Browse Math Statement problems Studdy Solved!

Problem 13501

Factor completely: $(x+6)^{6}+(x+6)^{7}$
Answer Attempt 1 out of 3

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Problem 13502

Solve for x . Give the exact answer and an answer rounded to 3 decimal places. ( 4 a) $\log x=1.6$
Exact answer: $\qquad$
Rounded answer: $\qquad$

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Problem 13503

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The function $f(x)=4 x^{4}-12 x^{3}+17 x^{2}-27 x+18$ has at least two rational roots. Use the rational root theorem to find those roots, then proceed to find all complex roots. (Note: roots may be integer, rational, irrational, and/or complex.)
Answer Attemptiout of 2
There is one root

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Problem 13504

Question 5 (1 point) Determine the exact value of $\sec \pi$ . 0 -1 1 undefined

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Problem 13505

a. Find the slant asymptote of the graph of the rational function. b. Follow the seven-step strategy and use the slant asymptote to graph the rational function. $f(x)=\frac{x^{3}+64}{x^{2}+5 x}$ a. Select the correct choice below and, if necessary, fill in the answer box to complete the choice. A. The equation of the slant asymptote is $\square$ (Type an equation.) B. There is no slant asymptote.

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Problem 13506

Question 8 (1 point) Determine the exact degree measure for $\frac{\pi}{6}$ . $60^{\circ}$ $20^{\circ}$ $30^{\circ}$ $45^{\circ}$

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Problem 13507

Question 10 (1 point) The radian measure of an angle is defined as the length of the arc that subtends the angle divided by the radius of the circle. True False

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Problem 13508

\begin{tabular}{|l|l|l|l|} \hline i) $\sqrt{0.64}$ & J) $\sqrt{0.04}$ & K) $\sqrt{\frac{128}{242}}$ & L) $\sqrt{\frac{12}{243}}$ \\ \hline m) $\sqrt{\frac{50}{98}}$ & n) $\sqrt{\frac{841}{49}}$ & o) $\sqrt{\frac{147}{300}}$ & p) $\sqrt{\frac{961}{144}}$ \\ \hline \end{tabular}

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Problem 13509

10. The complete solution to the equation $\sin x=\log x^{2}$ , where $x$ is in radian measure, is A. 2.32 B. $-0.55,2.32$ C. $-0.52,0.73$ D. 0.73

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Problem 13510

function $f(x)=2 x^{3}+4 x^{2}-3 x-6$ has at least one rational root. Use the rational root theorem to d that root, then proceed to find all complex roots. (Note: roots may be integer, rational, irrational, and/or mplex.)
Answer Attempt 1 out of 2
There is one root $\square$

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Problem 13511

a. Find the slant asymptote of the graph of the rational function b. Follow the seven-step strategy and use the slant asymptote to graph the rational function. $f(x)=\frac{x^{3}+64}{x^{2}+5 x}$
What is/are the $x$ -intercept(s)? Select the correct choice below and, if necessary, fill in the answer box within $y$ A. The $x$ -intercept(s) is/are - 4 (Type an integer or a simplified fraction. Use a comma to separate answers if needed.) B. There are no $x$ -intercepts
Find the vertical asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to comp A. The equation of the vertical asymptote(s) are $x=0, x=-5$ . (Type an equation. Use a comma to separate answers if needed) B. There is no vertical asymptote
Find the horizontal asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to com A. The equation of the horizontal asymptote is $\square$ (Type an equation.) B. There is no horizontal asymptote.

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Problem 13512

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敬 ${ }^{2}$ Find the missing number so that the equation has no solutions $3 x+18=\square x+12$ Submit

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Problem 13513

Find the area under the curve $y=\frac{1}{x}$ over the interval $[1,6]$ . $\square$ Find the average value of $y=\frac{1}{x}$ over the interval $[1,6]$ . $\square$

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Problem 13514

Determine where $f^{\prime}(x)=0$ . Use the Second Derivative Test to determine the local maxima and local minima of each function. Give the coordinates of the points. $f(x)=x+\frac{1}{x}$
Sorry, that's incorrect. Try again?
Local Maximum = $\square$
Local Minimum = $\square$

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Problem 13515

Find the partial fraction decomposition. $\frac{3 x^{2}-8 x+8}{x^{3}-2 x^{2}}$

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Problem 13516

Question
Logistic Curve The sales of a new stereo system over a period of time are expected to follow the logistic curve $f(x)=\frac{7000}{1+25 e^{-x}}$ where $x$ is measured in years. Determine the year in which the sales rate is a maximum. Truncate the answer to the integer.

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Problem 13517

Let $V=\mathbb{R}^{2}$ . For $\left(u_{1}, u_{2}\right),\left(v_{1}, v_{2}\right) \in V$ and $a \in \mathbb{R}$ define vector addition by $\left(u_{1}, u_{2}\right) \boxplus\left(v_{1}, v_{2}\right):=\left(u_{1}+v_{1}+3, u_{2}+v_{2}-1\right)$ and scalar multiplication by $a \square\left(u_{1}, u_{2}\right):=\left(a u_{1}+3 a-3, a u_{2}-a+1\right)$ . It can be shown that $(V, \boxplus, \square)$ is a vector space. Find the following: the sum: $(-5,5) \boxplus(-1,8)=(\square, \square)$ the scalar multiple: $-4$ $\square$ $(-5,5)=$ $\square$ $\square$ ) the zero vector: $\square$ $\|0\|=(\square, \square)$ the additive inverse " $-v$ " of $v=(x, y)$ : $\prime \prime-v \prime \prime=($ $\square$ $\square$ ) (Must be in terms of $x$ and $y$ )

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Problem 13518

Fill in the missing values to make the equations true. (a) $\log _{7} 2-\log _{7} 9=\log _{7}[$ $\square$ (b) $\log _{5} \square+\log _{5} 11=\log _{5} 99$ (c) $\log _{5} \frac{1}{27}=\square \log _{5} 3$

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Problem 13519

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If $-2=x y+5 y+3 x^{3}$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ .
Answer Attempt 1 out of 2

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Problem 13520

Question Find the absolute maximum and absolute minimum of the function on the given interval. $f(x)=x^{4 / 3}-16 x^{1 / 3} \text { on }[-1,8]$
Round answers to 3 decimal places.

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Problem 13521

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Question The function $f(x)=2 x^{4}+x^{3}-4 x^{2}-4 x-16$ has at least two rational roots. Use the ratio theorem to find those roots, then proceed to find all complex roots. (Note: roots may be integer, irrational, and/or complex.)
Answer Attempt 1 out of 2
There are $\square$ four roots :

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Problem 13522

Solve the following equation. $x^{2}+20=8 x$
The solution(s) is/are $x=$ $\square$ (Type an exact answer, using radicals and $i$ as needed. Use a comma to separate answers as needed

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Problem 13523

15 - 17: Convert the following exponential equations in logarithmic form or vice versa.
15. $7^{2}=49$ a. $\log _{49} 2=7$ c. $\log _{2} 49=7$ b. $\log _{7} 49=2$ d. $\log _{7} 2=49$
16. $(m-2)^{3}=x$ a. $\log _{m-2} 3=x$ c. $\log _{3} x=m-2$ b. $\log _{m-2} x=3$ d. $\log _{3} m-2=x$
17. $\log 5=m$ a. $\quad 1^{m}=5$ c. $5^{m}=1$ b. $10^{m}=5$ d. $5^{m}=10$

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Problem 13524

23. $f(x)=\frac{x+1}{x-1}$ on $[2,4]$

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Problem 13525

Simplify. Rationalize the denominator. $\frac{8}{-2+\sqrt{5}}$

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Problem 13526

Simplify. Rationalize the denominator. $\frac{-7}{8-\sqrt{2}}$

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Problem 13527

In Exercises $1,2,3,4,5,6,7,8,9$ , and 10, (a) find the intervals where the function $f$ is increasing and where it is decreasing, (b) find the relative extrema of $f$ , (c) find the intervals where the graph of $f$ is concave upward and wnere it is concave downward, and (d) find the inflection points, if any, of $f$ .
1. $f(x)=\frac{1}{3} x^{3}-x^{2}+x-6$

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Problem 13528

Question 4 of 25 Find all the zeros of the quadratic function. $y=x^{2}-5 x-14$
If there is more than one zero, separate them with commas

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Problem 13529

$\begin{array}{l} \text { 4) } \frac{2 x+1}{1}=\frac{-1}{2 x} \\ x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} \\ a= \\ b= \\ c= \end{array}$ $\begin{array}{l} \text { 5) } 3 x^{2}+10 x+9=6-8 x \\ x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} \\ a= \\ b= \\ c= \end{array}$ $\begin{array}{l} \text { 6) } 9=x(x+3) \\ x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} \\ a= \\ b= \\ c= \end{array}$

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Problem 13530

o to Polynomials, Add \& Subtract Question 21 10.3.59 Points:
Write the following polynomial in descending powers of the variable and with no miss ig powers. $\begin{array}{l} 8 x^{2}-67 \\ 8 x^{2}-67= \end{array}$ $\square$

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Problem 13531

b) Algebraically determine the solutions to the equation $6 \sin ^{2} x-6 \sin x+1=0$ , where $0 \leq x \leq 2 \pi$ . Give the solution correct to the nearest hundredth.

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Problem 13532

ii. $\mathcal{L}\left\{\cosh 2 t e^{4 t}\right\} \quad$ ; First Shift Theorem ; Teorem Anjakan Pertama

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Problem 13533

$\sin(x+y) = 3x$ Find $\frac{dy}{dx}$ .

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Problem 13534

Problème \# 5 : Si $a(a-7 b)=-b^{2}$ , Prouve que $\log \left(\frac{a+b}{3}\right)=\frac{\log a+\log b}{2}$

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Problem 13535

Which ordered pair is a solution to the inequality $8 y+3 x>-4$ ? $(4,-2)$ $(-3,1)$ $(-2,-1)$ $(-4,1)$

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Problem 13536

(a) The value of $f(1)$ is about 110 . (Round to the nearest whole number as needed.) (b) The value of $f^{-1}(110)$ is about $\square$ (Round to the nearest whole number as needed.)

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Problem 13537

$\sqrt{y} - \ln y = x + 8$
Find $\frac{dy}{du}$ .

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Problem 13538

Use the expression $5.2 \mathrm{u}-(10 \div 2)+13$ to answer $9-10$ .
9. Which part of the expression represents a quotient? Describe its parts.
10. Which part of the expression represents a product of two factors? Describe its parts. (Use the operation symbols in the math palette as needed. Do not simplify.) In this quotient, 10 is the dividend and 2 is the divisor.
10. The part of the expression that represents a product of two factors is $\square$ (Use the operation symbols in the math palette as needed. Do not simplify.)

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Problem 13539

(2) Simplify. Leave answers in simplest form using positive exponents in the final answer. a. $5^{19} \div 5^{-5}$ b. $\left(\frac{2}{3}\right)^{5} \cdot\left(\frac{4}{9}\right)^{-2}$

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Problem 13540

$x-3 y^{2}=6$

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Problem 13541

$\begin{array}{l}\text { Find } \frac{d y}{d t} \quad y=(t \sin t)^{6} \\ \frac{d y}{d t}=\text { ? }\end{array}$

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Problem 13542

Let $\boldsymbol{E}$ be the event where the sum of two rolled dice is less than 10 . List the outcomes in $\boldsymbol{E}^{\boldsymbol{c}}$ .

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Problem 13543

Evaluate the logarithmic expression without using a calculator. $\frac{\log \frac{1}{100000}}{\log \frac{1}{100000}=\square}$ (Type an integer or a simplified fraction.)

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Problem 13544

Determine whether the two functions are inverses. $t(x)=\frac{-6}{x-3} \text { and } v(x)=\frac{3 x-6}{x}$

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Problem 13545

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. $\log \left(\frac{1000}{\sqrt{a^{2}+b^{2}}}\right)=$

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Problem 13546

Find the zero(s), the horizontal intercept(s) and vertical intercept of the polynomial function $f(x)=2 x^{3}+7 x^{2}-20 x-70$
The zero(s) is/are $\square$ The horizontal intercept(s) is/are $\square$
The vertical intercept is $\square$

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Problem 13547

Given the function $g(n)=3 n^{4}+12 n^{3}-63 n^{2}$ : its $g$ -intercept is $\square$ its $n$ -intercepts are $\square$

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Problem 13548

Predict the products of the following neutralisation reaction: $\mathrm{HCl}(\mathrm{aq})+\mathrm{Ba}(\mathrm{OH})_{2} \rightarrow$

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Problem 13549

8. Now consider $f(x)=2 \csc \left(\frac{\pi}{2} x\right)+1$ . (a) (2 points) Compute $f(0), f(\pi / 6), f(\pi / 2)$ . (b) (1 point) Where are the asymptotes for this function? (c) (1 point) What is the domain? Set Notation (d) (1 point) What is the range? Interval Notation

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Problem 13550

Identify the zeros of $f(x)=-(x+1)^{3}(x-2)$ and their multiplicity. (Smallest to Largest) $x=$ $\square$ with multiplicity of $\square$ $x=$ $\square$ with multiplicity of $\square$ Question Help: Message instructor

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Problem 13551

Use the given polynomial function to identify the zeros of the function and the multiplicity of each zero Leave any remaining answer boxes empty. $f(x)=-4 x^{2}(x+6)^{2}(x-3)^{2}$ \begin{tabular}{|c|c|} \hline Zeros & Mult. \\ \hline $\square$ & $\square$ \\ $\square$ & $\square$ \\ $\square$ & $\square$ \\ $\square$ & $\square$ \\ $\square$ & \\ $\square$ \\ \hline \end{tabular}
Note: It is possible that some of the answer boxes will be empty!

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Problem 13552

Find the inverse function of $f(x)=\sqrt{4 x+8}$ . $f^{-1}(x)=$ $\square$

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Problem 13553

$\left[{ }^{x}\right]$ Rewrite the following equatic $y+10=\frac{1}{7}(x+7)$

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Problem 13554

$y+6=-5(x-9)$

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Problem 13555

9. (6405 \#3 p. 320) Let $R$ denote the region bounded by the curve $y=\frac{1}{x^{2}+1}$ , the $y$ -axis, the $x$ -axis, and the line $x=4$ . Set $S$ denote the solid generated when the region $R$ is revolved about the $y$ -axis. Find the volume of $S$ .

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Problem 13556

Predict the products of the following neutralisation reaction: $\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})+\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq}) \rightarrow$

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Problem 13557

Compute the value of the discriminant and give the number of real solutions of the quadratic equation. $-2 x^{2}+9 x-4=0$
Discriminant:
Number of real solutions: $\square$

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Problem 13558

For the following function $f$ , find the antiderivative $F$ that satisfies the given condition. $f(x)=6 \sqrt{x}+4 ; F(1)=4$
The antiderivative that satisfies the given condition is $F(x)=4 x \sqrt{x}+4 x+c$ .

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Problem 13559

Solve. $-4=-4+2 \tan (3 \theta+60)$

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Problem 13560

56. $\frac{5 a+2 b}{a-3 b}=\frac{1}{2}$ бол $\frac{a}{b}=$ ?

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Problem 13561

b) $\log (x-5)=2$

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Problem 13562

Write the standard form of the equation of the circle with the given center and radius. Center $(7,2), r=3$
Type the standard form of the equation of the circle.

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Problem 13563

Compute the integral $\int \frac{e^{x}}{\sin ^{2}\left(e^{x}\right)} d x=$ $\square$ $\text { 마온 }+C$ where $C$ is the constant of integration. Do not include the constant of integration in yo

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Problem 13564

Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the domain and range. $(x+5)^{2}+(y-3)^{2}=36$
The center is $\square$

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Problem 13565

f) $\ln 2 x-2 \ln x=1$

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Problem 13566

Solve using augmented matrix methods. $\begin{array}{rr} 2 x_{1}-x_{2}= & -5 \\ 3 x_{1}+2 x_{2}= & 3 \end{array}$

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Problem 13567

Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the relation's domain and range. $x^{2}+(y-3)^{2}=25$
What is the center of the circle?

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Problem 13568

Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equation. $x^{2}+y^{2}+6 x+4 y+12=0$

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Problem 13569

Use Cramer's rule to find the solution to the following system of linear equations $\begin{array}{l} x-5 y=9 \\ x+7 y=-8 \end{array}$
The determinant of the coefficient matrix is $D=$ $\square$ $\square$ $\square$ $\square$ $=$ $\begin{array}{l} x=\frac{\left|\begin{array}{ll} \square & \square \\ \square & \square \end{array}\right|}{D}=\square \\ y=\frac{\left|\begin{array}{l} \square \\ \square \end{array}\right|}{D}=\square \end{array}$ $\square$

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Problem 13570

uences and Series ee Dimensions tor Functions Ex 16.8.15 Find the maximum and minimum values of tial Differentiation A tions of Several Variables f(x, y) = = xy + 9 - x² - y² ts and Continuity al Differentiation when x² + y² ≤ 9. (answer) Chain Rule

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Problem 13571

Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equation. $x^{2}+y^{2}+6 x-4 y-12=0$

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Problem 13572

Find the domain of the function. $f(x)=\log _{4}\left(\frac{9}{x+8}\right)$
Write your answer as an interval or union of intervals.

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Problem 13573

Solve for $y$ in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. $e^{5 y}=7$ (G) $y=$ $\square$

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Problem 13574

Solve the equation. Write the solution set with the exact solutions. $\log _{6}(3-m)+\log _{6}(-m-2)=1$
If there is more than one solution, separate the answers with commas. There is no solution, $\}$ . The exact solution set is $\square$

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Problem 13575

Write the equation in logarithmic form. $10^{0}=1$
The equation in logarithmic form is $\square$ $e$ ㅁog_

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Problem 13576

The range set of $f(x)=x^{2}+2 x+2$ is $(-\infty, 1]$ $[1, \infty)$ $(-\infty,-1]$ $[-1, \infty)$

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Problem 13577

Find and evaluate composite functions: $f(x)=5 x^{2}-1$ and $g(x)=4 x-1$ $(f \circ g)(\mathrm{x}),(f \circ g)(-1),(g \circ f)(\mathrm{x})$ , and $(g \circ f)(2)$

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Problem 13578

Write an equivalent exponential equation. $\log _{2} 16=4$

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Problem 13579

Round your answers to the nearest thousandth. Do not round any intermediate computations. $\begin{array}{r} \left(\frac{2}{3}\right)^{-0.75}=\square \\ 3.2^{1.5}=\square \end{array}$

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Problem 13580

5. Given the expression $2 \cot (x)-2 \cot (x) \cos ^{2}(x)$ , a. Use technology to graph the expression [3 marks] b. Determine an equivalent trigonometric expression [2 marks] c. Then prove that your expression is equal to the given expression. [ 3 marks]

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Problem 13581

Write the following exponential equation in logarithmic form. Assume all variables are positive and not equal to one. $\begin{array}{l} 2^{c}=a \\ \log \mathrm{~b}(\mathrm{a})=\mathrm{c} \end{array}$

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Problem 13582

Write in logarithmic form: $b^{8}=2$ $\log _{b} 8=2$ $\log _{8} b=2$ $\log _{8} 2=b$ $\log _{b} 2=8$ $\log _{2} b=8$

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Problem 13583

Solve the equation. Simplify the answer as much as possible. $27^{x-6}=9^{2 x}$
The solution set is $\square$ \}.

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Problem 13584

Evaluate the following expression. $\log _{4} 64$

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Problem 13585

Evaluate the following expression. $\log _{5}\left(\frac{1}{25}\right)$

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Problem 13586

j) $4^{x}+4^{x-\frac{1}{2}}=45$

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Problem 13587

Find the domain of $y=\log (8+2 x)$ . The domain is: $\square$

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Problem 13588

QUESTION \#2: Complete without a calculator. (3 marks) Solve the equation $\cos ^{2} x-\cos x=0$ over the interval $\left[0^{\circ}, 360^{\circ}\right]$ . (3 marks: 1 mark for solving for $\cos x, 2$ marks for solving for $x$ )

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Problem 13589

26. Let $f$ be a rational function given by $f(x)=\frac{g(x)}{h(x)}$ . The graph has a vertical asymptote at the zero of a) $g(x)$ b) $h(x)$ c) $\frac{g(x)}{h(x)}$ d) $\frac{h(x)}{g(x)}$

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Problem 13590

Question 8 0/1 pt 5 8 Details
Find the inflection point(s) for the function shown below. If there is more than one, be sure to separate them by using a comma. If there is not an inflection point, type DNE in the answer box. If necessary, round all numbers to two decimal places. $f(x)=-4 x^{3}+36 x^{2}+324 x-8$ $\square$ Question Help: Message instructor Submit Question Jump to Answer

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Problem 13591

If $x=-1$ is a root of the polynomial $0=x^{3}+2 x^{2}-5 x-6$ , what are the other roots? $x=-3, x=2$ $x=-1, x=-3, x=2$ $x=0, x=-3, x=2$ $x=3, x=-2$

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Problem 13592

Find the arc length of the following curve on the given interval. $y=\frac{1}{3} x^{3 / 2} \text { on }[0,54]$

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Problem 13593

MATH102 (Calculus II) First exam - Page 2 of 4 April 25, 2024
1. $\left(21 / 2\right.$ points) The sum of the series $\sum_{k=0}^{\infty} \frac{5^{k} 3^{-k}}{2^{k}}$ is A. 6 B. 5 C. -6 D. -5
2. ( $21 / 2$ points) One of the following values of $p$ makes the series $\sum_{k=0}^{\infty} \frac{p^{k} k^{2}}{k^{3}+1}$ conditionally convergent. A. -1 B. 1 C. 2 D. 3
3. (2 $1 / 2$ points) The series $\sum_{k=0}^{\infty}(-1)^{k} \frac{3}{k^{2}+1}$ is A. conditionally convergent. B. divergent. C. absolutely convergent.
4. ( $21 / 2$ points) Which of the following series is convergent? A. $\sum_{k=1}^{\infty} \frac{k}{k^{2}+4}$ B. $\sum_{k=1}^{\infty} \frac{1}{k+3}$ $\begin{array}{l} \frac{k}{k^{2}+4}<\frac{n}{n^{2}}=\frac{1}{n} \times \frac{n}{n^{2}+4}>\frac{n}{2 n^{1}}=\frac{1}{2 n} \mathrm{dim} \\ \frac{1}{k+3}<\frac{1}{k+3}>\frac{1}{2 k} \text { Jir } \end{array}$ C. $\sum_{k=1}^{\infty} \frac{1}{k\left(1+\ln ^{2}(k)\right)}$ D. $\sum_{k=1}^{\infty}(-1)^{k} \frac{4 k+3}{3 k-5}$
5. ( $21 / 2$ points) One of the following values of $p$ makes the series $\sum_{n=1}^{\infty} \frac{n!}{p^{n}((n+1)!+1)}$ convergent A. 2 B. 0.2 C. 0.5 D. 1 $\begin{aligned} \lim & \frac{(n+1)!}{P^{n+1}((n+1+1)!+1)} \cdot \frac{P^{n}((n+1)!+1)}{n!} \\ & =\frac{(n+1) n!}{P^{2} \cdot P((n+2)(n+1)!+1)} P^{D^{2}((n+1)!+1)}=\ln \frac{(n+1)((n+1)!+1}{P((n+2)(n+1)!} \end{aligned}$ $\begin{array}{l} \lim \frac{(n+1) \cdot((n+1)!+1)}{P((n+2)!+1)}=\lim \frac{(n+1)((n+1)!+1)(n+1)!+(n}{P(n+2)!+P} \\ \left|\frac{1}{P}\right| \lim \frac{(n+1)((n+1)!+1)}{(n+2)!+1)} \quad P((n+2)!+1) \quad P(n+2)!+P \end{array}$

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Problem 13594

The expression $(x-7)\left(x^{2}+7 x+7\right)$ equals $A x^{3}+B x^{2}+C x+D$ where $A$ equals: $\square$ and $B$ equals: $\square$ and $C$ equals: $\square$ and $D$ equals: $\square$ Question Help: Message instructor

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Problem 13595

Evaluate the expression without using a calculato $\begin{array}{c} \log _{7} \frac{1}{49} \\ \log _{7} \frac{1}{49}= \end{array}$

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Problem 13596

13. $f(x)=x^{3}-x^{2}-x-15 ; g(x)=x-3$

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Problem 13597

Find the area of the surface generated when the given curve is revolved about the given axis. $y=22 \sqrt{x}$ , for $9 \leq x \leq 17$ ; about the $x$ -axis

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Problem 13598

Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation of the parabola's axis of symmetry. Use the graph to determine the domain and range of the function. $f(x)=6 x-x^{2}-13$

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Problem 13599

Consider the following matrix. $A=\left[\begin{array}{ccc} 2 & 1 & 0 \\ 3 & -1 & 2 \\ 0 & 1 & -1 \end{array}\right]$
Choose the correct description of $A$ . Find $A^{-1}$ if it exists.

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Problem 13600

Find the area of the surface generated when the given curve is revolved about the given axis. $y=(8 x)^{\frac{1}{3}}$ , for $0 \leq x \leq 8$ ; about the $y$ -axis

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Math Statement

Problem 13501

Factor completely: (x+6)6+(x+6)7(x+6)^{6}+(x+6)^{7}(x+6)6+(x+6)7Answer Attempt 1 out of 3

Problem 13502

Solve for x . Give the exact answer and an answer rounded to 3 decimal places. ( 4 a) log⁡x=1.6\log x=1.6logx=1.6Exact answer: \qquadRounded answer: \qquad

Problem 13503

Problem 13504

Question 5 (1 point) Determine the exact value of sec⁡π\sec \pisecπ. 0 -1 1 undefined

Problem 13505

Problem 13506

Question 8 (1 point) Determine the exact degree measure for π6\frac{\pi}{6}6π​. 60∘60^{\circ}60∘ 20∘20^{\circ}20∘ 30∘30^{\circ}30∘ 45∘45^{\circ}45∘

Problem 13507

Question 10 (1 point) The radian measure of an angle is defined as the length of the arc that subtends the angle divided by the radius of the circle. True False

Problem 13508

Problem 13509

10. The complete solution to the equation sin⁡x=log⁡x2\sin x=\log x^{2}sinx=logx2, where xxx is in radian measure, is A. 2.32 B. −0.55,2.32-0.55,2.32−0.55,2.32 C. −0.52,0.73-0.52,0.73−0.52,0.73 D. 0.73

Problem 13510

Problem 13511

Problem 13512

Learn with an example Watch a v敬 2{ }^{2}2 Find the missing number so that the equation has no solutions 3x+18=□x+123 x+18=\square x+123x+18=□x+12 Submit

Problem 13513

Find the area under the curve y=1xy=\frac{1}{x}y=x1​ over the interval [1,6][1,6][1,6]. □\square□ Find the average value of y=1xy=\frac{1}{x}y=x1​ over the interval [1,6][1,6][1,6]. □\square□

Problem 13514

Problem 13515

Find the partial fraction decomposition. 3x2−8x+8x3−2x2\frac{3 x^{2}-8 x+8}{x^{3}-2 x^{2}}x3−2x23x2−8x+8​

Problem 13516

Problem 13517

Problem 13518

Problem 13519

Question Watch VideoIf −2=xy+5y+3x3-2=x y+5 y+3 x^{3}−2=xy+5y+3x3 then find dydx\frac{d y}{d x}dxdy​ in terms of xxx and yyy.Answer Attempt 1 out of 2

Problem 13520

Question Find the absolute maximum and absolute minimum of the function on the given interval. f(x)=x4/3−16x1/3 on [−1,8]f(x)=x^{4 / 3}-16 x^{1 / 3} \text { on }[-1,8]f(x)=x4/3−16x1/3 on [−1,8]Round answers to 3 decimal places.

Problem 13521

Problem 13522

Solve the following equation. x2+20=8xx^{2}+20=8 xx2+20=8xThe solution(s) is/are x=x=x= □\square□ (Type an exact answer, using radicals and iii as needed. Use a comma to separate answers as needed

Problem 13523

Problem 13524

23. f(x)=x+1x−1f(x)=\frac{x+1}{x-1}f(x)=x−1x+1​ on [2,4][2,4][2,4]

Problem 13525

Simplify. Rationalize the denominator. 8−2+5\frac{8}{-2+\sqrt{5}}−2+5​8​

Problem 13526

Simplify. Rationalize the denominator. −78−2\frac{-7}{8-\sqrt{2}}8−2​−7​

Problem 13527

Problem 13528

Question 4 of 25 Find all the zeros of the quadratic function. y=x2−5x−14y=x^{2}-5 x-14y=x2−5x−14If there is more than one zero, separate them with commas

Problem 13529

Problem 13530

o to Polynomials, Add \& Subtract Question 21 10.3.59 Points:Write the following polynomial in descending powers of the variable and with no miss ig powers. 8x2−678x2−67=\begin{array}{l} 8 x^{2}-67 \\ 8 x^{2}-67= \end{array}8x2−678x2−67=​ □\square□

Problem 13531

b) Algebraically determine the solutions to the equation 6sin⁡2x−6sin⁡x+1=06 \sin ^{2} x-6 \sin x+1=06sin2x−6sinx+1=0, where 0≤x≤2π0 \leq x \leq 2 \pi0≤x≤2π. Give the solution correct to the nearest hundredth.

Problem 13532

ii. L{cosh⁡2te4t}\mathcal{L}\left\{\cosh 2 t e^{4 t}\right\} \quadL{cosh2te4t}; First Shift Theorem ; Teorem Anjakan Pertama

Problem 13533

sin⁡(x+y)=3x\sin(x+y) = 3xsin(x+y)=3x Find dydx\frac{dy}{dx}dxdy​.

Problem 13534

Problème \# 5 : Si a(a−7b)=−b2a(a-7 b)=-b^{2}a(a−7b)=−b2, Prouve que log⁡(a+b3)=log⁡a+log⁡b2\log \left(\frac{a+b}{3}\right)=\frac{\log a+\log b}{2}log(3a+b​)=2loga+logb​

Problem 13535

Which ordered pair is a solution to the inequality 8y+3x>−48 y+3 x>-48y+3x>−4 ? (4,−2)(4,-2)(4,−2) (−3,1)(-3,1)(−3,1) (−2,−1)(-2,-1)(−2,−1) (−4,1)(-4,1)(−4,1)

Problem 13536

(a) The value of f(1)f(1)f(1) is about 110 . (Round to the nearest whole number as needed.) (b) The value of f−1(110)f^{-1}(110)f−1(110) is about □\square□ (Round to the nearest whole number as needed.)

Problem 13537

y−ln⁡y=x+8\sqrt{y} - \ln y = x + 8y​−lny=x+8Find dydu\frac{dy}{du}dudy​.

Problem 13538

Problem 13539

(2) Simplify. Leave answers in simplest form using positive exponents in the final answer. a. 519÷5−55^{19} \div 5^{-5}519÷5−5 b. (23)5⋅(49)−2\left(\frac{2}{3}\right)^{5} \cdot\left(\frac{4}{9}\right)^{-2}(32​)5⋅(94​)−2

Problem 13540

x−3y2=6x-3 y^{2}=6x−3y2=6

Problem 13541

Find dydty=(tsin⁡t)6dydt= ? \begin{array}{l}\text { Find } \frac{d y}{d t} \quad y=(t \sin t)^{6} \\ \frac{d y}{d t}=\text { ? }\end{array} Find dtdy​y=(tsint)6dtdy​= ? ​

Problem 13542

Let E\boldsymbol{E}E be the event where the sum of two rolled dice is less than 10 . List the outcomes in Ec\boldsymbol{E}^{\boldsymbol{c}}Ec.

Problem 13543

Evaluate the logarithmic expression without using a calculator. log⁡1100000log⁡1100000=□\frac{\log \frac{1}{100000}}{\log \frac{1}{100000}=\square}log1000001​=□log1000001​​ (Type an integer or a simplified fraction.)

Problem 13544

Determine whether the two functions are inverses. t(x)=−6x−3 and v(x)=3x−6xt(x)=\frac{-6}{x-3} \text { and } v(x)=\frac{3 x-6}{x}t(x)=x−3−6​ and v(x)=x3x−6​

Problem 13545

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. log⁡(1000a2+b2)=\log \left(\frac{1000}{\sqrt{a^{2}+b^{2}}}\right)=log(a2+b2​1000​)=

Problem 13546

Find the zero(s), the horizontal intercept(s) and vertical intercept of the polynomial function f(x)=2x3+7x2−20x−70f(x)=2 x^{3}+7 x^{2}-20 x-70f(x)=2x3+7x2−20x−70The zero(s) is/are □\square□ The horizontal intercept(s) is/are □\square□The vertical intercept is □\square□

Problem 13547

Factor completely: $(x+6)^{6}+(x+6)^{7}$
Answer Attempt 1 out of 3

Solve for x . Give the exact answer and an answer rounded to 3 decimal places. ( 4 a) $\log x=1.6$
Exact answer: $\qquad$
Rounded answer: $\qquad$

Question 5 (1 point) Determine the exact value of $\sec \pi$ . 0 -1 1 undefined

Question 8 (1 point) Determine the exact degree measure for $\frac{\pi}{6}$ . $60^{\circ}$ $20^{\circ}$ $30^{\circ}$ $45^{\circ}$

10. The complete solution to the equation $\sin x=\log x^{2}$ , where $x$ is in radian measure, is A. 2.32 B. $-0.55,2.32$ C. $-0.52,0.73$ D. 0.73

Learn with an example Watch a v
敬 ${ }^{2}$ Find the missing number so that the equation has no solutions $3 x+18=\square x+12$ Submit

Find the area under the curve $y=\frac{1}{x}$ over the interval $[1,6]$ . $\square$ Find the average value of $y=\frac{1}{x}$ over the interval $[1,6]$ . $\square$

Find the partial fraction decomposition. $\frac{3 x^{2}-8 x+8}{x^{3}-2 x^{2}}$

Question Watch Video
If $-2=x y+5 y+3 x^{3}$ then find $\frac{d y}{d x}$ in terms of $x$ and $y$ .
Answer Attempt 1 out of 2

Question Find the absolute maximum and absolute minimum of the function on the given interval. $f(x)=x^{4 / 3}-16 x^{1 / 3} \text { on }[-1,8]$
Round answers to 3 decimal places.

Solve the following equation. $x^{2}+20=8 x$
The solution(s) is/are $x=$ $\square$ (Type an exact answer, using radicals and $i$ as needed. Use a comma to separate answers as needed

23. $f(x)=\frac{x+1}{x-1}$ on $[2,4]$

Simplify. Rationalize the denominator. $\frac{8}{-2+\sqrt{5}}$

Simplify. Rationalize the denominator. $\frac{-7}{8-\sqrt{2}}$

Question 4 of 25 Find all the zeros of the quadratic function. $y=x^{2}-5 x-14$
If there is more than one zero, separate them with commas

o to Polynomials, Add \& Subtract Question 21 10.3.59 Points:
Write the following polynomial in descending powers of the variable and with no miss ig powers. $\begin{array}{l} 8 x^{2}-67 \\ 8 x^{2}-67= \end{array}$ $\square$

b) Algebraically determine the solutions to the equation $6 \sin ^{2} x-6 \sin x+1=0$ , where $0 \leq x \leq 2 \pi$ . Give the solution correct to the nearest hundredth.

ii. $\mathcal{L}\left\{\cosh 2 t e^{4 t}\right\} \quad$ ; First Shift Theorem ; Teorem Anjakan Pertama

$\sin(x+y) = 3x$ Find $\frac{dy}{dx}$ .

Problème \# 5 : Si $a(a-7 b)=-b^{2}$ , Prouve que $\log \left(\frac{a+b}{3}\right)=\frac{\log a+\log b}{2}$

Which ordered pair is a solution to the inequality $8 y+3 x>-4$ ? $(4,-2)$ $(-3,1)$ $(-2,-1)$ $(-4,1)$

(a) The value of $f(1)$ is about 110 . (Round to the nearest whole number as needed.) (b) The value of $f^{-1}(110)$ is about $\square$ (Round to the nearest whole number as needed.)

$\sqrt{y} - \ln y = x + 8$
Find $\frac{dy}{du}$ .

(2) Simplify. Leave answers in simplest form using positive exponents in the final answer. a. $5^{19} \div 5^{-5}$ b. $\left(\frac{2}{3}\right)^{5} \cdot\left(\frac{4}{9}\right)^{-2}$

$x-3 y^{2}=6$

$\begin{array}{l}\text { Find } \frac{d y}{d t} \quad y=(t \sin t)^{6} \\ \frac{d y}{d t}=\text { ? }\end{array}$

Let $\boldsymbol{E}$ be the event where the sum of two rolled dice is less than 10 . List the outcomes in $\boldsymbol{E}^{\boldsymbol{c}}$ .

Evaluate the logarithmic expression without using a calculator. $\frac{\log \frac{1}{100000}}{\log \frac{1}{100000}=\square}$ (Type an integer or a simplified fraction.)

Determine whether the two functions are inverses. $t(x)=\frac{-6}{x-3} \text { and } v(x)=\frac{3 x-6}{x}$

Write the logarithm as a sum or difference of logarithms. Simplify each term as much as possible. $\log \left(\frac{1000}{\sqrt{a^{2}+b^{2}}}\right)=$

Find the zero(s), the horizontal intercept(s) and vertical intercept of the polynomial function $f(x)=2 x^{3}+7 x^{2}-20 x-70$
The zero(s) is/are $\square$ The horizontal intercept(s) is/are $\square$
The vertical intercept is $\square$

Given the function $g(n)=3 n^{4}+12 n^{3}-63 n^{2}$ : its $g$ -intercept is $\square$ its $n$ -intercepts are $\square$

Predict the products of the following neutralisation reaction: $\mathrm{HCl}(\mathrm{aq})+\mathrm{Ba}(\mathrm{OH})_{2} \rightarrow$

Identify the zeros of $f(x)=-(x+1)^{3}(x-2)$ and their multiplicity. (Smallest to Largest) $x=$ $\square$ with multiplicity of $\square$ $x=$ $\square$ with multiplicity of $\square$ Question Help: Message instructor

Find the inverse function of $f(x)=\sqrt{4 x+8}$ . $f^{-1}(x)=$ $\square$

$\left[{ }^{x}\right]$ Rewrite the following equatic $y+10=\frac{1}{7}(x+7)$

$y+6=-5(x-9)$

9. (6405 \#3 p. 320) Let $R$ denote the region bounded by the curve $y=\frac{1}{x^{2}+1}$ , the $y$ -axis, the $x$ -axis, and the line $x=4$ . Set $S$ denote the solid generated when the region $R$ is revolved about the $y$ -axis. Find the volume of $S$ .

Predict the products of the following neutralisation reaction: $\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})+\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq}) \rightarrow$

Compute the value of the discriminant and give the number of real solutions of the quadratic equation. $-2 x^{2}+9 x-4=0$
Discriminant:
Number of real solutions: $\square$

For the following function $f$ , find the antiderivative $F$ that satisfies the given condition. $f(x)=6 \sqrt{x}+4 ; F(1)=4$
The antiderivative that satisfies the given condition is $F(x)=4 x \sqrt{x}+4 x+c$ .

Solve. $-4=-4+2 \tan (3 \theta+60)$

56. $\frac{5 a+2 b}{a-3 b}=\frac{1}{2}$ бол $\frac{a}{b}=$ ?

b) $\log (x-5)=2$

Write the standard form of the equation of the circle with the given center and radius. Center $(7,2), r=3$
Type the standard form of the equation of the circle.

Compute the integral $\int \frac{e^{x}}{\sin ^{2}\left(e^{x}\right)} d x=$ $\square$ $\text { 마온 }+C$ where $C$ is the constant of integration. Do not include the constant of integration in yo

Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the domain and range. $(x+5)^{2}+(y-3)^{2}=36$
The center is $\square$

f) $\ln 2 x-2 \ln x=1$

Solve using augmented matrix methods. $\begin{array}{rr} 2 x_{1}-x_{2}= & -5 \\ 3 x_{1}+2 x_{2}= & 3 \end{array}$

Give the center and radius of the circle described by the equation and graph the equation. Use the graph to identify the relation's domain and range. $x^{2}+(y-3)^{2}=25$
What is the center of the circle?

Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equation. $x^{2}+y^{2}+6 x+4 y+12=0$

Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equation. $x^{2}+y^{2}+6 x-4 y-12=0$

Find the domain of the function. $f(x)=\log _{4}\left(\frac{9}{x+8}\right)$
Write your answer as an interval or union of intervals.

Solve for $y$ in the equation below. Round your answer to the nearest hundredth. Do not round any intermediate computations. $e^{5 y}=7$ (G) $y=$ $\square$