Function

Problem 8501

The top and bottom margins of a poster are 8 cm and the side margins are each 4 cm. If the area of printed material on the poster is fixed at 388 square centimeters, find the dimensions of the poster with the smallest area.
Width = _ (include units) Height = _ (include units)
Note: You can earn partial credit on this problem. printed material

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Problem 8502

For the polynomial function $f(x) = x^3 - 2x^2 - 5x + 6$ , we have $f(0) = 6$ , $f(2) = -4$ , $f(3) = 0$ , $f(-1) = 8$ , $f(1) = 0$ . Rewrite $f(x)$ as a product of linear factors. List the values in order from smallest to largest.

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Problem 8503

Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius $r$ . List the dimensions in non-decreasing order (the answer may depend on $r$ ).

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Problem 8504

Find the point P on the graph of the function $y = \sqrt{x}$ closest to the point $(2, 0)$ The $x$ coordinate of P is:

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Problem 8505

$\int \cos (3 \tan \theta) d \theta$

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Problem 8506

For some positive constant $C$ , a patient's temperature change, $T$ , due to a dose, $D$ , of a drug is given by $T = (\frac{C}{2} - \frac{D}{3})D^2$ .
What dosage maximizes the temperature change?
$D =$
The sensitivity of the body to the drug is defined as $dT/dD$ . What dosage maximizes sensitivity?
$D =$

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Problem 8507

7. The height above the ground of a bungee jumper is modelled by the quadratic function $h(t) = -5(t - 0.3)^2 + 110$ , where height, $h(t)$ , is in metres and time, $t$ , is in seconds.
a) When does the bungee jumper reach maximum height? Why is it a maximum?
b) What is the maximum height reached by the jumper?
c) Determine the height of the platform from which the bungee jumper jumps.

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Problem 8508

Given $f(x, y) = 3x^5 + 2xy^3 + 4y^2$ , find
$f_x(x, y) =$
$f_y(x, y) =$

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Problem 8509

The table shows the number of lattés Dana prepares in a coffee shop. Assume the relationship between the two quantities is linear. \begin{tabular}{|c|c|} \hline Time (h), $x$ & \begin{tabular}{c} Lattés \\ Prepared, $y$ \end{tabular} \\ \hline 3 & 21 \\ \hline 4 & 25 \\ \hline 5 & 29 \\ \hline 6 & 33 \\ \hline \end{tabular}
Find and interpret the rate of change.
The rate of change is $\square$ , so the number of lattes Dana prepares each hour is $\square$ Find and interpret the initial value.
The initial value is $\square$ so $\square$ lattés have already been made.

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Problem 8510

Find the average rate of change of $g(x)=-2 x^{2}-2 x$ from $x=-4$ to $x=1$ . Simplify your answer as much as possible.

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Problem 8511

$69. \int_{e}^{e^4} \frac{dx}{x\sqrt{\ln{x}}}$

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Problem 8512

$f(x) = -x^5 + 3x^3 - 3x$

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Problem 8513

Which statement is true?
The growth rate of the exponential function exceeds the growth rite of the linear function for $-1 \leq x \leq 3$ .
The growth rate of the exponential function exceeds the growth rate of the linear function for $0 \leq x \leq 3$ . The growth rate of the exponential function exceeds the growth rate of the linear function for $-1 \leq x \leq 1$ - The growth rate of the exponential function exceeds the growth rate of the linear function for $1 \leq x \leq 3$ . Mark this and return Save and Exit Next

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Problem 8514

Study the table. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-2 & 8 \\ \hline-1 & 2 \\ \hline 0 & 0 \\ \hline 1 & 2 \\ \hline 2 & 8 \\ \hline \hline \end{tabular}
Which best describes the function represented by the data in the table? linear with a common ratio of 4 linear with a common second difference of 4 quadratic with a common ratio of 4 quadratic with a common second difference of 4

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Problem 8515

Study this table. \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-3 & -2 \\ \hline-2 & 0 \\ \hline 0 & 4 \\ \hline 4 & 12 \\ \hline \hline \end{tabular}
Which best describes the function represented by the data in the table? linear with a common ratio of 2 linear with a common first difference of 2 quadratic with a common ratio of 2 quadratic with a common first difference of 2

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Problem 8516

$x(t) = at + b$ , where $a$ and $b$ are both nonzero.
Find the acceleration of the bug at any given time $t$ .

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Problem 8517

Find the value of $(f \circ g)(2)$ $f(x) = 5x + 2$ and $g(x) = 3x - 4$

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Problem 8518

```latex \textbf{Aufgabe 1}
\begin{enumerate} \item[a)] Stelle eine Exponentialfunktion auf, welche die Summe der weltweiten Exporte seit 1948 beschreibt. \item[b)] Wie hoch waren die US-Exporte im Jahr 1983? \item[c)] Begründe, warum die Grafik mit „Explosives Wachstum" überschrieben ist. \item[d)] \textit{In welchem Jahr erreichten die US-Exporte erstmals die Höhe von 10.000 Mrd. US-\$?} \end{enumerate}
\textbf{Explosives Wachstum}
Summe der weltweiten Exporte in Mrd. US-\$
\textbf{Zusätzliche Informationen:}
Es steht, dass es im Jahr 1948 59 waren und im Jahr 2010 14851.

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Problem 8519

14. For each quadratic relation, i) write the equation in factored form ii) determine the coordinates of the vertex iii) write the equation in vertex form iv) sketch the graph
a) $y = x^2 - 8x + 15$ b) $y = 2x^2 - 8x - 64$ c) $y = -4x^2 - 12x + 7$

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Problem 8520

$0 \le t \le 10$ $x_P(t)$ $x_Q(t)$ $v_Q(t)$ $a_Q(t)$
d) For $0 \le t \le 10$ , particles P and Q move along the x axis. The position of particle P can be modeled by $x_P(t)$ as shown in the figure above. The position of particle Q is defined by $x_Q(t)$ . Selected values of $x_Q(t)$ , $v_Q(t)$ , and $a_Q(t)$ are given in the table above. At what time $t$ are particles P and Q moving towards each other?

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Problem 8521

Evaluate the given definite integral. $\int_{-5}^{3} (3w - 4)(5w + 1) dw =$

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Problem 8522

If the demand function for math anxiety pills is $p = D(x) = \sqrt{16 - 2x}$ , determine the consumer surplus at the market price of $\$2$ dollars.
Consumer surplus = ______ dollars Submit Answer

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Problem 8523

Determine the following limit. $\lim_{w \to \infty} \frac{10w^2 + 7w + 3}{\sqrt{25w^4 + 5w^3}}$
Select the correct choice, and, if necessary, fill in the answer box to complete your choice. A. \lim_{w \to \infty} \frac{10w^2 + 7w + 3}{\sqrt{25w^4 + 5w^3}} = \text{________} (Simplify your answer.) B. The limit does not exist and is neither $\infty$ nor $-\infty$ .

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Problem 8524

A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. Complete parts (a) through (f) below. Height (inches), $x$ 27.75 27 25.5 26.5 26.75 Head Circumference (inches), $y$ 17.6 17.5 17.1 17.3 17.3
$H_0: \beta_1 = 0$ $H_1: \beta_1 \ne 0$
$H_0: \beta_0 = 0$ $H_1: \beta_0 \ne 0$
Determine the P-value for this hypothesis test. P-value $= 0.008$ (Round to three decimal places as needed.) What is the conclusion that can be drawn?
A. Do not reject $H_0$ and conclude that a linear relation does not exist between a child's height and head circumference at the level of significance $\alpha = 0.01$ . B. Reject $H_0$ and conclude that a linear relation does not exist between a child's height and head circumference at the level of significance $\alpha = 0.01$ . C. Reject $H_0$ and conclude that a linear relation exists between a child's height and head circumference at the level of significance $\alpha = 0.01$ . D. Do not reject $H_0$ and conclude that a linear relation exists between a child's height and head circumference at the level of significance $\alpha = 0.01$ .
(e) Use technology to construct a 95% confidence interval about the slope of the true least-squares regression line. Lower bound: Upper bound: (Round to three decimal places as needed.)

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Problem 8525

The population of Adamsville grew from 10,000 to 17,000 in 5 years. Assuming uninhibited exponential growth, what is the expected population in an additional 2 years? The expected population is 21,020.

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Problem 8526

Question 1 (Mandatory) (1 point) An amusement park usually charges $\$34$ per ticket, but wants to raise the price by $\$1$ per ticket. The revenue that could be generated is modelled by the function $R(x) = -125(x-12)^2 + 35\,000$ , where $x$ is the number of $\$1$ increases and the revenue, $R(x)$ , is in dollars. What should the ticket price be if the park wants to earn $\$15\,000$ ?

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Problem 8527

Question 3 (Mandatory) (1 point) Saved The population of a village can be modelled by the function $P(x) = -22.5x^2 + 428x + 1100$ , where x is the number of years since 1990. According to the model, when will the population be the highest?

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Problem 8528

Question 5 4 pts The business manager of a company that produces in-ground outdoor spas determines that the cost (in dollars) of producing $x$ spas in thousands of dollars is given by $C(x) = 0.04x^2 + 4.1x + 100$ Find the average rate of change in cost if production is changed from 10 in-ground outdoor spas to 11 in-ground outdoor spas. \$4,994 \$149,940 \$4,940 \$145,000

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Problem 8529

Question 6 (Mandatory) (1 point) A rocket is launched into the sky and follows a path modelled by the function $h(t) = -5(t-6.32)^2 + 200$ , where time, $t$ , is in seconds and height, $h(t)$ , is in metres. Approximately how high will the rocket be after 9 seconds?

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Problem 8530

Question 7 (Mandatory) (1 point) If a problem requires you to determine the value of the independent variable, $x$ , for a given value of the dependent variable, $f(x)$ , then substitute the number in for

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Problem 8531

Question 11 (Mandatory) (1 point) Determine which coordinate is the vertex of $f(x) = 4x^2 - 8x + 11$ without graphing the parabola.

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Problem 8532

Given a demand schedule, if the price is \$20, what could be the quantity demanded (Q1) if demand law holds? Options: 0, 100, 200, 400.

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Problem 8533

Find the limit as $x$ approaches 3 for the expression $5x^{2} + 4x + 2$ .

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Problem 8534

Evaluate the limit: $\lim _{x \rightarrow 196} \frac{\sqrt{x}-14}{x-196}$ to three decimal places or state DNE.

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Problem 8535

Find $f(99)$ given the function $f(x)=5-\frac{x}{99}$ .

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Problem 8536

Find the average rate of change of $f(t)=t^{2}-2t$ from $t=2$ to $t=5$ . Show your work.

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Problem 8537

$\sin 19^{\circ} = \cos(71)$ (since $71 = 90 - 19$ ).

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Problem 8538

Rewrite $\sec 77^{\circ}$ using its cofunction. What is the simplified answer? $\sec 77^{\circ}=\square$

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Problem 8539

Find the wavelength of light in mm with a frequency of 645 MHz. Provide the answer in mm to 3 significant figures.

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Problem 8540

Rewrite $\cot 18.6^{\circ}$ using its cofunction. What is $\cot 18.6^{\circ}=$ ? (Provide a simplified answer without the degree symbol.)

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Problem 8541

Find the wavelength of a photon with energy $6.89 \times 10^{-19} \mathrm{~J}$ .

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Problem 8542

Express $\sin \left(\alpha+10\right)$ using its cofunction for acute angles. Simplify your answer.

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Problem 8543

Find the energy of a photon with a wavelength of $999 \mu \mathrm{m}$ .

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Problem 8544

Express $\sec \left(\beta+20\right)$ using cofunctions for acute angles. Simplify your answer.

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Problem 8545

Find the limit: $\lim_{x \rightarrow -6} \frac{x+6}{x^{2}+x-30}$ and give your answer to three decimal places.

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Problem 8546

Express $\sec(\alpha + 10)$ using its cofunction for acute angles. Simplify your answer without the degree symbol.

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Problem 8547

Solve the equation for acute angles: $\sec \alpha=\csc \left(\alpha+10^{\circ}\right)$ . Find $\alpha=$ (integer or decimal).

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Problem 8548

Find the one-sided limit: $\lim _{x \rightarrow 0^{-}} \frac{2 \sin (x)}{3|x|}$ to three decimal places.

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Problem 8549

Find the frequency of light with a wavelength of $576 \mathrm{~nm}$ . Round to 3 significant figures, use scientific notation if needed.

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Problem 8550

Find the one-sided limit: $\lim _{x \rightarrow 7^{+}} \frac{x+9}{x-7}=$ (Enter DNE if it doesn't exist.)

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Problem 8551

Solve for acute angle $\beta$ in the equation: $\sec(4\beta - 25^{\circ}) = \csc(2\beta + 7^{\circ})$ .

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Problem 8552

Solve for $\beta$ in the equation: $\sec(4\beta - 25^\circ) = \csc(2\beta + 7^\circ)$ , where all angles are acute.

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Problem 8553

Find the exact value of $\tan 30^{\circ}$ . Simplify your answer using integers, fractions, or radicals.

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Problem 8554

Calculate the exact value of $\sec 30^{\circ}$ . Simplify your answer with integers or fractions.

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Problem 8555

Plot the function and estimate the limit value: $\lim _{x \rightarrow 0} \frac{\sin (2 x)}{\sin (4 x)}=$ (two decimal places).

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Problem 8556

Find the left and right limits of $\frac{7 x}{x-2}$ as $x$ approaches 2: $\lim _{x \rightarrow 2^{+}}$ and $\lim _{x \rightarrow 2^{-}}$ .

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Problem 8557

How much energy is in $2.50 \mathrm{~mol}$ of UV light at $235 \mathrm{~nm}$ ?

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Problem 8558

Calculate the number of photons in a laser pulse with energy $5.98 \mathrm{~mJ}$ and wavelength $675 \mathrm{~nm}$ .

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Problem 8559

Calculate the area between the curves $y=x^{3}-x$ and $y=3x$ . Area = ?

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Problem 8560

Graph the piecewise function $f(x)=\left\{\begin{aligned} x, & x<\frac{1}{2} \\ 3 x-1, & x \geq \frac{1}{2} .\end{aligned}\right.$ and find its domain and range.

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Problem 8561

Find the point on $g(t)$ if $(1,90)$ on $f(t)$ is translated 2 units right and reflected over the $x$ -axis.

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Problem 8562

In March, the website had 45125 views, which is $5\%$ less than February's views. Find January's views.

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Problem 8563

Solve for $g$ and $h$ in the equation $g(y h+b)=e+q$ . Find $g=$ and $h=$ .

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Problem 8564

Find $g(f(5 x))$ for $f(x)=2 x-1$ and $g(x)=3 x^{2}-7$ . Choose from: A, B, C, D.

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Problem 8565

Which function has a removable discontinuity at $x=-2$ and a non-removable one at $x=-1$ ? A) $f(x)=\frac{x+1}{x^{2}+3 x+2}$ B) $f(x)=\frac{x-1}{x^{2}+3 x+2}$ C) $f(x)=\frac{x+2}{x^{2}+3 x+2}$ D) $f(x)=\frac{x-2}{x^{2}+3 x+2}$

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Problem 8566

Find $g(f(5 x))$ for $f(x)=2 x-1$ and $g(x)=3 x^{2}-7$ . Choices: A. $150 x^{2}-15$ B. $300 x^{2}-60 x-4$ C. $60 x^{3}-60 x^{2}-20 x$ D. $750 x^{3}-75 x^{2}-70 x+7$ E. $30 x^{4}-15 x^{3}-70 x^{2}+35 x$

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Problem 8567

Compare two phone plans: Family Plan ( $81 + 46P$ ) and Mobile Share Plan ( $129 + 34P$ ). Find when costs are equal and which is better for 5 devices.

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Problem 8568

Compare two phone plans: Family Plan (\$81 + \$46P) vs. Mobile Share Plan (\$129 + \$34P). Find when costs equal and best for 5 devices.

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Problem 8569

Evaluate $f(x)=-x^{2}-5$ for $f(2)$ and $f(-1)$ . Find $f(2)=\square$ and $f(-1)=\square$ .

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Problem 8570

Given the function $f(x) = 0.4x^2 - 36x + 1000$ for drivers aged 16-74:
1. Calculate and simplify $f(50)$ .
2. Explain $f(50)$ as accidents per 50 million miles for 50-year-olds.
3. Describe $f(50)$ as a point on the graph of $f(x)$ .

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Problem 8571

A vehicle goes 25 mph and speeds up by 3 mph each second. Is it legal after 7 seconds?

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Problem 8572

What is the new water level in mL after adding 7.25 g of silver to 11.8 mL of water? Use the density of silver: $10.5 \mathrm{~g} / \mathrm{cm}^{3}$ .

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Problem 8573

Find a linear function $p(x)$ for the percentage of budget spent on food, starting at $25\%$ in 1950, decreasing $0.30\%$ per year.

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Problem 8574

Find a linear function $p(x)$ for the percentage spent on groceries, starting at $25\%$ in 1950 and decreasing by $0.30\%$ per year.

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Problem 8575

An entrepreneur's costs include \$28,750 plus \$1,900 per performance. Revenue from each sold-out show is \$2,525.
a. Cost function: $C(x)=$ b. Revenue function: $R(x)=$ c. Find the break-even point and explain its meaning.

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Problem 8576

Let $x$ be sold-out performances.
a. Cost function: $C(x)=28750+1900x$ . b. Revenue function: $R(x)=2525x$ . c. Find break-even point and explain its meaning. Choose A, B, or C to describe it.

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Problem 8577

Find cost $C(x)=28750+1900x$ , revenue $R(x)=2525x$ , and the break-even point. Explain its meaning.

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Problem 8578

A handyman company wants to place an office between Jonesville and Bellevue, 60 miles apart. With weights of 3 for Jonesville and 5 for Bellevue, how far from Bellevue should the office be? $d = \frac{5}{3+5} \times 60$ miles.

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Problem 8579

Evaluate $E(22)$ for the function $E(x)=\sqrt{4x+33}$ . What is $E(22)$ ?

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Problem 8580

Calculate $E(82)^{E(22)-8}$ where $E(x)=\sqrt{4x+33}$ .

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Problem 8581

Graph the function $f(x)=\left\{\begin{array}{ccc}\frac{1}{2} x & \text { if } & x \leq 0 \\ 3 & \text { if } & x>0\end{array}\right.$ and find its range.

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Problem 8582

Evaluate $E(82)$ where $E(82)=\sqrt{4(82)+33}$ .

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Problem 8583

Evaluate $F(5)$ , $F(-7)$ , and find $F(5) \cdot F(-7)$ where $F(x) = |x^3|$ .

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Problem 8584

Leila buys a dinosaur model for $x$ dollars plus $7\%$ tax. Which expressions show her total cost? Choose 2: A $\frac{107}{100} x$ B $0.7 x+x$ C $1.07 x$ D $x+\frac{7}{10} x$ E $1.7 x$

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Problem 8585

Compare costs of two phone plans: Family Plan: \$98 + \$39P; Mobile Share Plan: \$122 + \$35P. Find when costs equal.

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Problem 8586

Compare costs of two phone plans: Family Plan: \$98 + \$39P (up to 5 lines) vs. Mobile Share Plan: \$122 + \$35P (up to 10 lines). Find P for equal costs and recommend for 5 devices.

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Problem 8587

Graph the piecewise function $f(x) = \begin{cases} 0 & \text{if } x < -4 \\ -x & \text{if } -4 \leq x < 0 \\ x^2 & \text{if } x \geq 0 \end{cases}$ and find its range.

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Problem 8588

Ann used 80 g of cheese after a $60\%$ increase. How much cheese was originally needed in the recipe?

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Problem 8589

Compare wireless plans: Family Plan: \$98 + \$39P; Mobile Share Plan: \$122 + \$35P. Find P for equal cost and best for 5 devices.

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Problem 8590

Evaluate $G(-1)$ , $G(2)$ , and compute $[G(-1)]^{3}-[G(2)]^{2}+4 \cdot G(-1)=20$ .

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Problem 8591

Find the range of the function $f(x) = \begin{cases} 0 & \text{if } x \leq -4 \\ -x & \text{if } -4 < x < 0 \\ x^2 & \text{if } x \geq 0 \end{cases}$ .

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Problem 8592

Find the value of $\frac{{[G(-1)]^{3} - [G(2)]^{2} + 4 \cdot G(-1)}}{10}$ given $G(-1) = 20$ and $G(2) = -10$ .

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Problem 8593

Simplify the difference quotient for $f(x)= 3x + 7$ : $\frac{f(x+h)-f(x)}{h}$ , where $h \neq 0$ .

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Problem 8594

Find and simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ for the functions: 71. $f(x)=4x$ , 72. $f(x)=7x$ .

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Problem 8595

Calculate the cost to drive 150 miles at 23 mpg with gas at 327 cents/gal. Find the formula $C(m, g, d)$ . Then, find cost for 188 miles at 28 mpg and \$3.77/gal.

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Problem 8596

What is the domain of the ticket sales function if a theater sells up to 10 tickets? Options: 1. $[0, 10]$ 2. All integers 3. Whole numbers $[0, 10]$ 4. All real numbers.

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Problem 8597

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ for $f(x) = x^2 - 4x + 3$ , with $h \neq 0$ .

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Problem 8598

Calculate the cost to drive 150 miles with 23 mpg and gas at 327 cents/gallon. Also, find the cost formula $C(m, g, d)$ . Then, use it for 28 mpg over 188 miles at \$3.77/gallon.

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Problem 8599

Find the limit: $\lim _{x \rightarrow 2^{+}} \frac{x-6}{(x-2)^{2}}$ .

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Problem 8600

A man has stock worth \$2800. It drops by 8% and then gains 8% back. What is the stock's value after two days?

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1 ...83 84 85 86 87 88 89 ...103

Function

Problem 8501

Problem 8502

Problem 8503

Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius rrr. List the dimensions in non-decreasing order (the answer may depend on rrr).

Problem 8504

Find the point P on the graph of the function y=xy = \sqrt{x}y=x​ closest to the point (2,0)(2, 0)(2,0) The xxx coordinate of P is:

Problem 8505

∫cos⁡(3tan⁡θ)dθ\int \cos (3 \tan \theta) d \theta∫cos(3tanθ)dθ

Problem 8506

Problem 8507

Problem 8508

Given f(x,y)=3x5+2xy3+4y2f(x, y) = 3x^5 + 2xy^3 + 4y^2f(x,y)=3x5+2xy3+4y2, findfx(x,y)=f_x(x, y) =fx​(x,y)=fy(x,y)=f_y(x, y) =fy​(x,y)=

Problem 8509

Problem 8510

Find the average rate of change of g(x)=−2x2−2xg(x)=-2 x^{2}-2 xg(x)=−2x2−2x from x=−4x=-4x=−4 to x=1x=1x=1. Simplify your answer as much as possible.

Problem 8511

69.∫ee4dxxln⁡x69. \int_{e}^{e^4} \frac{dx}{x\sqrt{\ln{x}}}69.∫ee4​xlnx​dx​

Problem 8512

f(x)=−x5+3x3−3xf(x) = -x^5 + 3x^3 - 3xf(x)=−x5+3x3−3x

Problem 8513

Problem 8514

Problem 8515

Problem 8516

x(t)=at+bx(t) = at + bx(t)=at+b, where aaa and bbb are both nonzero.Find the acceleration of the bug at any given time ttt.

Problem 8517

Find the value of (f∘g)(2)(f \circ g)(2)(f∘g)(2) f(x)=5x+2f(x) = 5x + 2f(x)=5x+2 and g(x)=3x−4g(x) = 3x - 4g(x)=3x−4

Problem 8518

Problem 8519

Problem 8520

Problem 8521

Evaluate the given definite integral. ∫−53(3w−4)(5w+1)dw=\int_{-5}^{3} (3w - 4)(5w + 1) dw = ∫−53​(3w−4)(5w+1)dw=

Problem 8522

If the demand function for math anxiety pills is p=D(x)=16−2xp = D(x) = \sqrt{16 - 2x}p=D(x)=16−2x​, determine the consumer surplus at the market price of $2\$2$2 dollars.Consumer surplus = ______ dollars Submit Answer

Problem 8523

Problem 8524

Problem 8525

The population of Adamsville grew from 10,000 to 17,000 in 5 years. Assuming uninhibited exponential growth, what is the expected population in an additional 2 years? The expected population is 21,020.

Problem 8526

Problem 8527

Question 3 (Mandatory) (1 point) Saved The population of a village can be modelled by the function P(x)=−22.5x2+428x+1100P(x) = -22.5x^2 + 428x + 1100P(x)=−22.5x2+428x+1100, where x is the number of years since 1990. According to the model, when will the population be the highest?

Problem 8528

Problem 8529

Problem 8530

Question 7 (Mandatory) (1 point) If a problem requires you to determine the value of the independent variable, xxx, for a given value of the dependent variable, f(x)f(x)f(x), then substitute the number in for

Problem 8531

Question 11 (Mandatory) (1 point) Determine which coordinate is the vertex of f(x)=4x2−8x+11f(x) = 4x^2 - 8x + 11f(x)=4x2−8x+11 without graphing the parabola.

Problem 8532

Given a demand schedule, if the price is \$20, what could be the quantity demanded (Q1) if demand law holds? Options: 0, 100, 200, 400.

Problem 8533

Find the limit as xxx approaches 3 for the expression 5x2+4x+25x^{2} + 4x + 25x2+4x+2.

Problem 8534

Evaluate the limit: lim⁡x→196x−14x−196\lim _{x \rightarrow 196} \frac{\sqrt{x}-14}{x-196}x→196lim​x−196x​−14​ to three decimal places or state DNE.

Problem 8535

Find f(99)f(99)f(99) given the function f(x)=5−x99f(x)=5-\frac{x}{99}f(x)=5−99x​.

Problem 8536

Find the average rate of change of f(t)=t2−2tf(t)=t^{2}-2tf(t)=t2−2t from t=2t=2t=2 to t=5t=5t=5. Show your work.

Problem 8537

sin⁡19∘=cos⁡(71)\sin 19^{\circ} = \cos(71)sin19∘=cos(71) (since 71=90−1971 = 90 - 1971=90−19).

Problem 8538

Rewrite sec⁡77∘\sec 77^{\circ}sec77∘ using its cofunction. What is the simplified answer? sec⁡77∘=□\sec 77^{\circ}=\squaresec77∘=□

Problem 8539

Find the wavelength of light in mm with a frequency of 645 MHz. Provide the answer in mm to 3 significant figures.

Problem 8540

Rewrite cot⁡18.6∘\cot 18.6^{\circ}cot18.6∘ using its cofunction. What is cot⁡18.6∘=\cot 18.6^{\circ}=cot18.6∘=? (Provide a simplified answer without the degree symbol.)

Problem 8541

Find the wavelength of a photon with energy 6.89×10−19 J6.89 \times 10^{-19} \mathrm{~J}6.89×10−19 J.

Problem 8542

Express sin⁡(α+10)\sin \left(\alpha+10\right)sin(α+10) using its cofunction for acute angles. Simplify your answer.

Problem 8543

Find the energy of a photon with a wavelength of 999μm999 \mu \mathrm{m}999μm.

Problem 8544

Express sec⁡(β+20)\sec \left(\beta+20\right)sec(β+20) using cofunctions for acute angles. Simplify your answer.

Problem 8545

Find the limit: lim⁡x→−6x+6x2+x−30\lim_{x \rightarrow -6} \frac{x+6}{x^{2}+x-30}limx→−6​x2+x−30x+6​ and give your answer to three decimal places.

Problem 8546

Express sec⁡(α+10)\sec(\alpha + 10)sec(α+10) using its cofunction for acute angles. Simplify your answer without the degree symbol.

Problem 8547

Solve the equation for acute angles: sec⁡α=csc⁡(α+10∘)\sec \alpha=\csc \left(\alpha+10^{\circ}\right)secα=csc(α+10∘). Find α=\alpha=α= (integer or decimal).

Problem 8548

Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius $r$ . List the dimensions in non-decreasing order (the answer may depend on $r$ ).

Find the point P on the graph of the function $y = \sqrt{x}$ closest to the point $(2, 0)$ The $x$ coordinate of P is:

$\int \cos (3 \tan \theta) d \theta$

Given $f(x, y) = 3x^5 + 2xy^3 + 4y^2$ , find
$f_x(x, y) =$
$f_y(x, y) =$

Find the average rate of change of $g(x)=-2 x^{2}-2 x$ from $x=-4$ to $x=1$ . Simplify your answer as much as possible.

$69. \int_{e}^{e^4} \frac{dx}{x\sqrt{\ln{x}}}$

$f(x) = -x^5 + 3x^3 - 3x$

$x(t) = at + b$ , where $a$ and $b$ are both nonzero.
Find the acceleration of the bug at any given time $t$ .

Find the value of $(f \circ g)(2)$ $f(x) = 5x + 2$ and $g(x) = 3x - 4$

Evaluate the given definite integral. $\int_{-5}^{3} (3w - 4)(5w + 1) dw =$

If the demand function for math anxiety pills is $p = D(x) = \sqrt{16 - 2x}$ , determine the consumer surplus at the market price of $\$2$ dollars.
Consumer surplus = ______ dollars Submit Answer

Question 3 (Mandatory) (1 point) Saved The population of a village can be modelled by the function $P(x) = -22.5x^2 + 428x + 1100$ , where x is the number of years since 1990. According to the model, when will the population be the highest?

Question 7 (Mandatory) (1 point) If a problem requires you to determine the value of the independent variable, $x$ , for a given value of the dependent variable, $f(x)$ , then substitute the number in for

Question 11 (Mandatory) (1 point) Determine which coordinate is the vertex of $f(x) = 4x^2 - 8x + 11$ without graphing the parabola.

Find the limit as $x$ approaches 3 for the expression $5x^{2} + 4x + 2$ .

Evaluate the limit: $\lim _{x \rightarrow 196} \frac{\sqrt{x}-14}{x-196}$ to three decimal places or state DNE.

Find $f(99)$ given the function $f(x)=5-\frac{x}{99}$ .

Find the average rate of change of $f(t)=t^{2}-2t$ from $t=2$ to $t=5$ . Show your work.

$\sin 19^{\circ} = \cos(71)$ (since $71 = 90 - 19$ ).

Rewrite $\sec 77^{\circ}$ using its cofunction. What is the simplified answer? $\sec 77^{\circ}=\square$

Rewrite $\cot 18.6^{\circ}$ using its cofunction. What is $\cot 18.6^{\circ}=$ ? (Provide a simplified answer without the degree symbol.)

Find the wavelength of a photon with energy $6.89 \times 10^{-19} \mathrm{~J}$ .

Express $\sin \left(\alpha+10\right)$ using its cofunction for acute angles. Simplify your answer.

Find the energy of a photon with a wavelength of $999 \mu \mathrm{m}$ .

Express $\sec \left(\beta+20\right)$ using cofunctions for acute angles. Simplify your answer.

Find the limit: $\lim_{x \rightarrow -6} \frac{x+6}{x^{2}+x-30}$ and give your answer to three decimal places.

Express $\sec(\alpha + 10)$ using its cofunction for acute angles. Simplify your answer without the degree symbol.

Solve the equation for acute angles: $\sec \alpha=\csc \left(\alpha+10^{\circ}\right)$ . Find $\alpha=$ (integer or decimal).

Find the one-sided limit: $\lim _{x \rightarrow 0^{-}} \frac{2 \sin (x)}{3|x|}$ to three decimal places.

Find the frequency of light with a wavelength of $576 \mathrm{~nm}$ . Round to 3 significant figures, use scientific notation if needed.

Find the one-sided limit: $\lim _{x \rightarrow 7^{+}} \frac{x+9}{x-7}=$ (Enter DNE if it doesn't exist.)

Solve for acute angle $\beta$ in the equation: $\sec(4\beta - 25^{\circ}) = \csc(2\beta + 7^{\circ})$ .

Solve for $\beta$ in the equation: $\sec(4\beta - 25^\circ) = \csc(2\beta + 7^\circ)$ , where all angles are acute.

Find the exact value of $\tan 30^{\circ}$ . Simplify your answer using integers, fractions, or radicals.

Calculate the exact value of $\sec 30^{\circ}$ . Simplify your answer with integers or fractions.

Plot the function and estimate the limit value: $\lim _{x \rightarrow 0} \frac{\sin (2 x)}{\sin (4 x)}=$ (two decimal places).

Find the left and right limits of $\frac{7 x}{x-2}$ as $x$ approaches 2: $\lim _{x \rightarrow 2^{+}}$ and $\lim _{x \rightarrow 2^{-}}$ .

How much energy is in $2.50 \mathrm{~mol}$ of UV light at $235 \mathrm{~nm}$ ?

Calculate the number of photons in a laser pulse with energy $5.98 \mathrm{~mJ}$ and wavelength $675 \mathrm{~nm}$ .

Calculate the area between the curves $y=x^{3}-x$ and $y=3x$ . Area = ?

Graph the piecewise function $f(x)=\left\{\begin{aligned} x, & x<\frac{1}{2} \\ 3 x-1, & x \geq \frac{1}{2} .\end{aligned}\right.$ and find its domain and range.

Find the point on $g(t)$ if $(1,90)$ on $f(t)$ is translated 2 units right and reflected over the $x$ -axis.

In March, the website had 45125 views, which is $5\%$ less than February's views. Find January's views.

Solve for $g$ and $h$ in the equation $g(y h+b)=e+q$ . Find $g=$ and $h=$ .

Find $g(f(5 x))$ for $f(x)=2 x-1$ and $g(x)=3 x^{2}-7$ . Choose from: A, B, C, D.

Compare two phone plans: Family Plan ( $81 + 46P$ ) and Mobile Share Plan ( $129 + 34P$ ). Find when costs are equal and which is better for 5 devices.

Evaluate $f(x)=-x^{2}-5$ for $f(2)$ and $f(-1)$ . Find $f(2)=\square$ and $f(-1)=\square$ .

Given the function $f(x) = 0.4x^2 - 36x + 1000$ for drivers aged 16-74:
1. Calculate and simplify $f(50)$ .
2. Explain $f(50)$ as accidents per 50 million miles for 50-year-olds.
3. Describe $f(50)$ as a point on the graph of $f(x)$ .

What is the new water level in mL after adding 7.25 g of silver to 11.8 mL of water? Use the density of silver: $10.5 \mathrm{~g} / \mathrm{cm}^{3}$ .

Find a linear function $p(x)$ for the percentage of budget spent on food, starting at $25\%$ in 1950, decreasing $0.30\%$ per year.

Find a linear function $p(x)$ for the percentage spent on groceries, starting at $25\%$ in 1950 and decreasing by $0.30\%$ per year.