Browse Function problems Studdy Solved!

Problem 5701

$\lim _{x \rightarrow-\infty} \frac{-x^{2}+e x}{x-1}-\ln \left(e^{-x}+1\right)$

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Problem 5702

Compute $z$ for the percentile given: $\boldsymbol{P}_{\mathbf{4 3}} \mathbf{( 4 3 ^ { \text { th } }}$ percentile $)$ Table for required value of $z$

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Problem 5703

Suppose that the functions $f$ and $g$ are defined for all real numbers $x$ as follows. $\begin{array}{l} f(x)=3 x^{2} \\ g(x)=x^{3} \end{array}$
Write the expressions for $(f+g)(x)$ and $(f-g)(x)$ and evaluate $(f \cdot g)(-1)$ . $\begin{array}{l} (f+g)(x)= \\ (f-g)(x)= \\ (f \cdot g)(-1)= \end{array}$ $\square$ $\square$ $\square$

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Problem 5704

Suppose that the functions $s$ and $t$ are defined for all real numbers $x$ as follows. $\begin{array}{l} s(x)=4 x \\ t(x)=3 x-1 \end{array}$
Write the expressions for $(s \cdot t)(x)$ and $(s+t)(x)$ and evaluate $(s-t)(-2)$ . $\begin{array}{r} (s \cdot t)(x)= \\ (s+t)(x)= \\ (s-t)(-2)= \end{array}$ $\square$ $\square$ $\square$

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Problem 5705

Click on the word/phrase that would correctly complete the sentence.
You $\qquad$ take the log of a negative number. can cannot will Should not

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Problem 5706

The expected value of random variable $X$ a. is the same as the median b. Exists if the random variable is limited c. always exists d. Is well defined if $\mathbb{E}|X|<\infty$

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Problem 5707

A particle moves along the $x$ -axis so that at time $t \geq 0$ its position is given by $x(t)=t^{3}-6 t^{2}+33$ . Determine the total distance traveled by the particle from $0 \leq t \leq 5$ .

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Problem 5708

A particle moves along the $x$ -axis with velocity given by $v(t)=4 \pi \cos (\pi t)$ for time $t \geq 0$ . If the particle is at position $x=1$ at time $t=2$ , what is the position of the particle at time $t=\frac{5}{6}$ ?

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Problem 5709

$g(x) = \frac{2x+5}{x-1}$
اشتق $g$

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Problem 5710

S4N $7: 01$ 24 Nov 2024 at 17:2...
Hwi If $\psi(x)=A \sin \frac{\pi x}{9} e^{-\frac{E_{0} t}{\hbar} t} 0 \leqslant x \leqslant 9$ (1) $A=$ ? (normalizatron) (2) $\left\langle P_{x}\right\rangle$ (3) $\langle E\rangle$ (4) $\langle x\rangle$

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Problem 5711

C/Jsers/ahmad/Downloads/4507091111202211\%20(1).pdf 9) If $f(x)=\left\{\begin{array}{ll}\frac{x^{2}-9}{x+3} & x \neq-3 \\ c & x=-3\end{array}\right.$
If $f(x)$ is continuous for all $x \in R$ , then $c=$ a) 3 b) 6 c) 0 d) -6 10) If $y=7$ is a horizontal asymptote of a rational function $f(x)$ , then which of the following must be true : a) $\lim _{x \rightarrow 7} f(x)=\infty$ b) $\lim _{x \rightarrow \infty} f(x)=7$ c) $\lim _{x \rightarrow 0} f(x)=7$ d) $\lim _{x \rightarrow 7} f(x)=0$

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Problem 5712

Select all of the following tables which represent $y$ as a function of $x$ and are one-to-one.
\begin{tabular}{|r|r|r|r|} \hline $x$ & 4 & 6 & 11 \\ \hline $y$ & 5 & 10 & 13 \\ \hline \end{tabular}
\begin{tabular}{|r|r|r|r|} \hline $x$ & 4 & 6 & 6 \\ \hline $y$ & 5 & 10 & 13 \\ \hline \end{tabular}
\begin{tabular}{|r|r|r|r|} \hline $x$ & 4 & 6 & 11 \\ \hline $y$ & 5 & 10 & 10 \\ \hline \end{tabular}

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Problem 5713

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For the linear function $f(x)=2-\frac{1}{6} x$ ; (a) evaluate $f(-6)$ and $f(12)$ ; (b) find the zero of $f$ ; and $(c)$ graph $f$ . How can the graph of $f$ be used to determine the zero of $f$ ? (a) $f(-6)=$ $\square$ (Type an integer or a simplified fraction.) $f(12)=$ $\square$ (Type an integer or a simplified fraction.) (b) The zero of $f$ is $\square$ . (Type an integer or a simplified fraction.) (c) Choose the correct graph below. A. B. c. D.
How can the graph of $f$ be used to determine the zero of $f$ ? A. Determine the zero of $f$ by finding the $y$ -coordinate of the point where the line intersects the $y$ -axis. B. Determine the zero of $f$ by finding the $x$ -coordinate of the point where the line intersects the $y$ -axis. C. Determine the zero of $f$ by finding the $y$ -coordinate of the point where the line intersects the $x$ -axis. D. Determine the zero of $f$ by finding the $x$ -coordinate of the point where the line intersects the $x$ -axis.

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Problem 5714

Enter your answer as a fraction or as a number rounded to three decimal places. Find the area bounded by the graphs of $y=x^{2}$ and $y=32-x^{2}$ for $0 \leq x \leq 9$ . Area = $\square$

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Problem 5715

Write an equation (any form) for the quadratic graphed below $y=\square$

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Problem 5716

Question 10
A population numbers 14,000 organisms initially and decreases by $9 \%$ each year. A) Suppose $P$ represents population, and $t$ the number of years of decrease. Write an exponential model to represent this situation. $P=$ B) What will the population $P$ be in 13 years? Round to two decimal places. $P=$ Question Help: Video 1 Video 2 Message instructor Post to forum Submit Question

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Problem 5717

Graph $f(x)=x^{2}-8 x+15$ below by first selecting the correct shape, clicking the vertex, then clicking an $x$ -Intercept. Clear All Draw:

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Problem 5718

$\int \frac{1}{v(\operatorname{Ln} v-1)} d v$

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Problem 5719

Problem 4: (6 points) Determine a Horton equation to fit the following times and infiltration capacities. \begin{tabular}{|lc|} \hline \begin{tabular}{l} Time \\ $(\mathbf{h r})$ \end{tabular} & \begin{tabular}{c} $\boldsymbol{f}$ \\ $(\mathbf{i n} . / \mathrm{hr})$ \end{tabular} \\ \hline 1 & 6.34 \\ 2 & 5.20 \\ 6.5 & 2.50 \\ $\infty$ & 1.20 \\ \hline \end{tabular}

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Problem 5720

For Exercises 25-30, assume that $\theta$ is an acute angle. (See Example 2)
25. If $\cos \theta=\frac{\sqrt{21}}{7}$ , find $\csc \theta$ .
26. If $\sin \theta=\frac{\sqrt{17}}{17}$ , find $\cot \theta$ .
27. If $\sec \theta=\frac{3}{2}$ , find $\sin \theta$ .
28. If $\csc \theta=3$ , find $\cos \theta$ .
29. If $\tan \theta=\frac{\sqrt{15}}{9}$ , find $\cos \theta$ .
30. If $\cot \theta=\frac{\sqrt{3}}{2}$ , find $\cos \theta$ .
Objective 3: Determine Trigonometric Function Values for Speçal Angles For Exercise 31, use the isosceles right triangle and the $30^{\circ}-60^{\circ}-90^{\circ}$ triangle to complete the table. (See Examples 3-4) 31. \begin{tabular}{|c|c|c|c|c|c|c|} \hline $\theta$ & $\sin \theta$ & $\cos \theta$ & $\tan \theta$ & $\csc \theta$ & $\sec \theta$ & $\cot \theta$ \\ \hline $30^{\circ}=\frac{\pi}{6}$ & & & & & & \\ \hline $45^{\circ}=\frac{\pi}{4}$ & & & & & $-\vdots$ \\ \hline $60^{\circ}=\frac{\pi}{3}$ & & & & & & \\ \hline \end{tabular}
32. a. Evaluate $\sin 60^{\circ}$ . b. Evaluate $\sin 30^{\circ}+\sin 30^{\circ}$ .

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Problem 5721

\begin{align}
1. & \quad f(x) = 3\left(e^{x} + e^{-x}\right) \\
3. & \quad f(w) = \frac{e^{w} + 2}{e^{w}} \\
5. & \quad f(x) = 2 e^{3x-1} \end{align}

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Problem 5722

Question 11 (1 point) A research lab recorded the radioactive decay of a 120 mg sample of uranium-239. The data table shows the amount of uranium-239 remaining at various times. \begin{tabular}{|c|c|c|c|c|c|} \hline Minutes & 0 & 30 & 60 & 90 & 120 \\ \hline \begin{tabular}{c} Amount of \\ Uranium (mg) \end{tabular} & 120.0 & 49.5 & 20.4 & 8.4 & 3.5 \\ \hline \end{tabular} a) Create a scatter plot, and draw a curve of best fit for the data using exponential regression. b) Use your graph to estimate the half-life of uranium-239.

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Problem 5723

For the linear function $f(x)=2-\frac{1}{3} x$ ; (a) evaluate $f(-3)$ and $f(6)$ ; (b) find the zero of $f$ ; and $(c)$ graph $f$ . How can the graph of $f$ be used to determine the zero of $f$ ? (a) $f(-3)=$ $\square$ (Type an integer or a simplified fraction.) $f(6)=$ $\square$ (Type an integer or a simplified fraction.) (b) The zero of $f$ is $\square$ . (Type an integer or a simplified fraction.) (c) Choose the correct graph below. A. B. c. D.
How can the graph of $f$ be used to determine the zero of $f$ ? A. Determine the zero of $f$ by finding the $y$ -coordinate of the point where the line intersects the $y$ -axis. B. Determine the zero of $f$ by finding the $x$ -coordinate of the point where the line intersects the $y$ -axis. C. Determine the zero of $f$ by finding the $x$ -coordinate of the point where the line intersects the $x$ -axis. D. Determine the zero of $f$ by finding the $y$ -coordinate of the point where the line intersects the $x$ -axis.

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Problem 5724

If you wanted a more accurate way to fit the trend line to the data, a method called least squares could be used. This method finds the largest distance between the data points and the trend line.
Select one: a. TRUE b. FALSE

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Problem 5725

If $s(x)=x-7$ and $t(x)=4 x^{2}-x+3$ , which expression is equivalent to $(t \circ s)(x) ?$ $4(x-7)^{2}-x-7+3$ $4(x-7)^{2}-(x-7)+3$ $\left(4 x^{2}-x+3\right)-7$ $\left(4 x^{2}-x+3\right)(x-7)$

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Problem 5726

A researcher believes, among other things, the town one lives in within the state influences the likelihood of contracting cancer. He has data from three towns and has decided to code the towns as follows $X=$ Town, where: $X=0$ if C'burg, $X=1$ if B'burg; $X=2$ if L'burg. This is an appropriate means for including qualitative data into his analysis.
Select one: a. TRUE b. FALSE

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Problem 5727

Given $f(x)=7 x$ and $g(x)=7 x^{2}+9$ , find the following expressions. (a) $(f \circ g)(4)$ (b) $(g \circ f)(2)$ (c) $(f \circ f)(1)$ (d) $(g \circ g)(0)$ (a) $(f \circ g)(4)=$ $\square$ (Simplify your answer.)

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Problem 5728

Given $f(x)=7 x$ and $g(x)=7 x^{2}+9$ , find the following expressions. (a) $(f \circ g)(4)$ (b) $(g \circ f)(2)$ (c) $(f \circ f)(1)$ (d) $(g \circ g)(0)$ (a) $(f \circ g)(4)=847 \quad$ (Simplify your answer.) (b) $(g \circ f)(2)=$ $\square$ (Simplify your answer.)

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Problem 5729

$\lim _{x \rightarrow 1} \frac{e^{x}-e}{x-1}$

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Problem 5730

$\lim _{x \rightarrow 0} \frac{1-e^{-x}}{\sin x}$

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Problem 5731

For $f(x)=\sqrt{x}$ and $g(x)=6 x+1$ , find the following composite functions and state the domain of each. (a) $f \circ g$ (b) $g \circ f$ (c) $f \circ f$ (d) $g \circ g$

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Problem 5732

For $f(x)=7 x-6$ and $g(x)=\frac{1}{7}(x+6)$ , find $(f \circ g)(x)$ and $(g \circ f)(x)$ . Then determine whether $(f \circ g)(x)=(g \circ f)(x)$ .
What is $(f \circ g)(x)$ ? $(f \circ g)(x)=$

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Problem 5733

For $f(x)=r x+s$ and $g(x)=\frac{1}{r}(x-s), r \neq 0$ , find $(f \circ g)(x)$ and $(g \circ f)(x)$ . Then determine whether $(f \circ g)(x)=(g \circ f)(x)$ .
What is $(f \circ g)(x)$ ? $(f \circ g)(x)=$

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Problem 5734

Find functions $f$ and $g$ so that $f \circ g=H$ . $H(x)=(6 x+1)^{9}$
Choose the correct pair of functions. A. $f(x)=x^{9}, g(x)=6 x+1$ c. $f(x)=6 x+1, g(x)=x^{9}$ B. $f(x)=\frac{x-1}{6}, g(x)=\sqrt[9]{x}$ D. $f(x)=\sqrt[9]{x}, g(x)=\frac{x-1}{6}$

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Problem 5735

Find functions $f$ and $g$ so that $f \circ g=H$ . $H(x)=\sqrt{x^{2}+17}$
Choose the correct pair of functions. A. $f(x)=\sqrt{x}-17, g(x)=x^{2}$ c. $f(x)=\sqrt{x}, g(x)=x^{2}+17$ B. $f(x)=x^{2}, g(x)=\sqrt{x}-17$ D. $f(x)=x^{2}+17, g(x)=\sqrt{x}$

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Problem 5736

8. Let $f:[a, b] \rightarrow \mathbb{R}$ be continuous on $[a, b]$ and differenchable in $(a, b)$ . Show that if $\lim _{x \rightarrow a} f^{\prime}(x)=A$ , then $f^{\prime}(a)$ exists and equals $A$ . [Hint: Use the definition of $f^{\prime}(a)$ and the Mean Value Theorem.]
9. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by $f(x):=2 x^{4}+x^{4} \sin (1 / x)$ for $x \neq 0$ and $f(0):=0$ . Show that $f$ has an absolute minimum at $x=0$ , but that its derivative has both positive and negative values in every neighborhood of 0 .

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Problem 5737

Complete the sentence below. If every horizontal line intersects the graph of a function at no more than one point, $f$ is $a(n)$ $\qquad$ function.
If every horizontal line intersects the graph of a function at no more than one point, $f$ is $a(n)$ $\square$ function. composite inverse one-to-one

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Problem 5738

Complete the sentence below. If $f$ is a one-to-one function and $f(9)=8$ , then $f^{-1}(8)=$ $\qquad$ .
If $f$ is a one-to-one function and $f(9)=8$ , then $f^{-1}(8)=$ $\square$ 8. 9. $\frac{1}{8}$ .

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Problem 5739

Evaluate $\lim _{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x^{2}-49}$

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Problem 5740

Complete the sentence below. If $f^{-1}$ denotes the inverse of a function $f$ , then the graphs of $f$ and $f^{-1}$ are symmetric with respect to the line $\qquad$ .
If $f^{-1}$ denotes the inverse of a function $f$ , then the graphs of $f$ and $f^{-1}$ are symmetric with respect to the line $\square$ $\begin{array}{l} y=x^{2} \\ y=x+1 \\ y=x \\ y=x^{2}+1 \end{array}$

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Problem 5741

Find the area of the shaded region. Enter your answer as a reduced fraction.

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Problem 5742

For the function on the right, determine whether the function is one-to-one.
Is the function one-to-one? Yes No

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Problem 5743

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

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Problem 5744

Find the area of the shaded region.

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Problem 5745

Consider the functions $f(x)=x^{3}-9$ and $g(x)=\sqrt[3]{x+9}$ (a) Find $f(g(x))$ . (b) Find $g(f(x))$ . (c) Determine whether the functions $f$ and $g$ are inverses of each other.

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Problem 5746

The domain of a one-to-one function $f$ is $[1, \infty)$ , and its range is $[-3, \infty)$ . State the domain and the range of $f^{-1}$ .
What is the domain of $\mathrm{f}^{-1}$ ? The domain of $\mathrm{r}^{-1}$ is $[-3, \infty)$ . (Type your answer in interval notation.) What is the range of $f^{-1}$ ? The range of $f^{-1}$ is $\square$ (Type your answer in interval notation.)

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Problem 5747

Translate each graph as specified below. (a) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=x^{2}+1$ . (b) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=(x+5)^{2}$ .

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Problem 5748

Example. $A$ sinusoidal function has an amplitude of 2 units, a period of $180^{\circ}$ and a maximum at $(0,3)$ . Write a possible equation for this function.

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Problem 5749

For the following quadratic function, (a) find the vertex, the axis of symmetry, and the maximum or minimum function value, and (b) graph the function. $f(x)=2 x^{2}-4 x+3$

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Problem 5750

The function $\mathrm{D}(\mathrm{h})=7 e^{-0.64 h}$ can be used to find the number of milligrams D of a certain drug that is in a patient's bloodstream h hours after the drug has been administered. How many milligrams will be present after 1 hour? After 11 hours?
After 1 hour, there will be $\square$ milligrams. (Round to two decimal places as needed.)

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Problem 5751

Q3: $\operatorname{For} z \in \mathbb{C}$ , show that: (a) $\sin \bar{z}=\overline{\sin z}$ ; (b) $\cosh \bar{z}=\overline{\cosh z}$ .

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Problem 5752

Monthly sales of a particular computer are expected to decline at the following rate of $S^{\prime}(t)$ computers per month, where $t$ is time in months and $S(t)$ is the number of computers sold each month. $S^{\prime}(t)=-30 t^{\frac{2}{3}}-50$
The company plans to stop manufacturing this computer when monthly sales reach 800 computers. If monthly sales now $(t=0)$ are 2,060 computers, find $\mathrm{S}(\mathrm{t})$ . Use a graphing calculator to approximate the solution of the equation $S(t)=800$ . $S(t)=$ $\square$

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Problem 5753

Find the exact value of the logarithm without using a calculator. $\log _{12} 144$ $\square$ (Type an integer or a simplified fraction.)

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Problem 5754

Find the domain of the function. $g(x)=\ln (x+9)$
The domain of g is $\square$ (Type your answer in interval notation.)

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Problem 5755

Suppose that $\mathrm{G}(\mathrm{x})=\log _{3}(2 \mathrm{x}+1)-2$ . (a) What is the domain of G ? (b) What is $\mathrm{G}(13)$ ? What point is on the graph of G ? (c) If $\mathrm{G}(\mathrm{x})=2$ , what is x ? What point is on the graph of G ? (d) What is the zero of G?

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Problem 5756

Suppose that $G(x)=\log _{3}(2 x+1)-2$ (a) What is the domain of G ? (b) What is $\mathrm{G}(13)$ ? What point is on the graph of G ? (c) If $\mathrm{G}(\mathrm{x})=2$ , what is x ? What point is on the graph of G ? (d) What is the zero of G ? (a) The domain of G is $\square$ . (Type your answer in interval notation.)

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Problem 5757

The period of is
Select one:

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Problem 5758

Step 1 of 1 $0 / 8$ Correct lowing logarithmic expression. Round off your answer to two decimal places. $\ln (\log (391))$ ur answer (opens in new window) $\square$

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Problem 5759

(1 point) The region bounded by $y=e^{-x^{2}}, y=0, x=0$ , and $x=1$ is revolved about the $y$ -axis. Find the volume of the resulting solid. Answer: $\square$

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Problem 5760

(1 point) Find the volume of the solid that results when the region bounded by $y=\sqrt{x}, y=0$ and $x=9$ is revolved about the line $x=9$ . Volume $=$ $\square$

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Problem 5761

Find the volume of the solid obtained by rotating the region bounded by the curves $y=x^{2}, \quad y=1$ about the line $y=2$ .
Answer: $\square$

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Problem 5762

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

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Problem 5763

Shown below is the graph of a force function (in newtons) that increases to its maximum value and then remains constant. How much work (in joules) is done by the force in moving the object a distance of 7.5 meters?
Work = $\square$ joules

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Problem 5764

(1 point)
A $1000-\mathrm{lb}$ wrecking ball hangs from a 50 - ft cable of density $10 \mathrm{lb} / \mathrm{ft}$ attached to a crane. Calculate the work done if the crane lifts the ball from ground level to 50 ft in the air by drawing in the cable. $W=$ $\square$ ft-lbs.

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Problem 5765

(1 point) A force of 1 pounds is required to hold a spring stretched 0.4 feet beyond its natural length. How much work (in foot-pounds) is done in stretching the spring from its natural length to 1 feet beyond its natural length? $\square$ Preview My Answers Submit Answers
You have attempted this problem 0 times

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Problem 5766

The graph shows the number of views $y$ (in thousands) for a new online video, $t$ days after it was posted. Use transformations on a parent function to model these data. Españo
Number of Views by Day Number $t$ - Day Number $y$ - Number of Views (1000s) Basic Functions Quadratic function: $y=t^{2}$ Square root function: $y=\sqrt{t}$ Absolute value function: $y=|t|$ Reciprocal function: $y=\frac{1}{t}$
Steps for Graphing Multiple Transformations of Functions To graph a function requiring multiple transformations, use the following order.
1. Horizontal translation (shift)
2. Horizontal and vertical stretch and shrink
3. Reflections across the $x$ - and $y$ -axis.
4. Vertical translation (shift) Save For Later Submit Assignment

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Problem 5767

A chain 63 meters long whose mass is 27 kilograms is hanging over the edge of a tall building and does not touch the ground. How much work is required to lift the top 5 meters of the chain to the top of the building? Use that the acceleration due to gravity is 9.8 meters per second squared. Your answer must include the correct units.
Work = $\square$

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Problem 5768

The functions $f$ and $g$ are defined $f(x)=x^{2}-x-4 \quad \text { and } \quad g(x)=\frac{x-3}{9 x-5}$
Find $f(x+8)$ and $g\left(\frac{x}{4}\right)$ . Write your answers without pare possible. $\begin{array}{l} f(x+8)= \\ g\left(\frac{x}{4}\right)=\square \end{array}$

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Problem 5769

Use the graph of $y=f(x)$ to answer the following.
Part 1 of 8 (a) Determine $f(-2)$ . $f(-2)=$ $\square$
Part 2 of 8 (b) Determine $f(3)$ . $f(3)=\square$

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Problem 5770

Español
Suppose that the function $g$ is defir $g(x)=\left\{\begin{array}{cl} -3 & \text { if } x<-1 \\ 0 & \text { if } x=-1 \\ 1 & \text { if } x>-1 \end{array}\right.$
Graph the function $g$ .

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Problem 5771

Score: 1/2 Penalty: none Linear Functions Complete: 50\%
Question Show Examples near Graph in Context (MC)
Nora needs to lease out a music studio to record her new album. The studio charges an initial studio-use fee of $\$ 100$ plus an hourly fee of $\$ 50$ . Write an equation for $P$ , in terms of $t$ , ation Given Linear Situation representing the amount of money Nora would have to pay to use the studio for $t$ hours. inear Function Coefficients Iation)

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Problem 5772

Describe the transformations of the parent function $f(x)=|x|$
1. $g(x)=-|x|+5$

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Problem 5773

\begin{problem} A plane flying at an altitude of 4 miles travels on a path directly over a radar tower.
(a) Express the distance $d(t)$ (in miles) between the plane and the tower as a function of the angle $t$ in standard position from the tower to the plane.
$d(t) = \square \csc \square \square \sin [$ \end{problem}

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Problem 5774

In Exercises 57-60, calculate the integral, assuming that $\int_{0}^{1} f(x) d x=1, \quad \int_{0}^{2} f(x) d x=4, \quad \int_{1}^{4} f(x) d x=7$
57. $\int_{0}^{4} f(x) d x$
58. $\int_{1}^{2} f(x) d x$

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Problem 5775

Find the exact value. Write your answer using a simplified fraction and rationalize the denominator, if necessary. $\cos ^{-1}\left(\cos \frac{7 \pi}{6}\right)=$ $\square$

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Problem 5776

Assume that life insurance covers a period of $n$ years from the moment the contract is signed. If the insured person dies during this period, the so-called sum insmed is paid. If death does not occur during this time, the contract ends without any payout. Suppose that the premium for this msurance is calculated as $101 \%$ of the expected value of the payout. Find the formula for the preminm if the insured person's lifetime is a random variable with an exponential distribution with parameter $\lambda>0$ , and the sum insured is $․$

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Problem 5777

The half-life of Radium-226 is 1590 years. If a sample contains 100 mg , how many mg will remain after 1000 years?

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Problem 5778

9 At practice, Cadesia swims 2 laps every 5 minutes. If she continues to swim at a constant rate, which method could be used to determine the number of minutes it takes her to swim 12 laps?
A Multiply 12 by 2.5
B Multiply 12 by 5
C Divide 12 by 2.5
D Divide 12 by 10

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Problem 5779

Find the domain of the following function. $f(x)=\frac{x+2}{x^{2}-49}$

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Problem 5780

Graph the following function on the axes provided. $f(x)=\left\{\begin{array}{lll} 5 & \text { for } & x \leq-5 \\ -x+14 & \text { for } & x>5 \end{array}\right.$
Click and drag to make a line. Click the line to delete it. Click on an endpoint of a line to change it.

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Problem 5781

The number of bacteria in a certain sample increases according to the following function, where $y_{0}$ is the initial number present, and $y$ is the number present at time $t$ (in hours). $y=y_{0} e^{0.029 t}$
How many hours does it take for the size of the sample to double? Do not round any intermediate computations, and round your answer to the nearest tenth. $\square$ hours

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Problem 5782

1. Complete the sentence below.
If the domain of a one-to-one function $f$ is $[4, \infty)$ , the range of its inverse, $f^{-1}$ , is $\qquad$ .
If the domain of a one-to-one function $f$ is $[4, \infty)$ , the range of its inverse, $f^{-1}$ , is (1) $\qquad$ (1) $[4, \infty)$ . $(-\infty, \infty)$ . $(-\infty, 4]$ .

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Problem 5783

1. The life expectancy in a demographic model is a random variable with a distribution given by the density $g(t)=\frac{\mu}{1-e^{-100 \mu}} e^{-\mu t} 1_{[0,100]}(t)$ for some parameter $\mu>0$ . Determine the median and the mean life expectancy in this model.

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Problem 5784

For the function $f(x)=5 x-1$ , find each of the following. (a) $f(p)$ $f(p)=5 p-1$ (Simplify your answer.) (b) $f(-r)$ $f(-r)=-5 r-1$ (Simplify your answer.) (c) $f(m-2)$ $f(m-2)=$ $\square$ (Simplify your answer.)

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Problem 5785

3) Evaluate $\int_{4}^{12} \frac{1}{\sqrt[3]{x-4}} d x$

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Problem 5786

2 . In Exercises 23-28, graph three periods of the function. Use your understanding of transformations, not your grapher. Be sure to show the scale on both axes.
23. $y=5 \sin 2 x$
24. $y=3 \cos \frac{x}{2}$
25. $y=0.5 \cos 3 x$
26. $y=20 \sin 4 x$

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Problem 5787

Carlos has a part-time job at an ice skating rink selling hot cocoa. He decided to plot the number of hot cocoas he sold relative to the day's high temperature and then draw the line of best fit. What does the slope of the line represent?

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Problem 5788

16 Find the slope and $y$ -intercept from the following graph of a linear equation. (A) slope $=4$ and $y$ -intercept $=3$

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Problem 5789

Two carts, $A$ and $B$ , are connected by a rope 39 ft long that passes over a pulley $P$ . The point $Q$ is on the floor 12 ft directly beneath $P$ and between the carts. Cart A is being pulled away from $Q$ at a speed of $2 \mathrm{ft} / \mathrm{s}$ . How fast is cart B moving toward $Q$ at the instant when cart A is 5 ft from $Q$ ? $\square$ $f t / s$

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Problem 5790

Solve for $x$ in the equation $a \sec x = 3$ .

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Problem 5791

Solve for $x$ if $\sec x=3$ .

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Problem 5792

Solve $9 \cot ^{2} \frac{1}{2} x=4$ for $-180^{\circ} \leq x \leq 180^{\circ}$ .

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Problem 5793

Solve $2 \operatorname{cosec}(2 x-1)=3$ for $-\pi \leq x \leq \pi$ .

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Problem 5794

Calculate the integral $\int_{1}^{5}\left(x+\frac{2}{x^{2}}\right) d x$ using the trapezium rule at $x=1,2,3,4,5$ , rounded to two decimal places.

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Problem 5795

Find the limit as $x$ approaches -2 for $\frac{x^{3}+8}{x+2}$ .

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Problem 5796

Analyze the function $f\left(x_{1}, x_{2}\right)=x_{1}^{2} x_{2}^{2}$ . Is it constant, increasing, or decreasing returns to scale?

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Problem 5797

Does Lagrange's mean value theorem apply to $f(x)=x^{1/3}$ on $[-1, 1]$ ? What can we conclude?

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Problem 5798

A ball is thrown from 5 feet high. Its height is modeled by $f(x)=-0.1 x^{2}+0.8 x+5$ . Find the max height and distance from release.

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Problem 5799

A ball is thrown from 5 feet high. Its height is given by $f(x)=-0.2 x^{2}+1.4 x+5$ . Find its max height and distance from release.

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Problem 5800

A ball is thrown from 7 feet high. Its height is modeled by $f(x)=-0.2 x^{2}+2.1 x+7$ . Find max height and distance.

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Function

Problem 5701

lim⁡x→−∞−x2+exx−1−ln⁡(e−x+1)\lim _{x \rightarrow-\infty} \frac{-x^{2}+e x}{x-1}-\ln \left(e^{-x}+1\right)limx→−∞​x−1−x2+ex​−ln(e−x+1)

Problem 5702

Compute zzz for the percentile given: P43(43 th \boldsymbol{P}_{\mathbf{4 3}} \mathbf{( 4 3 ^ { \text { th } }}P43​(43 th percentile ))) Table for required value of zzz

Problem 5703

Problem 5704

Problem 5705

Click on the word/phrase that would correctly complete the sentence.You \qquad take the log of a negative number. can cannot will Should not

Problem 5706

The expected value of random variable XXX a. is the same as the median b. Exists if the random variable is limited c. always exists d. Is well defined if E∣X∣<∞\mathbb{E}|X|<\inftyE∣X∣<∞

Problem 5707

A particle moves along the xxx-axis so that at time t≥0t \geq 0t≥0 its position is given by x(t)=t3−6t2+33x(t)=t^{3}-6 t^{2}+33x(t)=t3−6t2+33. Determine the total distance traveled by the particle from 0≤t≤50 \leq t \leq 50≤t≤5.

Problem 5708

A particle moves along the xxx-axis with velocity given by v(t)=4πcos⁡(πt)v(t)=4 \pi \cos (\pi t)v(t)=4πcos(πt) for time t≥0t \geq 0t≥0. If the particle is at position x=1x=1x=1 at time t=2t=2t=2, what is the position of the particle at time t=56t=\frac{5}{6}t=65​ ?

Problem 5709

g(x)=2x+5x−1g(x) = \frac{2x+5}{x-1}g(x)=x−12x+5​اشتق g g g

Problem 5710

Problem 5711

Problem 5712

Problem 5713

Problem 5714

Enter your answer as a fraction or as a number rounded to three decimal places. Find the area bounded by the graphs of y=x2y=x^{2}y=x2 and y=32−x2y=32-x^{2}y=32−x2 for 0≤x≤90 \leq x \leq 90≤x≤9. Area = □\square□

Problem 5715

Write an equation (any form) for the quadratic graphed below y=□y=\squarey=□

Problem 5716

Problem 5717

Graph f(x)=x2−8x+15f(x)=x^{2}-8 x+15f(x)=x2−8x+15 below by first selecting the correct shape, clicking the vertex, then clicking an xxx-Intercept. Clear All Draw:

Problem 5718

∫1v(Ln⁡v−1)dv\int \frac{1}{v(\operatorname{Ln} v-1)} d v∫v(Lnv−1)1​dv

Problem 5719

Problem 5720

Problem 5721

\begin{align*}1. & \quad f(x) = 3\left(e^{x} + e^{-x}\right) \\3. & \quad f(w) = \frac{e^{w} + 2}{e^{w}} \\5. & \quad f(x) = 2 e^{3x-1} \end{align*}

Problem 5722

Problem 5723

Problem 5724

If you wanted a more accurate way to fit the trend line to the data, a method called least squares could be used. This method finds the largest distance between the data points and the trend line.Select one: a. TRUE b. FALSE

Problem 5725

Problem 5726

Problem 5727

Problem 5728

Problem 5729

lim⁡x→1ex−ex−1\lim _{x \rightarrow 1} \frac{e^{x}-e}{x-1}limx→1​x−1ex−e​

Problem 5730

lim⁡x→01−e−xsin⁡x\lim _{x \rightarrow 0} \frac{1-e^{-x}}{\sin x}limx→0​sinx1−e−x​

Problem 5731

For f(x)=xf(x)=\sqrt{x}f(x)=x​ and g(x)=6x+1g(x)=6 x+1g(x)=6x+1, find the following composite functions and state the domain of each. (a) f∘gf \circ gf∘g (b) g∘fg \circ fg∘f (c) f∘ff \circ ff∘f (d) g∘gg \circ gg∘g

Problem 5732

Problem 5733

Problem 5734

Problem 5735

Problem 5736

Problem 5737

Problem 5738

Complete the sentence below. If fff is a one-to-one function and f(9)=8f(9)=8f(9)=8, then f−1(8)=f^{-1}(8)=f−1(8)= \qquad .If fff is a one-to-one function and f(9)=8f(9)=8f(9)=8, then f−1(8)=f^{-1}(8)=f−1(8)= □\square□ 8. 9. 18\frac{1}{8}81​.

Problem 5739

Evaluate lim⁡x→7x+2−3x2−49\lim _{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x^{2}-49}limx→7​x2−49x+2​−3​

Problem 5740

Problem 5741

Find the area of the shaded region. Enter your answer as a reduced fraction.

Problem 5742

For the function on the right, determine whether the function is one-to-one.Is the function one-to-one? Yes No

Problem 5743

29. ∫(x2−x+1)dxx2+x\int \frac{\left(x^{2}-x+1\right) d x}{x^{2}+x}∫x2+x(x2−x+1)dx​

Problem 5744

Find the area of the shaded region.

Problem 5745

Consider the functions f(x)=x3−9f(x)=x^{3}-9f(x)=x3−9 and g(x)=x+93g(x)=\sqrt[3]{x+9}g(x)=3x+9​ (a) Find f(g(x))f(g(x))f(g(x)). (b) Find g(f(x))g(f(x))g(f(x)). (c) Determine whether the functions fff and ggg are inverses of each other.

Problem 5746

Problem 5747

Translate each graph as specified below. (a) The graph of y=x2y=x^{2}y=x2 is shown. Translate it to get the graph of y=x2+1y=x^{2}+1y=x2+1. (b) The graph of y=x2y=x^{2}y=x2 is shown. Translate it to get the graph of y=(x+5)2y=(x+5)^{2}y=(x+5)2.

Problem 5748

Example. AAA sinusoidal function has an amplitude of 2 units, a period of 180∘180^{\circ}180∘ and a maximum at (0,3)(0,3)(0,3). Write a possible equation for this function.

Problem 5749

For the following quadratic function, (a) find the vertex, the axis of symmetry, and the maximum or minimum function value, and (b) graph the function. f(x)=2x2−4x+3f(x)=2 x^{2}-4 x+3f(x)=2x2−4x+3

Problem 5750

Problem 5751

Q3: For⁡z∈C\operatorname{For} z \in \mathbb{C}Forz∈C, show that: (a) sin⁡zˉ=sin⁡z‾\sin \bar{z}=\overline{\sin z}sinzˉ=sinz; (b) cosh⁡zˉ=cosh⁡z‾\cosh \bar{z}=\overline{\cosh z}coshzˉ=coshz.

Problem 5752

$\lim _{x \rightarrow-\infty} \frac{-x^{2}+e x}{x-1}-\ln \left(e^{-x}+1\right)$

Compute $z$ for the percentile given: $\boldsymbol{P}_{\mathbf{4 3}} \mathbf{( 4 3 ^ { \text { th } }}$ percentile $)$ Table for required value of $z$

Click on the word/phrase that would correctly complete the sentence.
You $\qquad$ take the log of a negative number. can cannot will Should not

The expected value of random variable $X$ a. is the same as the median b. Exists if the random variable is limited c. always exists d. Is well defined if $\mathbb{E}|X|<\infty$

A particle moves along the $x$ -axis so that at time $t \geq 0$ its position is given by $x(t)=t^{3}-6 t^{2}+33$ . Determine the total distance traveled by the particle from $0 \leq t \leq 5$ .

A particle moves along the $x$ -axis with velocity given by $v(t)=4 \pi \cos (\pi t)$ for time $t \geq 0$ . If the particle is at position $x=1$ at time $t=2$ , what is the position of the particle at time $t=\frac{5}{6}$ ?

$g(x) = \frac{2x+5}{x-1}$
اشتق $g$

Enter your answer as a fraction or as a number rounded to three decimal places. Find the area bounded by the graphs of $y=x^{2}$ and $y=32-x^{2}$ for $0 \leq x \leq 9$ . Area = $\square$

Write an equation (any form) for the quadratic graphed below $y=\square$

Graph $f(x)=x^{2}-8 x+15$ below by first selecting the correct shape, clicking the vertex, then clicking an $x$ -Intercept. Clear All Draw:

$\int \frac{1}{v(\operatorname{Ln} v-1)} d v$

\begin{align}
1. & \quad f(x) = 3\left(e^{x} + e^{-x}\right) \\
3. & \quad f(w) = \frac{e^{w} + 2}{e^{w}} \\
5. & \quad f(x) = 2 e^{3x-1} \end{align}

If you wanted a more accurate way to fit the trend line to the data, a method called least squares could be used. This method finds the largest distance between the data points and the trend line.
Select one: a. TRUE b. FALSE

$\lim _{x \rightarrow 1} \frac{e^{x}-e}{x-1}$

$\lim _{x \rightarrow 0} \frac{1-e^{-x}}{\sin x}$

For $f(x)=\sqrt{x}$ and $g(x)=6 x+1$ , find the following composite functions and state the domain of each. (a) $f \circ g$ (b) $g \circ f$ (c) $f \circ f$ (d) $g \circ g$

Complete the sentence below. If $f$ is a one-to-one function and $f(9)=8$ , then $f^{-1}(8)=$ $\qquad$ .
If $f$ is a one-to-one function and $f(9)=8$ , then $f^{-1}(8)=$ $\square$ 8. 9. $\frac{1}{8}$ .

Evaluate $\lim _{x \rightarrow 7} \frac{\sqrt{x+2}-3}{x^{2}-49}$

For the function on the right, determine whether the function is one-to-one.
Is the function one-to-one? Yes No

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

Consider the functions $f(x)=x^{3}-9$ and $g(x)=\sqrt[3]{x+9}$ (a) Find $f(g(x))$ . (b) Find $g(f(x))$ . (c) Determine whether the functions $f$ and $g$ are inverses of each other.

Translate each graph as specified below. (a) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=x^{2}+1$ . (b) The graph of $y=x^{2}$ is shown. Translate it to get the graph of $y=(x+5)^{2}$ .

Example. $A$ sinusoidal function has an amplitude of 2 units, a period of $180^{\circ}$ and a maximum at $(0,3)$ . Write a possible equation for this function.

For the following quadratic function, (a) find the vertex, the axis of symmetry, and the maximum or minimum function value, and (b) graph the function. $f(x)=2 x^{2}-4 x+3$

Q3: $\operatorname{For} z \in \mathbb{C}$ , show that: (a) $\sin \bar{z}=\overline{\sin z}$ ; (b) $\cosh \bar{z}=\overline{\cosh z}$ .

Find the exact value of the logarithm without using a calculator. $\log _{12} 144$ $\square$ (Type an integer or a simplified fraction.)

Find the domain of the function. $g(x)=\ln (x+9)$
The domain of g is $\square$ (Type your answer in interval notation.)

The period of is
Select one:

Step 1 of 1 $0 / 8$ Correct lowing logarithmic expression. Round off your answer to two decimal places. $\ln (\log (391))$ ur answer (opens in new window) $\square$

(1 point) The region bounded by $y=e^{-x^{2}}, y=0, x=0$ , and $x=1$ is revolved about the $y$ -axis. Find the volume of the resulting solid. Answer: $\square$

(1 point) Find the volume of the solid that results when the region bounded by $y=\sqrt{x}, y=0$ and $x=9$ is revolved about the line $x=9$ . Volume $=$ $\square$

Find the volume of the solid obtained by rotating the region bounded by the curves $y=x^{2}, \quad y=1$ about the line $y=2$ .
Answer: $\square$

Shown below is the graph of a force function (in newtons) that increases to its maximum value and then remains constant. How much work (in joules) is done by the force in moving the object a distance of 7.5 meters?
Work = $\square$ joules

Use the graph of $y=f(x)$ to answer the following.
Part 1 of 8 (a) Determine $f(-2)$ . $f(-2)=$ $\square$
Part 2 of 8 (b) Determine $f(3)$ . $f(3)=\square$

Español
Suppose that the function $g$ is defir $g(x)=\left\{\begin{array}{cl} -3 & \text { if } x<-1 \\ 0 & \text { if } x=-1 \\ 1 & \text { if } x>-1 \end{array}\right.$
Graph the function $g$ .

Describe the transformations of the parent function $f(x)=|x|$
1. $g(x)=-|x|+5$