Browse Math Statement problems Studdy Solved!

Problem 19001

Use $\log _{b} 2 \approx 0.393, \log _{b} 3 \approx 0.552$ , and $\log _{b} 5 \approx 0.801$ to approximate the value of the given logarithm to 3 decimal places. Assume that $b>0$ and $b \neq 1$ . $\log _{b} 15 \approx$

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Problem 19002

Используя $\delta-\varepsilon$ -определение непрерывности покажите, что функция $f(x)=x^{3}$ всюду непрерывна.

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Problem 19003

Add, using the rule for order of operations if necessary: $[10+(-6)]+[8+(-12)]=$ $\square$ Submit Question

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Problem 19004

Berechne den Grenzwert der Folge $\left(\sum_{k=1}^{n} \frac{k}{3(n+1)^{2}+4 k}\right)_{n \in \mathbb{N}}$ mit dem Sandwichsatz.

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Problem 19005

\begin{tabular}{c|c|c|c|} \hline Entered & Answer Preview & Result \\ \hline-12.75 & -12.75 & correct \\ \hline \end{tabular}
The answer above is correct.
A jogger runs around a circular track of radius 70 ft . Let $(x, y)$ be her coordinates, where the origin is the center of the track. When the jogger's coordinates are $(42,56)$ , her $x$ -coordinate is changing at a rate of $17 \mathrm{ft} / \mathrm{s}$ . Find $d y / d t$ . $d y / d t=-12.75 \mathrm{ft} / \mathrm{s}$ $\square$

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Problem 19006

k. $\left.\begin{array}{rr} +x y=-1 & \left(3 x^{2}+x y=-1\right. \\ x^{2}-3 x y=13 \end{array}\right)$

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Problem 19007

Solve using the quadratic formula. Approximate answers to the nearest tenth. $x^{2}-2 x+1=0$ $\square$ Type your answer, then press Enter. Follow these examples: $\begin{array}{c} x=1 \text { or } 3 \\ x=-5.3 \text { or }-0.1 \end{array}$

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Problem 19008

The function $f(x)=\frac{x+24}{x-6}$ is one-to-one. For the function, a. Find an equation for $f^{-1}(x)$ , the inverse function. b. Verify that your equation is correct by showing that $f\left(f^{-1}(x)\right)=x$ and $f^{-1}(f(x))=x$ . a. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Simplify your answer. Use integers or fractions for any numbers in the expression.) A. $f^{-1}(x)=$ $\square$ , for $\mathrm{x} \neq$ $\square$ B. $f^{-1}(x)=$ $\square$ , for $x \leq$ $\square$ C. $f^{-1}(x)=$ $\square$ , for $x \geq$ $\square$ D. $f^{-1}(x)=$ $\square$ , for all $x$

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Problem 19009

Используя $\delta-\varepsilon$ -определение непрерывности покажите, что функция $f(x)=x^{3}$ всюду непрерывна.

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Problem 19010

Determine each feature of the graph of the given function. $f(x)=\frac{4 x-16}{x^{2}-x-12}$
Answer Attempt 1 out of 2
Horizontal Asymptote: $y=$ $\square$ No horizontal asymptote
Vertical Asymptote: $x=$ $\square$ No vertical asymptote $x$ -Intercept: $\square$ ,0) No $x$ -intercept $\square$ $y$ -Intercept: (0, $\square$ No $y$ -intercept $\qquad$
Hole: $\square$ $\square$ , ) No hole

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Problem 19011

Express the radical in simplified form. 4) $\sqrt{72}$

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Problem 19012

Find the vertical asymptotes, if any, and the values of $x$ corresponding to holes, if any, of the graph of the rational function. $f(x)=\frac{x}{x+7}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an equation. Use commas to separate answers as needed.) A. There are no vertical asymptotes but there is(are) hole(s) corresponding to $\square$ . B. The vertical asymptote(s) is(are) $\square$ . There are no holes. C. The vertical asymptote(s) is(are) $\square$ and hole(s) corresponding to $\square$ . D. There are no discontinuities.

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Problem 19013

Simplify: $-4 w(4 t)$ $\square$
Submit Question

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Problem 19014

What is the solution to the following system of equations? $\begin{array}{l} y=5 x-1 \\ x=-4-4 y \end{array}$
Enter your answer by filling in the boxes. $\square$ $\square$

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Problem 19015

Simplify. Assume all variables represent positive real numbers. $\sqrt[3]{-27 x^{6}}$

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Problem 19016

Find the vertical asymptotes, if any, and the values of $x$ corresponding to holes, if any, of the graph of the rational function. $f(x)=\frac{x}{x^{2}+12}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an integer or a fraction. Use a comma to separate answers as needed.) A. The vertical asymptote(s) is (are) $x=$ $\square$ and hole(s) corresponding to $x=$ $\square$ . B. There are no vertical asymptotes but there is (are) hole(s) corresponding to $x=$ $\square$ . C. The vertical asymptote(s) is (are) $x=$ $\square$ . There are no holes. D. There are no discontinuities.

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Problem 19017

Evaluate the definite integral. $\int_{4}^{67} \frac{2 \sqrt{z}-3}{\sqrt[3]{z}} d z$

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Problem 19018

Find the horizontal asymptote, if any, of the graph of the rational function. $f(x)=\frac{17 x}{7 x^{2}+5}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The horizontal asymptote is $\square$ . (Type an equation.) B. There is no horizontal asymptote.

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Problem 19019

Use the properties of logarithms to expand $\log \frac{z^{4}}{y}$ . Each logarithm should involve only one variable and should not have any exponents or fractions. Assume that all variables are positive. $\log \frac{z^{4}}{y}=$ $\log$ $\square$

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Problem 19020

Q4) Find the differential equation whose general solution $y=A \cos (\ln x)+B \sin (\ln x), x>0$ .

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Problem 19021

Solve: $\frac{2}{3} t=6$ $\mathrm{t}=$

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Problem 19022

In certain deep parts of oceans, the pressure of sea water, $P$ , in pounds per square foot, at a depth of $d$ feet below the surface, is given by the following equation: $P=12+\frac{8 d}{13}$
If a scientific team uses special equipment to measures the pressure under water and finds it to be 596 pounds per square foot, at what depth is the team making their measurements?
Answer: The team is are measuring at $\square$ feet below the surface. Submit Question

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Problem 19023

Question 7/10
Solve the following problem. Give your answer in its lowest form. $\frac{1}{4}-\frac{1}{8}=$ $\square$ ASF-24 Submit

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Problem 19024

$\mathrm{I}=\int_{\gamma} \frac{x y}{z \sqrt{1+5 z}} d s \quad \gamma:\left\{\begin{array}{l}x=t \sin t \\ y=t \cos t \\ z=t^{2}\end{array} \quad t \in\left[0, \frac{\pi}{3}\right]\right.$

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Problem 19025

6. $(6,5)$ and $(-2,1)$ $\mathrm{m}=$

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Problem 19026

Find the unknown number in the proportion $\frac{3}{9}=\frac{2}{x}$ $\square$ Submit Question

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Problem 19027

Esercizi di riepilogo 558 Completa inserendo, al posto dei puntini, il simbo10 opportuno $(<,=,>)$ . a. $(-2)^{3}$ . b. m.c.m. $(12,5,6)$ $\qquad$ m.c.m. $(6,10,8)$ c. $(-3+5)^{4}$ $\qquad$ $(-5+3)^{3}$ d. $-|-4| \ldots \ldots . .(-3)^{3}$ e. 1 - M.C.D. $(21,36,18)$ $\qquad$ $-2^{0}$ f. $(-2)(+3)(-5)$ $\qquad$ $(-2)^{3}$ g. $(-13)^{17}$ $\qquad$ $(-14)^{18}$ h. $\mid$ M.C.D. $(14,16,18)-$ m.c.m. $(9,12) \mid$ $\qquad$ $7^{1}$ i. $(-2)(-3)(-5)$ $\qquad$ $(-3)^{3}$ j. $|6-|3-(-4)||$ $\qquad$ $4^{0}$

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Problem 19028

$\lim _{h \rightarrow 0} \frac{\sin \left(\frac{\pi}{3}+h\right)-\sin \frac{\pi}{3}}{h}$

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Problem 19029

(a) Graph the equations in the system. (b) Solve the system by using the substitution method. $\begin{array}{l} x^{2}+y^{2}=25 \\ x+y=-1 \end{array}$
Part: $0 / 2$

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Problem 19030

Solve $36 x^{2}-1764=0$ by factoring. a) Factor $36 x^{2}-1764=0$ to rewrite the equation. $\square$ $=0$ b) The solution set is: $\{$ $\square$ \}

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Problem 19031

Simplify. $4 \sin 2 x \cos 2 x$

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Problem 19032

$x-14 \leq 5$

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Problem 19033

Name: $\text { 2. } \cos (2 x+y)=5 x$

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Problem 19034

Vid ( $\frac{1}{4}$ . The equation of line $a$ is $y=\frac{52}{67} x-24$ . Line $b$ is parallel to line $a$ . What is the slope of line $b$ ? (x) Simplify your answer and write it as a proper fraction, improper fraction, or integer. $\square$ Submit Work it out Not feeling ready yet? These can help: Reciprocals Slope-intercept form: find the slope and $y$ -interce

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Problem 19035

(3) Line $g$ has a slope of $\frac{40}{77}$ . Line $h$ is perpendicular to $g$ . What is the slope of line $h$ ? $\square$ Submit If Work it out Not feeling ready yet? These can help:

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Problem 19036

for Unit 4 Question 12, 4.3.28
Use synthetic division to find the function values. Then ch $f(x)=x^{3}-12 x^{2}+47 x-60 ;$ find $f(3), f(-4)$ , and $f(5)$ . $\qquad$ $\square$ $f(3)=x^{2}-9 x+20$ (Simplify your answer.) $f(-4)=x^{2}-16 x+111-\frac{504}{x-4}$ (Simplify your answer.) $\square$ $\square$ $f(5)=x^{2}-7 x+12-\frac{10}{x+5}$ (Simplify your answer.) Iiew an example Get more help

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Problem 19037

31) $\frac{x}{\sqrt{x-4}}$ A) $\{x \mid x \geq 4\}$ B) all real numbers C) $\{x \mid x \neq 4\}$ D) $\{x \mid x>4\}$

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Problem 19038

Simplify each of the expressions below. Your final simplification should not contain negative exponents. Homework Help a. $\left(5 x^{3}\right)\left(-3 x^{-2}\right)$ b. $\left(4 p^{2} q\right)^{3}$ c. $\frac{3 m^{t}}{m^{-1}}$

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Problem 19039

4. Assuming that $\operatorname{gcd}(a, b)=1$ , prove the following: (b) $\operatorname{gcd}(2 a+b, a+2 b)=1$ or 3 .

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Problem 19040

Simplify exch of the expressions below. Y A. $\left(5 e^{6}\right)\left(-9 \pi^{-2}\right)$

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Problem 19041

The functions $f$ and $g$ are defined as follows. $\begin{array}{l} f(x)=\frac{x^{2}}{x-6} \\ g(x)=\frac{x+9}{x^{2}+17 x+72} \end{array}$
For each function, find the domain. Write each answer as an interval or union of intervals.
Domain of $f$ : $\square$
Domain of $g$ : $\square$

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Problem 19042

4. Factorize: $a^{2}-7 a$ $\qquad$
Level 2: Slightly Challenging
5. Factorize: $3 x^{2}-12 x+12$
6. Factorize: $x^{2}+2 x-8$
7. Factorize: $4 y^{2}-16$
8. Factorize: $5 x^{3}-10 x^{2}+15 x$ $\qquad$
Level 3: Medium Difficulty
9. Factorize: $x^{3}+2 x^{2}-x-2$
10. Factorize: $2 a^{2}-3 a-9$
11. Factorize: $6 x^{2}+13 x+5$
12. Factorize: $9 x^{3}-27 x^{2}+12 x$

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Problem 19043

Given an arithmetic progression with $u_{21}=65$ and $d=-2$ , find the value of the first term.

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Problem 19044

Solve: $\frac{x}{11}-\frac{x}{2}=7+\frac{7 x}{22}$ Select one: a. $x=-\frac{77}{8}$ b. $x=\frac{77}{3}$ c. $x=-\frac{9}{22}$ d. $x=-\frac{22}{9}$ e. $x=-22$

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Problem 19045

Factor $y^{3}-5 y^{2}+6 y-30$ completely. $y^{3}-5 y^{2}+6 y-30=$ $\square$

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Problem 19046

1. Factor. $h^{2}+11 h+24$

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Problem 19047

Solve the system by the addition method. $\begin{array}{l} x^{2}+y^{2}=13 \\ x^{2}-y^{2}=5 \end{array}$

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Problem 19048

b) $2 x^{2}-5 x=7 \quad \rightarrow \quad 2 x$

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Problem 19049

2. $x\left(x^{2}-3 x+3\right)(4 x-7)=0$
3. $\left(4 a^{2}-16\right)\left(a^{2}+9\right)=0$
4. $0=\left(p^{2}-5 p+6\right)(p+1)(p-2)$
5. $\left(x^{2}+2 x+2\right)(2 x-3) x=0$

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Problem 19050

umich.instructure.com Quiz: Prepwork... WN 2025। POL... Atlas | navigate... Google Calenda... Wolverine Acc 0... Fit
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Prepwork 11.6 Started: Dec 3 at 12:17pm Quiz Instructions Watch the videos for Section 11.6. Question 1
What is $\lim _{x \rightarrow \infty} \frac{x^{2}+5}{x^{8}}$ ? That is what is the long run behavior?
Edit View Insert Format Tools Table 12pt Paragraph B I $\underline{U}$ A - $\mathrm{T}^{2}$ ！ MacBook Air 80 F3 F4 F5 40 DII 57 58

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Problem 19051

Find the inverse of the function $f(x)=\sqrt{x}+4$ . $f^{-1}(x)=(x+4)^{2}, x \geq 4$ $f^{-1}(x)=(x-4)^{2}, x \geq 0$ $f^{-1}(x)=(x-4)^{2}, x \geq 4$ $f^{-1}(x)=(x+4)^{2}, x \geq 0$ Clear my selection

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Problem 19052

The population (in thousands) of people of a city is approximated by the function $\mathrm{P}(\mathrm{t})=1400(2)^{0.1048 t}$ , where t is the number of years since 2010. a. Find the population of this group in 2018. b. Predict the population in 2026. a. The population of this group in 2018 is $\square$ (Round to the nearest thousand as needed.)

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Problem 19053

(4) Solve the following equation for $0 \leq x<2 \pi$ $5 \sin x-4 \sqrt{3}=3 \sin x-5 \sqrt{3}$ (10) Let $A=121^{\circ}, C=34^{\circ}$ and $b=18$ . Use Law of Sines to solve for $c$ .

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Problem 19054

$2 x-1=2 \sin x+\cos x$

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Problem 19055

14) $\sum_{n=8}^{\infty} n^{7} x^{n}$ find the interval of convergence

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Problem 19056

4) $\begin{array}{l}14 x-2 y=6 \\ 7 x-4 y=12\end{array}$

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Problem 19057

$6 \sin ^{2} x=5 \cos x-2$

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Problem 19058

Calculate a) $(6+2) \times 4$ b) $6+(2 \times 4)$

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Problem 19059

$\int x^{2} e^{x^{3}} d x$

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Problem 19060

Use the function below to answer the following questions. $y=\log _{2}(x+6)$ (a) Use transformations of the graph of $y=\log _{2} x$ to graph the given function. (b) Write the domain and range in interval notation. (c) Write an equation of the asymptote.
Part: $0 / 3$
Part 1 of 3 (a) Use transformations of the graph of $y=\log _{2} x$ to graph the given function.

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Problem 19061

State what this comparison operator means: >
Type your answer here (max 400 chars.)

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Problem 19062

Write an expression for the perimeter of this shape. Simplify your answer fully.

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Problem 19063

Using the rational root theorem, list out all possible/candidate rational roots of $f(x)=-5 x^{5}+19 x+25 x^{2}-2 x^{4}+17 x^{3}-10$ . Express your answer as inte or as fractions in simplest form. Use commas to separate.

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Problem 19064

Divide. $\left(4 x^{3}-17 x-8\right) \div\left(2 x^{2}-5\right)$
Write your answer in the following form: Quotient $+\frac{\text { Remainder }}{2 x^{2}-5}$ . $\frac{4 x^{3}-17 x-8}{2 x^{2}-5}=\square+\frac{\square}{2 x^{2}-5}$

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Problem 19065

$4 \sin (0.5 x-1)$ amplitude: period: c horizontal shift: $\square$

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Problem 19066

First use front end rounding to estimate the answer. Then multiply to find the exact answer. $\begin{array}{r} 19.4 \\ \times 2.8 \\ \hline \end{array}$
The estimate is $\square$ The answer is $\square$ $\square$ .

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Problem 19067

Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1. $\sin \left(\frac{19 \pi}{12}\right)$

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Problem 19068

Question 3
Find the vertex of the graph of $g(x)=-2 x^{2}+20 x-44$ . $(-5,-194)$ $(5,106)$ $(5,6)$ $(0,-44)$ $(-5,-94)$

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Problem 19069

$y=6+2$ R. The serpe is $\square$
$\square$ 1

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Problem 19070

$10(x+4)+1$

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Problem 19071

Simplify the expression: $\frac{\frac{1}{\cos \theta}-\cos \theta}{\cos \theta}$ a. $\sec ^{2} \theta$ b. $\cot ^{2} \theta$ $\frac{\frac{1}{\cos \theta}-\cos \theta}{\cos \theta}$ c. $\tan ^{2} \theta$ d. 1

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Problem 19072

Solve for $x$ : $\log _{2}(x+5)=5$ 5 20 27 0

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Problem 19073

implify. $11 x^{2} y^{3}\left(16 x^{2} y^{3}\right)$ Attempt 1 out of 2

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Problem 19074

Determine the zeros of the quadratic function $f(x)=6 x^{2}+13 x+5$ . $-\frac{1}{2},-\frac{5}{3}$ $\frac{1}{2}, \frac{5}{3}$ $-\frac{1}{3},-\frac{5}{2}$ $\frac{1}{3}, \frac{5}{2}$

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Problem 19075

Determine all solutions of the equation $-2 w^{2}+14=0$ . $-2,7$ $-7,7$ $-\sqrt{7}, \sqrt{7}$ $-2,-\sqrt{7}, \sqrt{7}$

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Problem 19076

Check your answer: What is $(3 x-2)\left(x^{3}+2 x^{2}+4 x-1\right){ }^{2}$ Use your work from the previous slide to answer. $3 x^{4}+4 x^{3}+8 x^{2}-11 x-2$ $3 x^{4}+4 x^{3}+8 x^{2}-11 x+2$ $3 x^{3}+4 x^{2}+8 x-11 x+2$ $3 x^{4}+8 x^{3}+16 x^{2}$

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Problem 19077

Evaluate the function at the given values of $x$ . Round to 4 decimal places, if necessary. $g(x)=3^{x}$
Part: $0 / 4$
Part 1 of 4 $g(-2)=$ $\square$

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Problem 19078

Evaluate the following expression without using a calculator. $\begin{array}{c} 3^{\log _{3} 2} \\ 3^{\log _{3} 2}= \end{array}$

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Problem 19079

(15 points) Solve the equation below, finding all real solutions. Write your final answer(s) in the box provided. $\log _{6}(2 x-1)+\log _{6}(x)=1$

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Problem 19080

Evaluate the function at the given values of $x$ . Round to 4 decimal places, if necessary. $g(x)=3^{x}$
Part 1 of 4 $g(-2)=0.1111$
Part: 1 / 4
Part 2 of 4 $g(5.7)=$ $\square$

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Problem 19081

Use synthetic division to find the quotient and remainder for $\frac{-2 x^{3}-5 x^{2}-3 x^{2}+3}{x+1}$

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Problem 19082

Find the inverse of the function. $\begin{array}{l} f(x)=\sqrt[3]{13 x+10} \\ f^{-1}(x)= \end{array}$ $\square$
Calculator
Check Answer

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Problem 19083

Solve the quadratic equation by completing the square: $x^{2}+14 x+7=18$ Give the equation after completing the square, but before taking the square root. Your answer should look like: $(x-a)^{2}=b$ The equation is: $\square$ Give all solutions to the equation. The solutions are: $x=$ $\square$ Calculator

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Problem 19084

Find the solution of the system of equations. $\left\{\begin{array}{l} x-5 y=-20 \\ -4 x-5 y=5 \end{array}\right.$
Show your work here $\begin{array}{l} x= \\ y= \end{array}$

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Problem 19085

$\$ 18,000$ is invested in an account paying 3.1\% interest compounded continuously. The amount $A(t)$ in the account after $t$ years is given by the exponential function $A(t)=18,000 e^{0.031 t}$ .
1. Determine the amount in the account after 8 years. (Round to two decimal places) $\square$
2. How many years will it take for the account to grow to $\$ 24,000$ ? (Round to 3 decimal places) $\square$

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Problem 19086

stion 15 yet wered rked out of 0 Flag estion
Decide whether the function is even, odd, or neither. $g(x)=x^{3}-5 x$
Select one: a. Even b. Odd c. Neither odd nor even
Clear my choice

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Problem 19087

Find the domain of the following rational function. $H(x)=\frac{-3 x^{2}}{(x-3)(x+3)}$

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Problem 19088

5) $4 x^{2}-9 y^{2}+80 x+144 y-752=0$ A) Vertices: $(-10,16),(-10,0)$
Foci: $(-10,8+4 \sqrt{13}),(-10,8-4 \sqrt{13})$ B) Vertices: $(2,8),(-22,8)$
Foci: $(-10+4 \sqrt{13}, 8),(-10-4 \sqrt{13}, 8)$ C) Vertices: $(20,10),(-4,10)$
Foci: $(8+4 \sqrt{13}, 10),(8-4 \sqrt{13}, 10)$ D) Vertices: $(8,18),(8,2)$
Foci: $(8,10+4 \sqrt{13}),(8,10-4 \sqrt{13})$

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Problem 19089

Use properties of logarithms to condense the logarithmic expression. logarithmic expressions. $\begin{array}{l} \ln x+\ln 17 \\ \ln x+\ln 17= \end{array}$ $\square$

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Problem 19090

12
Find the solution of the system of equations. $\left\{\begin{array}{l} 5 x+2 y=4 \\ 2 x-2 y=10 \end{array}\right.$
Show your work here $\begin{array}{l} x= \\ y= \end{array}$

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Problem 19091

Solve the equation: $\log _{6}(x)+\log _{6}(x+16)=2$ The solution(s) is (are) $x=$ $\square$
Calculator

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Problem 19092

Use properties of logarithms to condense the logarithmic expression. expressions if possible. $\begin{array}{l} 2 \ln (x+9)-3 \ln x \\ 2 \ln (x+9)-3 \ln x= \end{array}$ $\square$

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Problem 19093

9. Find $g^{\prime}(x)$ if $g(x)=\int_{4 x}^{x^{2}} 6+\cos t d t$

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Problem 19094

Use your calculator to find the real zero(s) and the relative minimum of the function $f(x)=3 x^{3}-3 x^{2}-6 x-4$
The real zero(s) is (are) $\square$ Round to 4 decimal places The relative minimum is $\square$ Round to 4 decimal places
Calculator

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Problem 19095

opening of each. 8) $x=y^{2}+12 y+30$ A) Vertex: $(5,5)$
Focus: $\left(5, \frac{19}{4}\right)$ Axis of Sym.: $x=5$ Opens: Down B) Vertex: $(-6,-6)$
Focus: $\left(-\frac{23}{4},-6\right)$ Axis of Sym: $y=-6$ Opens: Right C) Vertex: $(-6,-6)$
Focus: $\left(-6,-\frac{23}{4}\right)$ Axis of Sym: $:=-6$ Opens: Up D) Verte: $(-6,-6)$
Focus: $\left(-6,-\frac{25}{4}\right)$ Axis of Sym: $x=-6$ Opens: Down

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Problem 19096

(18) Solve for $x: a+b(x-c)=0$ (A) $\frac{a+b c}{b}$ (B) $\frac{b c-a}{b}$ (C) $c-a$ (19) Solve for $x: x^{2}-x+3=0$ (A) $x=$ (C) $x=-\frac{3}{2}, x=\frac{5}{2}$ (D) $x=3, x=-$ (20) Solve for $x: 2 x^{2}-9 x+3=0$ (C) $x=1, x=3$ (A) $x=$ (D) $x=4, x=9$ (21) Solve the inequality: $-3 a+7>19$ (A) $a<-4$ (B) $a<12$ (C) $a>-4$ 2) Find the interval solution for $x$ : (A) $(-2,+2]$ (B) $\left[-\frac{9}{4}, 2\right)$ $-6<4 x+3$ (C) $(-6$

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Problem 19097

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms. Then, use a calculator to obtain a decimal approximation for the solution. $11^{x}=67$
The solution set expressed in terms of logarithms is $\square$ \}. (Use a comma to separate answers as needed. Simplify your answer. Use integers or fractions for any numbers in the expression. Use In for natural logarithm and log for common logarithm.)

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Problem 19098

1. [-/1 Points]
DETAILS MY NOTES
TANAPCALC10 8.3.003. ASK YOUR TEACHER PRACTICE AN
Find the critical point of the function. Then use the second derivative test to classify the nature of this point, if possible. (If an answer does not exist, enter DNE.) $f(x, y)=x^{2}-y^{2}-8 x+2 y+4$ critical point $(x, y)=$ $\square$ classification $\square$ Finally, determine the relative extrema of the function. (If an answer does not exist, enter DNE.) relative minimum value $\square$ relative maximum value $\square$ Need Help? Read It Watch it Submit Answer

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Problem 19099

(19) Solve for $x: x^{2}-x+3=0$ (C) $x=-\frac{3}{2}, x=\frac{5}{2}$ (D) $x=$

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Problem 19100

https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=35611257\&tags=autosave\#question4525502_0
Your best submission for each question part is used for your score.
2. [-/1 Points]
DETAILS MY NOTES TANAPCALC10 8.3.005.MI. ASK YOUR TEACHER PRACTICE AI
Find the critical point of the function. Then use the second derivative test to classify the nature of this point, if possible. (If an answer does not exist, enter DNE.) $\begin{array}{r} f(x, y)=x^{2}+2 x y+2 y^{2}-6 x+10 y+4 \\ (x, y)=(\square) \quad-\text {-Select-- v } \end{array}$
Finally, determine the relative extrema of the function. (If an answer does not exist, enter DNE.) relative minimum value $\square$ relative maximum value $\square$ Need Help? Read It Master It Submit Answer

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Math Statement

Problem 19001

Problem 19002

Используя δ−ε\delta-\varepsilonδ−ε-определение непрерывности покажите, что функция f(x)=x3f(x)=x^{3}f(x)=x3 всюду непрерывна.

Problem 19003

Add, using the rule for order of operations if necessary: [10+(−6)]+[8+(−12)]=[10+(-6)]+[8+(-12)]=[10+(−6)]+[8+(−12)]= □\square□ Submit Question

Problem 19004

Berechne den Grenzwert der Folge (∑k=1nk3(n+1)2+4k)n∈N\left(\sum_{k=1}^{n} \frac{k}{3(n+1)^{2}+4 k}\right)_{n \in \mathbb{N}}(∑k=1n​3(n+1)2+4kk​)n∈N​ mit dem Sandwichsatz.

Problem 19005

Problem 19006

k. +xy=−1(3x2+xy=−1x2−3xy=13)\left.\begin{array}{rr} +x y=-1 & \left(3 x^{2}+x y=-1\right. \\ x^{2}-3 x y=13 \end{array}\right)+xy=−1x2−3xy=13​(3x2+xy=−1)

Problem 19007

Problem 19008

Problem 19009

Используя δ−ε\delta-\varepsilonδ−ε-определение непрерывности покажите, что функция f(x)=x3f(x)=x^{3}f(x)=x3 всюду непрерывна.

Problem 19010

Problem 19011

Express the radical in simplified form. 4) 72\sqrt{72}72​

Problem 19012

Problem 19013

Simplify: −4w(4t)-4 w(4 t)−4w(4t) □\square□Submit Question

Problem 19014

What is the solution to the following system of equations? y=5x−1x=−4−4y\begin{array}{l} y=5 x-1 \\ x=-4-4 y \end{array}y=5x−1x=−4−4y​Enter your answer by filling in the boxes. □\square□ □\square□

Problem 19015

Simplify. Assume all variables represent positive real numbers. −27x63\sqrt[3]{-27 x^{6}}3−27x6​

Problem 19016

Problem 19017

Evaluate the definite integral. ∫4672z−3z3dz\int_{4}^{67} \frac{2 \sqrt{z}-3}{\sqrt[3]{z}} d z∫467​3z​2z​−3​dz

Problem 19018

Problem 19019

Use the properties of logarithms to expand log⁡z4y\log \frac{z^{4}}{y}logyz4​. Each logarithm should involve only one variable and should not have any exponents or fractions. Assume that all variables are positive. log⁡z4y=\log \frac{z^{4}}{y}=logyz4​= log⁡\loglog □\square□

Problem 19020

Q4) Find the differential equation whose general solution y=Acos⁡(ln⁡x)+Bsin⁡(ln⁡x),x>0y=A \cos (\ln x)+B \sin (\ln x), x>0y=Acos(lnx)+Bsin(lnx),x>0.

Problem 19021

Solve: 23t=6\frac{2}{3} t=632​t=6 t=\mathrm{t}=t=

Problem 19022

Problem 19023

Question 7/10Solve the following problem. Give your answer in its lowest form. 14−18=\frac{1}{4}-\frac{1}{8}=41​−81​= □\square□ ASF-24 Submit

Problem 19024

Problem 19025

6. (6,5)(6,5)(6,5) and (−2,1)(-2,1)(−2,1) m=\mathrm{m}=m=

Problem 19026

Find the unknown number in the proportion 39=2x\frac{3}{9}=\frac{2}{x}93​=x2​ □\square□ Submit Question

Problem 19027

Problem 19028

lim⁡h→0sin⁡(π3+h)−sin⁡π3h\lim _{h \rightarrow 0} \frac{\sin \left(\frac{\pi}{3}+h\right)-\sin \frac{\pi}{3}}{h}limh→0​hsin(3π​+h)−sin3π​​

Problem 19029

(a) Graph the equations in the system. (b) Solve the system by using the substitution method. x2+y2=25x+y=−1\begin{array}{l} x^{2}+y^{2}=25 \\ x+y=-1 \end{array}x2+y2=25x+y=−1​Part: 0/20 / 20/2

Problem 19030

Solve 36x2−1764=036 x^{2}-1764=036x2−1764=0 by factoring. a) Factor 36x2−1764=036 x^{2}-1764=036x2−1764=0 to rewrite the equation. □\square□ =0=0=0 b) The solution set is: {\{{ □\square□ \}

Problem 19031

Simplify. 4sin⁡2xcos⁡2x4 \sin 2 x \cos 2 x4sin2xcos2x

Problem 19032

x−14≤5x-14 \leq 5x−14≤5

Problem 19033

Name: 2. cos⁡(2x+y)=5x\text { 2. } \cos (2 x+y)=5 x 2. cos(2x+y)=5x

Problem 19034

Problem 19035

(3) Line ggg has a slope of 4077\frac{40}{77}7740​. Line hhh is perpendicular to ggg. What is the slope of line hhh ? □\square□ Submit If Work it out Not feeling ready yet? These can help:

Problem 19036

Problem 19037

31) xx−4\frac{x}{\sqrt{x-4}}x−4​x​ A) {x∣x≥4}\{x \mid x \geq 4\}{x∣x≥4} B) all real numbers C) {x∣x≠4}\{x \mid x \neq 4\}{x∣x=4} D) {x∣x>4}\{x \mid x>4\}{x∣x>4}

Problem 19038

Simplify each of the expressions below. Your final simplification should not contain negative exponents. Homework Help a. (5x3)(−3x−2)\left(5 x^{3}\right)\left(-3 x^{-2}\right)(5x3)(−3x−2) b. (4p2q)3\left(4 p^{2} q\right)^{3}(4p2q)3 c. 3mtm−1\frac{3 m^{t}}{m^{-1}}m−13mt​

Problem 19039

4. Assuming that gcd⁡(a,b)=1\operatorname{gcd}(a, b)=1gcd(a,b)=1, prove the following: (b) gcd⁡(2a+b,a+2b)=1\operatorname{gcd}(2 a+b, a+2 b)=1gcd(2a+b,a+2b)=1 or 3 .

Problem 19040

Simplify exch of the expressions below. Y A. (5e6)(−9π−2)\left(5 e^{6}\right)\left(-9 \pi^{-2}\right)(5e6)(−9π−2)

Problem 19041

Problem 19042

Problem 19043

Given an arithmetic progression with u21=65u_{21}=65u21​=65 and d=−2d=-2d=−2, find the value of the first term.

Problem 19044

Solve: x11−x2=7+7x22\frac{x}{11}-\frac{x}{2}=7+\frac{7 x}{22}11x​−2x​=7+227x​ Select one: a. x=−778x=-\frac{77}{8}x=−877​ b. x=773x=\frac{77}{3}x=377​ c. x=−922x=-\frac{9}{22}x=−229​ d. x=−229x=-\frac{22}{9}x=−922​ e. x=−22x=-22x=−22

Problem 19045

Factor y3−5y2+6y−30y^{3}-5 y^{2}+6 y-30y3−5y2+6y−30 completely. y3−5y2+6y−30=y^{3}-5 y^{2}+6 y-30=y3−5y2+6y−30= □\square□

Problem 19046

1. Factor. h2+11h+24h^{2}+11 h+24h2+11h+24

Problem 19047

Solve the system by the addition method. x2+y2=13x2−y2=5\begin{array}{l} x^{2}+y^{2}=13 \\ x^{2}-y^{2}=5 \end{array}x2+y2=13x2−y2=5​

Используя $\delta-\varepsilon$ -определение непрерывности покажите, что функция $f(x)=x^{3}$ всюду непрерывна.

Add, using the rule for order of operations if necessary: $[10+(-6)]+[8+(-12)]=$ $\square$ Submit Question

Berechne den Grenzwert der Folge $\left(\sum_{k=1}^{n} \frac{k}{3(n+1)^{2}+4 k}\right)_{n \in \mathbb{N}}$ mit dem Sandwichsatz.

k. $\left.\begin{array}{rr} +x y=-1 & \left(3 x^{2}+x y=-1\right. \\ x^{2}-3 x y=13 \end{array}\right)$

Используя $\delta-\varepsilon$ -определение непрерывности покажите, что функция $f(x)=x^{3}$ всюду непрерывна.

Express the radical in simplified form. 4) $\sqrt{72}$

Simplify: $-4 w(4 t)$ $\square$
Submit Question

What is the solution to the following system of equations? $\begin{array}{l} y=5 x-1 \\ x=-4-4 y \end{array}$
Enter your answer by filling in the boxes. $\square$ $\square$

Simplify. Assume all variables represent positive real numbers. $\sqrt[3]{-27 x^{6}}$

Evaluate the definite integral. $\int_{4}^{67} \frac{2 \sqrt{z}-3}{\sqrt[3]{z}} d z$

Use the properties of logarithms to expand $\log \frac{z^{4}}{y}$ . Each logarithm should involve only one variable and should not have any exponents or fractions. Assume that all variables are positive. $\log \frac{z^{4}}{y}=$ $\log$ $\square$

Q4) Find the differential equation whose general solution $y=A \cos (\ln x)+B \sin (\ln x), x>0$ .

Solve: $\frac{2}{3} t=6$ $\mathrm{t}=$

Question 7/10
Solve the following problem. Give your answer in its lowest form. $\frac{1}{4}-\frac{1}{8}=$ $\square$ ASF-24 Submit

6. $(6,5)$ and $(-2,1)$ $\mathrm{m}=$

Find the unknown number in the proportion $\frac{3}{9}=\frac{2}{x}$ $\square$ Submit Question

$\lim _{h \rightarrow 0} \frac{\sin \left(\frac{\pi}{3}+h\right)-\sin \frac{\pi}{3}}{h}$

(a) Graph the equations in the system. (b) Solve the system by using the substitution method. $\begin{array}{l} x^{2}+y^{2}=25 \\ x+y=-1 \end{array}$
Part: $0 / 2$

Solve $36 x^{2}-1764=0$ by factoring. a) Factor $36 x^{2}-1764=0$ to rewrite the equation. $\square$ $=0$ b) The solution set is: $\{$ $\square$ \}

Simplify. $4 \sin 2 x \cos 2 x$

$x-14 \leq 5$

Name: $\text { 2. } \cos (2 x+y)=5 x$

(3) Line $g$ has a slope of $\frac{40}{77}$ . Line $h$ is perpendicular to $g$ . What is the slope of line $h$ ? $\square$ Submit If Work it out Not feeling ready yet? These can help:

31) $\frac{x}{\sqrt{x-4}}$ A) $\{x \mid x \geq 4\}$ B) all real numbers C) $\{x \mid x \neq 4\}$ D) $\{x \mid x>4\}$

Simplify each of the expressions below. Your final simplification should not contain negative exponents. Homework Help a. $\left(5 x^{3}\right)\left(-3 x^{-2}\right)$ b. $\left(4 p^{2} q\right)^{3}$ c. $\frac{3 m^{t}}{m^{-1}}$

4. Assuming that $\operatorname{gcd}(a, b)=1$ , prove the following: (b) $\operatorname{gcd}(2 a+b, a+2 b)=1$ or 3 .

Simplify exch of the expressions below. Y A. $\left(5 e^{6}\right)\left(-9 \pi^{-2}\right)$

Given an arithmetic progression with $u_{21}=65$ and $d=-2$ , find the value of the first term.

Solve: $\frac{x}{11}-\frac{x}{2}=7+\frac{7 x}{22}$ Select one: a. $x=-\frac{77}{8}$ b. $x=\frac{77}{3}$ c. $x=-\frac{9}{22}$ d. $x=-\frac{22}{9}$ e. $x=-22$

Factor $y^{3}-5 y^{2}+6 y-30$ completely. $y^{3}-5 y^{2}+6 y-30=$ $\square$

1. Factor. $h^{2}+11 h+24$

Solve the system by the addition method. $\begin{array}{l} x^{2}+y^{2}=13 \\ x^{2}-y^{2}=5 \end{array}$

b) $2 x^{2}-5 x=7 \quad \rightarrow \quad 2 x$

(4) Solve the following equation for $0 \leq x<2 \pi$ $5 \sin x-4 \sqrt{3}=3 \sin x-5 \sqrt{3}$ (10) Let $A=121^{\circ}, C=34^{\circ}$ and $b=18$ . Use Law of Sines to solve for $c$ .

$2 x-1=2 \sin x+\cos x$

14) $\sum_{n=8}^{\infty} n^{7} x^{n}$ find the interval of convergence

4) $\begin{array}{l}14 x-2 y=6 \\ 7 x-4 y=12\end{array}$

$6 \sin ^{2} x=5 \cos x-2$

Calculate a) $(6+2) \times 4$ b) $6+(2 \times 4)$

$\int x^{2} e^{x^{3}} d x$

State what this comparison operator means: >
Type your answer here (max 400 chars.)

Using the rational root theorem, list out all possible/candidate rational roots of $f(x)=-5 x^{5}+19 x+25 x^{2}-2 x^{4}+17 x^{3}-10$ . Express your answer as inte or as fractions in simplest form. Use commas to separate.

$4 \sin (0.5 x-1)$ amplitude: period: c horizontal shift: $\square$

First use front end rounding to estimate the answer. Then multiply to find the exact answer. $\begin{array}{r} 19.4 \\ \times 2.8 \\ \hline \end{array}$
The estimate is $\square$ The answer is $\square$ $\square$ .

Use an Addition or Subtraction Formula to find the exact value of the expression, as demonstrated in Example 1. $\sin \left(\frac{19 \pi}{12}\right)$

Question 3
Find the vertex of the graph of $g(x)=-2 x^{2}+20 x-44$ . $(-5,-194)$ $(5,106)$ $(5,6)$ $(0,-44)$ $(-5,-94)$

$y=6+2$ R. The serpe is $\square$
$\square$ 1

$10(x+4)+1$

Solve for $x$ : $\log _{2}(x+5)=5$ 5 20 27 0

implify. $11 x^{2} y^{3}\left(16 x^{2} y^{3}\right)$ Attempt 1 out of 2

Determine the zeros of the quadratic function $f(x)=6 x^{2}+13 x+5$ . $-\frac{1}{2},-\frac{5}{3}$ $\frac{1}{2}, \frac{5}{3}$ $-\frac{1}{3},-\frac{5}{2}$ $\frac{1}{3}, \frac{5}{2}$