}\right) d u$ $\int \frac{1}{3} \sin (u) d u$ none of these $\int u^{2} \sin \left(u^{3}\right) d u$

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Problem 5514

Evaluate the function at the given values of $x$ . Round to 4 decimal places, if necessary. $f(x)=2^{x}$
Part 1 of 4 $f(-3)=0.125$
Part: $1 / 4$
Part 2 of 4 $f(4.9)=$ $\square$

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Problem 5515

Find $\frac{dy}{dx}$ for the function $y = \cos^2(3x + 2)$ .

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Problem 5516

Part 7 of 7 HW Score: $39.75 \%, 32.2$ of 81 points Points: 0 of 1 Save
For the polynomial function below. (a) List each real zero and its multiplicity. (b) Determine whether the graph crosses or touches the $x$ -axis at each $x$ -intercept. (c) Determine the maximum number of turning points on the graph. (d) Determine the end behavior; that is, find the power function that the graph of $f$ resembles for large values of $|x|$ . $f(x)=-2(x-9)(x+9)^{2}$ the mulupicity or the splanet cero is <. (Type a whole number.) (b) The graph crosses the $x$ -axis at the larger $x$ -intercept.
The graph touches the $x$ -axis at the smaller $x$ -intercept. (c) The maximum number of turning points on the graph is 2 . (Type a whole number.) (d) Type the power function that the graph of f resembles for large values of $|\mathrm{x}|$ . $\mathrm{y}=\square$

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Problem 5517

A charter flight charges a fare of $\$ 300$ per person plus $\$ 5$ per person for each unsold seat on the plane. The plane holds 100 passengers. Let $x$ represent the number of unsold seats. Complete parts (a) through (d). (a) Find an expression for the total revenue received for the flight $R(x)$ . (Hint: Multiply the number of people flying, $100-\mathrm{x}$ , by the price per ticket) $R(x)=30000+200 x-5 x^{2}$ (b) Choose the correct graph of the function, $\mathrm{R}(\mathrm{x})$ , below. A. B. c. D. (c) The number of unsold seats that will produce the maximum revenue is 20. (Round to the nearest whole number as needed.) (d) The maximum revenue is $\$$ $\square$ (Round to the nearest whole number as needed.)

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Problem 5518

. Use Technology a) Predict the form of the graph of $y=\tan x+2$ .
Verify your prediction using graphing technology. b) Predict the form of the graph of $y=3 \tan x$ .
Verify your prediction using graphing 24. technology. c) Predict the form of the graph of $y=\tan \left(x-\frac{\pi}{4}\right)$ . Verify your prediction using graphing technology. d) Predict the form of the graph of $y=\tan 3 x$ . Verify your prediction using graphing technology.

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Problem 5519

Find the slope of the line graphed below.

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Problem 5520

(5) More Examples for Practice Q./Lef $f(x)=0.2,0<x<5$
Find $O p(x<2.8) \quad p(2) p(x>1.5) \quad p(2<4)$

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Problem 5521

The accompanying table shows the number of bacteria present in a certain culture over a 5 hour period, where x is the time, in hours, and y is the number of bacterie. Write an exponential regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, determine the number of bacteria present after 11 hours, to the nearest whole number. \begin{tabular}{|c|c|} \hline Hours $(x)$ & Bacteria $(y)$ \\ \hline 0 & 1800 \\ \hline 1 & 1950 \\ \hline 2 & 2154 \\ \hline 3 & 2424 \\ \hline 4 & 2730 \\ \hline 5 & 3034 \\ \hline \end{tabular} $\square$ Open Statitisis Colculator
Answer Attempt i but of 2
Regression Equation: $\square$ Final Answer: $\square$ Sillamit Answer

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Problem 5522

1. Use the definition to find the derivative of each of the following functions: (a) $f(x):=x^{3}$ for $x \in \mathbb{R}$ , (c) $h(x):=\sqrt{x}$ for $x>0$ , (b) $g(x):=1 / x$ for $x \in \mathbb{R}, x \neq 0$ , (d) $k(x):=1 / \sqrt{x}$ for $x>0$ .

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Problem 5523

Let $f(x)$ and $g(x)$ be differentiable functions Evaluate $f^{\prime}(-3)$ for the function $f(x)=\left(x^{2}+2 x-3\right) \frac{g(x+2)}{\left(x^{3}+1\right) g(2 x+5)} .$ (a) $-\frac{2}{13}$ (b) $\frac{13}{2}$ $f(x)=\frac{g(x+2) \cdot(x-1)}{g(2 x+5)}$ (c) -1 (d) $0 \quad x+2=$ (e) $\frac{2}{13} 4-3$

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Problem 5524

Question 2 $0 / 1$ pt 5 9 Details
The function $f(x)=3^{x}$ is often referred to as a tripling function because $f(x)$ triples whenever $x$ changes by 1 . But this is not the only example of a tripling function. Give two more distinct examples of tripling functions (functions whose values triple whenever the independent variable changes by 1 ). - $f(x)=3^{x}$ - $g(x)=$ $\square$ - $h(x)=$ $\square$

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Problem 5525

4. A certain apartment building, which you don't want to live in, opened in 1992. In 1998, the number of mice infesting that building was 6 . In 2018, there were 120 mice. Let $M$ represent the number of mice in years since 1992. (6 pts) Page 2 of 3 Copyright © 2024 Department of Statistics and Data Sciences. All rights reserved. a. Write $M$ as an exponential function of $t$ . Interpret what the parameters tell us about the growth in the number of mice over time. (4 pts) b. What is the predicted number of mice in the building in 2024 based on the exponential model? (2 pt)

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Problem 5526

Exercice 3 Soient $f$ et $g$ deux fonctions définies par: $f(x)=x^{2}-2 x+3$ et $g(x)=\sqrt{x+1}$ 展共 Donner les tableaux de variations des fonctions $f$ et $g$ . b. Représenter les courbes représentatives $\left(C_{f}\right)$ et $\left(C_{g}\right)$ dans un repère orthonormé ( $O, \vec{i}, \vec{j}$ ) CVI Déterminer graphiquement $g([-1 ; 0])$ et $g([0 ;+\infty[)$ 2 Soit $h$ la fonction définie sur $[-1 ;+\infty[$ par : $h(x)=x+4-2 \sqrt{x+1}$ al Vérifier que : $(\forall x \in[-1 ;+\infty[) ; h(x)=(f \circ g)(x)$ 5 Étudier la monotonie de la fonction $h$ sur les intervalles $[0 ;+\infty[$ et $[-1 ; 0]$ à partir de celle de $f$ et $g$ . Puis déduire les extremums de $h$ sur l'intervalle $[-1 ;+\infty[$ s'ils existent. $\left.\gamma \varepsilon_{k}\right]$ Montrer que : $\left(\forall a \in\left[-1 ;+\infty[) ; \sqrt{a+1}-\sqrt{a} \leq \frac{1}{2}\right.\right.$

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Problem 5527

The function $f(x)=x^{2}+1$ and $g(x)=3-x$ , determine an equation for the combined function $y=f(x)-g(x)$ . $y=x^{2}-x+2$ $y=x^{2}+x-2$ $y=x^{2}+x+4$ $y=x^{2}-x+4$

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Problem 5528

Find the area of the "triangular" region in the first quadrant that is bounded above by the curve $y=. . e^{\frac{x}{2}}$ , below by the curve $y=e^{-\frac{x}{2}}$ , and on the right by the line $x=2 \ln 2$ .

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Problem 5529

Find the requested function value. $f(x)=5 x+2, g(x)=-2 x^{2}-2 x-9$
Find $(g \circ f)(-7)$

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Problem 5530

If $r>0$ is a rational number, let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by $f(x):=x^{r} \sin (1 / x)$ for $x \neq 0$ , and $f(0):=0$ . Determine those values of $r$ for which $f^{\prime}(0)$ exists.

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Problem 5531

Evaluate the definite integral. $\int_{1}^{6} \frac{1}{x \sqrt{16 x^{2}-7}} d x$

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Problem 5532

Find $\int_{1}^{e^{2}} \frac{6}{x} d x$

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Problem 5533

If $A$ and $B$ are positive constants, find all critical points of $f(w)=\frac{A}{w^{2}}-\frac{5 B}{w} .$
Number of critical points: Choose one

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Problem 5534

Find a formula for the family of cubic polynomials with an inflection point at the origin. Cubic polynomials are all of the form $f(x)=A x^{3}+B x^{2}+C x+D$ . Use $A, B, C$ , and $D$ for the coefficients which cannot be determined using the given information. $f(x)=$ $\square$

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Problem 5535

Find a formula for the family of cubic polynomials with an inflection point at the origin. Cubic polynomials are all of the form $f(x)=A x^{3}+B x^{2}+C x+D$ . Use $A, B, C$ , and $D$ for the coefficients which cannot be determined using the given information. $f(x)=$ $\square$

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Problem 5536

find $A, B, C$ , and $D$ using partial Lractions $\frac{s}{s^{4}-1}=\frac{A}{s-1}+\frac{B}{s+1}+\frac{c x+1}{s^{2}+1}$

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Problem 5537

(1)
4. Give an example of a function with no absolute minimum or maximum.

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Problem 5538

Question 14 1 pts
Solve the problem that involves computing expected values in a game of chance.
A game is played using one die. If the die is rolled and shows a 2 , the player wins $\$ 8$ . If the die shows any number other than 2, the player wins nothing. If there is a charge of $\$ 1$ to play the game, what is the game's expected value? \ $7.00 -\$1 \$0.33 .$ \quad .33$

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Problem 5539

A particle is moving with the given data. Find the position of the part (b) $a(t)=2 t+1 s(0)=3, v(0)=-L$

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Problem 5540

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

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Problem 5541

A ball is thrown from 8 feet high. Its height is given by $f(x)=-0.1 x^{2}+0.8 x+8$ . Find the max height and distance from release.

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Problem 5542

A ball is thrown from 5 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+1.4 x+5$ . Find its max height and distance from the throw point.

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Problem 5543

A ball is thrown from 8 feet high. Model: $f(x)=-0.4 x^{2}+2.1 x+8$ . Find max height and distance from release. Max height: $\square$ feet, distance: $\square$ feet. Round to nearest tenth.

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Problem 5544

A ball is thrown from 7 feet high. Its height is modeled by $f(x)=-0.3 x^{2}+2.1 x+7$ . Find the max height and distance from release.

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Problem 5545

Given the function $f(x)=-0.2 x^{2}+1.4 x+8$ , find the maximum height and horizontal distance when it hits the ground.

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Problem 5546

A ball is thrown from 6 feet high, modeled by $f(x)=-0.1 x^{2}+0.7 x+6$ . Find its max height and distance from launch.

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Problem 5547

A ball is thrown from 8 feet high. Its height, $f(x)=-0.2 x^{2}+1.7 x+8$ , models its path. Find the max height and distance.

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Problem 5548

A ball is thrown from 8 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+1.7 x+8$ . Find the max height and distance from release.

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Problem 5549

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

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Problem 5550

A ball is thrown from 7 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+0.7 x+7$ . Find the max height and distance.

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Problem 5551

A ball is thrown from 6 feet high, modeled by $f(x)=-0.2 x^{2}+1.2 x+6$ . Find its max height and distance from launch.

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Problem 5552

A ball is thrown from 6 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+1.2 x+6$ . Find the max height and distance from release.

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Problem 5553

A ball is thrown from 7 feet high. Its height is modeled by $f(x)=-0.6 x^{2}+2.7 x+7$ . Find the max height and distance.

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Problem 5554

A ball is thrown from 6 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+1.2 x+6$ . Find max height and distance from throw point.

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Problem 5555

A ball is thrown from 6 feet high. Its height $f(x)=-0.2 x^{2}+1.7 x+6$ . Find the max height and distance from release. Max height: $\square$ feet, distance: $\square$ feet.

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Problem 5556

A ball is thrown from 6 feet high, modeled by $f(x)=-0.1 x^{2}+1.2 x+6$ . Find max height and horizontal distance before hitting ground.

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Problem 5557

A ball is thrown from 7 feet high. Its height is given by $f(x)=-0.1 x^{2}+0.6 x+7$ . Find its max height and distance from release.

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Problem 5558

Find the maximum height of the ball modeled by $f(x)=-0.6 x^{2}+2.7 x+7$ and the distance from the throw point.

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Problem 5559

A ball is thrown from 8 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+0.6 x+8$ . Find its max height and distance from launch.

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Problem 5560

Solve for $c$ in the equation $w=\frac{z-c}{r}$ . What is $c$ ?

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Problem 5561

Compare refrigerator prices:
(a) Superstore markup of $40\%$ on \$699. How much does Sam pay?
(b) Department store with $20\%$ discount. What’s the price?
(c) Which is true? Superstore more expensive, department store more, or same price?

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Problem 5562

Ann wants to buy golf clubs for \$369. Calculate prices at a pro shop and a distributor, then compare them.
(a) Pro shop marks up by 10% then 40%. What is the final price? (b) Distributor marks up by 50%. What is the final price? (c) Which is cheaper? Pro shop, distributor, or the same?

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Problem 5563

Find the function for gas price starting at 2.25, increasing at 4% per year: $f(x)=2.25(1+0.04)^{x}$

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Problem 5564

What is the monthly growth rate in the expression $f(x)=12(1.035)^{x}$ for a drama club? A. $0.35\%$ B. $1.035\%$ C. $3.5\%$ D. $12\%$

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Problem 5565

Calculate the present value of Ben's \$100,000 sale: \$20,000 today + \$20,000 for 4 years at 4% interest. Choices: A. \$87,096 B. \$88,384 C. \$92,598 D. \$93,964

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Problem 5566

Find the time $t$ (in minutes) when the altitude $a=3400t+600$ reaches 21,000 feet.

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Problem 5567

How long (in minutes) to download a 100 MB file at 75 KB/s based on the trend from the given speeds and times?

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Problem 5568

Find density $D$ given volume $V=100.0 \mathrm{~mL}$ and mass $M=1.50 \mathrm{~kg}$ . Use $D=\frac{M}{V}$ .

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Problem 5569

Calculate the windchill temperature difference at $10^{\circ} \mathrm{F}$ for wind speeds of 5 mph and 25 mph.

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Problem 5570

Find the present value of a $\$ 5,000$ bonus in 5 years at $5\%$ interest, compounded quarterly. A. $\$ 3,896$ B. $\$ 3,900$ C. $\$ 3,918$ D. $\$ 6,381$

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Problem 5571

Use the function $f(x)=\sqrt{x-5}$ to find $f(x)$ for $x=1, 5, 86, 105$ . Simplify where possible.

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Problem 5572

If $\frac{\tan \theta+\tan 30^{\circ}}{1-\tan \theta \tan 30^{\circ}}+1=0$ , find $\tan \theta$ in surd form.

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Problem 5573

If $\frac{\tan \theta+\tan 30^{\circ}}{1-\tan \theta \tan 30^{\circ}}+1=0$ , find $\tan \theta$ in surd form.

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Problem 5574

Solve $\frac{\tan \theta+\tan 30^{\circ}}{1-\tan \theta \tan 30^{\circ}}+1=0$ for $\tan \theta$ in surd form.

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Problem 5575

Solve $\frac{\tan \theta+\tan 30^{\circ}}{1-\tan \theta \tan 30^{\circ}}+1=0$ for $\tan \theta$ in surd form.

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Problem 5576

Find the domain of the piecewise function $f(x)=\begin{cases} 2+x & \text{if } x<0 \\ x^{2} & \text{if } x \geq 0 \end{cases}$ .

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Problem 5577

Define the function $f(x)=\begin{cases} 2+x & \text{if } x<0 \\ x^{2} & \text{if } x \geq 0 \end{cases}$ . Find its domain, intercepts, graph, and range.

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Problem 5578

Find $f(x)=\operatorname{int}(2 x)$ for: (a) $f(3.3)$ , (b) $f(2.8)$ , (c) $f(-3.2)$ .

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Problem 5579

Find the slope of the tangent line to $y=x^{3}$ at the point (1,1).

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Problem 5580

Estimate the slope of the tangent line to $y=x^{1/2}$ at the point $(1,1)$ .

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Problem 5581

Gas company charges: (a) Cost for 30 therms? (b) Cost for 200 therms? (c) Model function $C(x)$ . (d) Graph $C(x)$ .

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Problem 5582

Shannon hits golf balls every 5 minutes. How many were in the full bucket? Data: 5 min: 54, 10 min: 47, 15 min: 40, 20 min: 33, 25 min: 26.

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Problem 5583

Find the charges for using 30 and 200 therms, and create a function $C(x)$ for the monthly charge.

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Problem 5584

Find the wind chill $W$ for $t=5^{\circ} C$ and $v=19 \mathrm{~m/s}$ . Use the formula provided. $W \approx \square^{\circ} C$

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Problem 5585

Calculate the wind chill $W$ for $t=5^{\circ} \mathrm{C}$ and $v=1 \mathrm{~m/s}$ . Use the formula provided. $W \approx \square^{\circ} \mathrm{C}$

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Problem 5586

Calculate the wind chill $W$ for $t=5^{\circ} \mathrm{C}$ and $v=39 \mathrm{~m/s}$ . Round to the nearest degree.

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Problem 5587

Find $(f+g)(x)$ for $f(x)=\{5 x+4 \text{ if } x<2, x^{2}+4 x \text{ if } x \geq 2\}$ and $g(x)=\{-3 x+1 \text{ if } x \leq 0, x-7 \text{ if } x>0\}$ .

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Problem 5588

Terri's function machine gives outputs: 3 → 8, 10 → 29, 20 → 59. Find outputs for 5, -1, and $x$ ; also, write the equation.

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Problem 5589

Determine which function best models the coyote population $N$ after $t$ years from the given data:
1. $N(t)=0.5 t^{2}+1$
2. $N(t)=1.95^{t}$
3. $N(t)=0.5 t^{3}-t^{2}+5 t+1$
4. $N(t)=2 t+1$

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Problem 5590

Find a function with the same $y$ -intercept as $y=\frac{2}{3} x-3$ .

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Problem 5591

Yolanda deposited \$1000 at 2% and \$3000 at 7%. Find total interest earned in 1 year and percent interest on total.
(a) Total interest: \$\square (b) Percent interest: \%

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Problem 5592

Find the $y$ -intercept of the function from the points: (1, 8), (2, 6), (3, 4), (4, 2).

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Problem 5593

Find $g(-3)$ by substituting -3 into $g(x)=2x^{2}-5$ and simplify.

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Problem 5594

Calculate $f(3)$ by substituting 3 into $f(x)$ : $f(3)=-\frac{2}{3}(3)+3$ and simplify.

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Problem 5595

What function results from horizontally stretching $y=\sqrt{x}$ and reflecting it in the $x$ -axis? Options are:
1. $y=-\sqrt{2 x}$
2. $y=\sqrt{\frac{1}{2}(-x)}$
3. $y=\sqrt{2(-x)}$
4. $y=-\sqrt{\frac{1}{2} x}$

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Problem 5596

Which function's graph is $y=\frac{1}{x}$ shifted right 5 units and up 2 units? $y=\frac{1}{x+5}+2$

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Problem 5597

Solve the following equations for the indicated variable:
27. $I=P r t$ for $P$
28. $C=2 \pi r$ for $r$
29. $T=D+p m$ for $p$
30. $P=C+M C$ for $M$
31. $A=\frac{1}{2} h(a+b)$ for $a$
32. $A=\frac{1}{2} h(a+b)$ for $b$
33. $S=P+$ Prt for $r$
34. $S=P+$ Prt for $t$
35. $B=\frac{F}{S-V}$ for $S$
36. $S=\frac{C}{1-r}$ for $r$

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Problem 5598

Find $(g \circ f \circ h)(x)$ for $f(x)=4x-8$ , $g(x)=x^4$ , and $h(x)=\sqrt[5]{x}$ .

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Problem 5599

Find the function $(g \circ f \circ h)(x)$ for $f(x)=4x-6$ , $g(x)=x^3$ , and $h(x)=\sqrt[4]{x}$ .

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Problem 5600

Evaluate $(f \circ g)(x)$ and find its domain. Given $f(x)=\frac{5}{x^{2}+36}$ and $g(x)=\sqrt{4+x}$ .

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Function

Problem 5501

integrate cos⁡x\cos xcosx

Problem 5502

differentiats cos⁡x\cos ^{x}cosx

Problem 5503

differentiate cos⁡(x).\cos (x) .cos(x).

Problem 5504

Evaluate the exponential function for the indicated value of xxx. h(x)=−12(12)x+7 for x=−8h(x)=-\frac{1}{2}\left(\frac{1}{2}\right)^{x}+7 \text { for } x=-8h(x)=−21​(21​)x+7 for x=−8 □\square□Additional Materials

Problem 5505

7. The population of a town, P(t)P(t)P(t), is modelled by the function P(t)=6t2+110t+3000P(t)=6 t^{2}+110 t+3000P(t)=6t2+110t+3000, where ttt is time in years. Note: t=0t=0t=0 represents the year 2000. a) When will the population reach 6000 ? b) What will the population be in 2030?

Problem 5506

Problem 5507

Let y=ln⁡(x2+y2)y=\ln \left(x^{2}+y^{2}\right)y=ln(x2+y2). Determine the derivative y′y^{\prime}y′ at the point (e3−9,3)\left(\sqrt{e^{3}-9}, 3\right)(e3−9​,3). y′(e3−9)=y^{\prime}\left(\sqrt{e^{3}-9}\right)=y′(e3−9​)=

Problem 5508

Problem 5509

Problem 5510

Problem 5511

Problem 5512

Problem 5513

Problem 5514

Evaluate the function at the given values of xxx. Round to 4 decimal places, if necessary. f(x)=2xf(x)=2^{x}f(x)=2xPart 1 of 4 f(−3)=0.125f(-3)=0.125f(−3)=0.125Part: 1/41 / 41/4Part 2 of 4 f(4.9)=f(4.9)=f(4.9)= □\square□

Problem 5515

Find dydx\frac{dy}{dx}dxdy​ for the function y=cos⁡2(3x+2) y = \cos^2(3x + 2) y=cos2(3x+2).

Problem 5516

Problem 5517

Problem 5518

Problem 5519

Find the slope of the line graphed below.

Problem 5520

(5) More Examples for Practice Q./Lef f(x)=0.2,0<x<5f(x)=0.2,0<x<5f(x)=0.2,0<x<5Find Op(x<2.8)p(2)p(x>1.5)p(2<4)O p(x<2.8) \quad p(2) p(x>1.5) \quad p(2<4)Op(x<2.8)p(2)p(x>1.5)p(2<4)

Problem 5521

Problem 5522

Problem 5523

Problem 5524

Problem 5525

Problem 5526

Problem 5527

The function f(x)=x2+1f(x)=x^{2}+1f(x)=x2+1 and g(x)=3−xg(x)=3-xg(x)=3−x, determine an equation for the combined function y=f(x)−g(x)y=f(x)-g(x)y=f(x)−g(x). y=x2−x+2y=x^{2}-x+2y=x2−x+2 y=x2+x−2y=x^{2}+x-2y=x2+x−2 y=x2+x+4y=x^{2}+x+4y=x2+x+4 y=x2−x+4y=x^{2}-x+4y=x2−x+4

Problem 5528

Find the area of the "triangular" region in the first quadrant that is bounded above by the curve y=..ex2y=. . e^{\frac{x}{2}}y=..e2x​, below by the curve y=e−x2y=e^{-\frac{x}{2}}y=e−2x​, and on the right by the line x=2ln⁡2x=2 \ln 2x=2ln2.

Problem 5529

Find the requested function value. f(x)=5x+2,g(x)=−2x2−2x−9f(x)=5 x+2, g(x)=-2 x^{2}-2 x-9f(x)=5x+2,g(x)=−2x2−2x−9Find (g∘f)(−7)(g \circ f)(-7)(g∘f)(−7)

Problem 5530

If r>0r>0r>0 is a rational number, let f:R→Rf: \mathbb{R} \rightarrow \mathbb{R}f:R→R be defined by f(x):=xrsin⁡(1/x)f(x):=x^{r} \sin (1 / x)f(x):=xrsin(1/x) for x≠0x \neq 0x=0, and f(0):=0f(0):=0f(0):=0. Determine those values of rrr for which f′(0)f^{\prime}(0)f′(0) exists.

Problem 5531

Evaluate the definite integral. ∫161x16x2−7dx\int_{1}^{6} \frac{1}{x \sqrt{16 x^{2}-7}} d x∫16​x16x2−7​1​dx

Problem 5532

Find ∫1e26xdx\int_{1}^{e^{2}} \frac{6}{x} d x∫1e2​x6​dx

Problem 5533

If AAA and BBB are positive constants, find all critical points of f(w)=Aw2−5Bw.f(w)=\frac{A}{w^{2}}-\frac{5 B}{w} .f(w)=w2A​−w5B​.Number of critical points: Choose one

Problem 5534

Problem 5535

Problem 5536

find A,B,CA, B, CA,B,C, and DDD using partial Lractions ss4−1=As−1+Bs+1+cx+1s2+1\frac{s}{s^{4}-1}=\frac{A}{s-1}+\frac{B}{s+1}+\frac{c x+1}{s^{2}+1}s4−1s​=s−1A​+s+1B​+s2+1cx+1​

Problem 5537

(1)4. Give an example of a function with no absolute minimum or maximum.

Problem 5538

Problem 5539

A particle is moving with the given data. Find the position of the part (b) a(t)=2t+1s(0)=3,v(0)=−La(t)=2 t+1 s(0)=3, v(0)=-La(t)=2t+1s(0)=3,v(0)=−L

Problem 5540

A ball is thrown from 7 feet high. Its height is 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 the max height and distance from launch.

Problem 5541

A ball is thrown from 8 feet high. Its height is given by f(x)=−0.1x2+0.8x+8f(x)=-0.1 x^{2}+0.8 x+8f(x)=−0.1x2+0.8x+8. Find the max height and distance from release.

Problem 5542

A ball is thrown from 5 feet high. Its height is modeled by f(x)=−0.1x2+1.4x+5f(x)=-0.1 x^{2}+1.4 x+5f(x)=−0.1x2+1.4x+5. Find its max height and distance from the throw point.

Problem 5543

A ball is thrown from 8 feet high. Model: f(x)=−0.4x2+2.1x+8f(x)=-0.4 x^{2}+2.1 x+8f(x)=−0.4x2+2.1x+8. Find max height and distance from release. Max height: □\square□ feet, distance: □\square□ feet. Round to nearest tenth.

Problem 5544

A ball is thrown from 7 feet high. Its height is modeled by f(x)=−0.3x2+2.1x+7f(x)=-0.3 x^{2}+2.1 x+7f(x)=−0.3x2+2.1x+7. Find the max height and distance from release.

Problem 5545

Given the function f(x)=−0.2x2+1.4x+8f(x)=-0.2 x^{2}+1.4 x+8f(x)=−0.2x2+1.4x+8, find the maximum height and horizontal distance when it hits the ground.

Problem 5546

A ball is thrown from 6 feet high, modeled by f(x)=−0.1x2+0.7x+6f(x)=-0.1 x^{2}+0.7 x+6f(x)=−0.1x2+0.7x+6. Find its max height and distance from launch.

Problem 5547

A ball is thrown from 8 feet high. Its height, f(x)=−0.2x2+1.7x+8f(x)=-0.2 x^{2}+1.7 x+8f(x)=−0.2x2+1.7x+8, models its path. Find the max height and distance.

Problem 5548

A ball is thrown from 8 feet high. Its height is modeled 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 from release.

Problem 5549

A ball is thrown from 8 feet high with height 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 from release.

integrate $\cos x$

differentiats $\cos ^{x}$

differentiate $\cos (x) .$

Evaluate the exponential function for the indicated value of $x$ . $h(x)=-\frac{1}{2}\left(\frac{1}{2}\right)^{x}+7 \text { for } x=-8$ $\square$
Additional Materials

7. The population of a town, $P(t)$ , is modelled by the function $P(t)=6 t^{2}+110 t+3000$ , where $t$ is time in years. Note: $t=0$ represents the year 2000. a) When will the population reach 6000 ? b) What will the population be in 2030?

Let $y=\ln \left(x^{2}+y^{2}\right)$ . Determine the derivative $y^{\prime}$ at the point $\left(\sqrt{e^{3}-9}, 3\right)$ . $y^{\prime}\left(\sqrt{e^{3}-9}\right)=$

Evaluate the function at the given values of $x$ . Round to 4 decimal places, if necessary. $f(x)=2^{x}$
Part 1 of 4 $f(-3)=0.125$
Part: $1 / 4$
Part 2 of 4 $f(4.9)=$ $\square$

Find $\frac{dy}{dx}$ for the function $y = \cos^2(3x + 2)$ .

(5) More Examples for Practice Q./Lef $f(x)=0.2,0<x<5$
Find $O p(x<2.8) \quad p(2) p(x>1.5) \quad p(2<4)$

The function $f(x)=x^{2}+1$ and $g(x)=3-x$ , determine an equation for the combined function $y=f(x)-g(x)$ . $y=x^{2}-x+2$ $y=x^{2}+x-2$ $y=x^{2}+x+4$ $y=x^{2}-x+4$

Find the area of the "triangular" region in the first quadrant that is bounded above by the curve $y=. . e^{\frac{x}{2}}$ , below by the curve $y=e^{-\frac{x}{2}}$ , and on the right by the line $x=2 \ln 2$ .

Find the requested function value. $f(x)=5 x+2, g(x)=-2 x^{2}-2 x-9$
Find $(g \circ f)(-7)$

If $r>0$ is a rational number, let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by $f(x):=x^{r} \sin (1 / x)$ for $x \neq 0$ , and $f(0):=0$ . Determine those values of $r$ for which $f^{\prime}(0)$ exists.

Evaluate the definite integral. $\int_{1}^{6} \frac{1}{x \sqrt{16 x^{2}-7}} d x$

Find $\int_{1}^{e^{2}} \frac{6}{x} d x$

If $A$ and $B$ are positive constants, find all critical points of $f(w)=\frac{A}{w^{2}}-\frac{5 B}{w} .$
Number of critical points: Choose one

find $A, B, C$ , and $D$ using partial Lractions $\frac{s}{s^{4}-1}=\frac{A}{s-1}+\frac{B}{s+1}+\frac{c x+1}{s^{2}+1}$

(1)
4. Give an example of a function with no absolute minimum or maximum.

A particle is moving with the given data. Find the position of the part (b) $a(t)=2 t+1 s(0)=3, v(0)=-L$

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

A ball is thrown from 8 feet high. Its height is given by $f(x)=-0.1 x^{2}+0.8 x+8$ . Find the max height and distance from release.

A ball is thrown from 5 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+1.4 x+5$ . Find its max height and distance from the throw point.

A ball is thrown from 8 feet high. Model: $f(x)=-0.4 x^{2}+2.1 x+8$ . Find max height and distance from release. Max height: $\square$ feet, distance: $\square$ feet. Round to nearest tenth.

A ball is thrown from 7 feet high. Its height is modeled by $f(x)=-0.3 x^{2}+2.1 x+7$ . Find the max height and distance from release.

Given the function $f(x)=-0.2 x^{2}+1.4 x+8$ , find the maximum height and horizontal distance when it hits the ground.

A ball is thrown from 6 feet high, modeled by $f(x)=-0.1 x^{2}+0.7 x+6$ . Find its max height and distance from launch.

A ball is thrown from 8 feet high. Its height, $f(x)=-0.2 x^{2}+1.7 x+8$ , models its path. Find the max height and distance.

A ball is thrown from 8 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+1.7 x+8$ . Find the max height and distance from release.

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

A ball is thrown from 7 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+0.7 x+7$ . Find the max height and distance.

A ball is thrown from 6 feet high, modeled by $f(x)=-0.2 x^{2}+1.2 x+6$ . Find its max height and distance from launch.

A ball is thrown from 6 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+1.2 x+6$ . Find the max height and distance from release.

A ball is thrown from 7 feet high. Its height is modeled by $f(x)=-0.6 x^{2}+2.7 x+7$ . Find the max height and distance.

A ball is thrown from 6 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+1.2 x+6$ . Find max height and distance from throw point.

A ball is thrown from 6 feet high. Its height $f(x)=-0.2 x^{2}+1.7 x+6$ . Find the max height and distance from release. Max height: $\square$ feet, distance: $\square$ feet.

A ball is thrown from 6 feet high, modeled by $f(x)=-0.1 x^{2}+1.2 x+6$ . Find max height and horizontal distance before hitting ground.

A ball is thrown from 7 feet high. Its height is given by $f(x)=-0.1 x^{2}+0.6 x+7$ . Find its max height and distance from release.

Find the maximum height of the ball modeled by $f(x)=-0.6 x^{2}+2.7 x+7$ and the distance from the throw point.

A ball is thrown from 8 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+0.6 x+8$ . Find its max height and distance from launch.

Solve for $c$ in the equation $w=\frac{z-c}{r}$ . What is $c$ ?

Compare refrigerator prices:
(a) Superstore markup of $40\%$ on \$699. How much does Sam pay?
(b) Department store with $20\%$ discount. What’s the price?
(c) Which is true? Superstore more expensive, department store more, or same price?

Ann wants to buy golf clubs for \$369. Calculate prices at a pro shop and a distributor, then compare them.
(a) Pro shop marks up by 10% then 40%. What is the final price? (b) Distributor marks up by 50%. What is the final price? (c) Which is cheaper? Pro shop, distributor, or the same?

Find the function for gas price starting at 2.25, increasing at 4% per year: $f(x)=2.25(1+0.04)^{x}$

What is the monthly growth rate in the expression $f(x)=12(1.035)^{x}$ for a drama club? A. $0.35\%$ B. $1.035\%$ C. $3.5\%$ D. $12\%$

Find the time $t$ (in minutes) when the altitude $a=3400t+600$ reaches 21,000 feet.

Find density $D$ given volume $V=100.0 \mathrm{~mL}$ and mass $M=1.50 \mathrm{~kg}$ . Use $D=\frac{M}{V}$ .

Calculate the windchill temperature difference at $10^{\circ} \mathrm{F}$ for wind speeds of 5 mph and 25 mph.

Find the present value of a $\$ 5,000$ bonus in 5 years at $5\%$ interest, compounded quarterly. A. $\$ 3,896$ B. $\$ 3,900$ C. $\$ 3,918$ D. $\$ 6,381$

Use the function $f(x)=\sqrt{x-5}$ to find $f(x)$ for $x=1, 5, 86, 105$ . Simplify where possible.

If $\frac{\tan \theta+\tan 30^{\circ}}{1-\tan \theta \tan 30^{\circ}}+1=0$ , find $\tan \theta$ in surd form.

If $\frac{\tan \theta+\tan 30^{\circ}}{1-\tan \theta \tan 30^{\circ}}+1=0$ , find $\tan \theta$ in surd form.

Solve $\frac{\tan \theta+\tan 30^{\circ}}{1-\tan \theta \tan 30^{\circ}}+1=0$ for $\tan \theta$ in surd form.