Math Statement

Problem 2201

Follow the instructions below.
Write $b^{3} \cdot b^{2}$ without exponents. $b^{3} \cdot b^{2}=$ $\square$
Fill in the blank. $b^{3} \cdot b^{2}=b^{[ }$

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Problem 2202

Simplify. $\left(u^{4}\right)^{5}$
Write your answer without parentheses.

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Problem 2203

Find the differential of $y=\cos (-6 \pi x)$ .

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Problem 2204

$001 \quad 10.0$ points For an arithmetic sequence $a_{1}=13 \text { and } d=-\frac{1}{2} .$
Find the term $a_{23}$ of the sequence. $002 \quad 10.0$ points Consider an arithmetic sequence where $a_{1}=10 \text { and } d=5 \text {. }$
Find the term $a_{27}$ of the sequence.

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Problem 2205

Compute (a) $\Delta y$ and (b) dy for the given values of $x$ and $\mathrm{dx}=\Delta x$ . $y=7-x^{2}, \quad x=-2, \quad \Delta x=.4$ (a) $\Delta y=$ $\square$ (b) $d y=$ 16 $\square$

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Problem 2206

Solve the inequality for $u$ . $1-5 u \leq-9$
Simplify your answer as much as possible.

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Problem 2207

Factor the common factor out of each expression. Date 1) $-28 n^{5}+56 n^{2}+63 n$ A) $7 n\left(-4 n^{4}+8 n+9\right)$ 2) $-24 r^{6}-8 r^{5}-80 r^{4}$ B) $7 n\left(-4 n^{4}+n+3\right)$ A) $-8 r^{4}\left(3 r^{2}+r+10\right)$ C) $7 n\left(-28 n^{5}+56 n^{2}+63 n\right)$ D) $7 n\left(-4 n^{5}+8 n^{2}+9 n\right)$ B) $-8 r^{4}\left(3 r^{3}+r^{2}+10 r\right)$ C) $-8 r^{4}\left(3 r^{3}+r^{2}+10\right)$ D) $-8 r^{4}\left(3 r^{3}+r+10\right)$ 3) $8 m^{3}-6 m+10$ A) $2\left(4 m^{3}-3 m+5\right)$ 4) $40-30 x+70 x^{2}$ B) $2\left(4 m^{4}-3 m^{2}+5\right)$ A) $10\left(4-3 x+7 x^{2}\right)$ C) $2 m\left(4 m^{3}-3 m+5\right)$ B) $10 x\left(2-3 x+7 x^{3}\right)$ D) $m\left(4 m^{3}-3 m^{2}+5\right)$ C) $20\left(20-15 x^{2}+35 x^{3}\right)$ D) $10 x\left(4-3 x+7 x^{2}\right)$

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Problem 2208

Without calculation, find one eigenvalue and two linearly independent eigenvectors of $A=\left[\begin{array}{lll}2 & 2 & 2 \\ 2 & 2 & 2 \\ 2 & 2 & 2\end{array}\right]$ . Justify your answer.
One eigenvalue of $A$ is $\lambda=0$ because the columns of $A$ are linearly dependent. Two linearly independent eigenvectors of $A$ are $\square$ because the entries of each vector sum to 0 . (Use a comma to separate answers as needed.)

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Problem 2209

1. Find the derivatives of the following functions: a) $y=\frac{x^{3}}{\sinh x}$ b) $y=\tanh ^{3} 2 x$ c) $y=e^{\cosh 4 x^{2}}$

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Problem 2210

$\begin{array}{l}\text { b) } y=\ln \left(\frac{x^{2} \cdot \sqrt{2 x+1}}{\cos ^{4} x}\right) \\ \operatorname{Ln} x^{2}+\ln \sqrt{2 x+1}-\ln \cos ^{4} x \\ 2 \ln x+\frac{1}{2} \ln 2 x+1-4 \ln \cos x \\ 2 x \frac{1}{x}+\frac{1}{2} \times 2-4(=\sin x) \\ \frac{2}{2 x}+1-4[-\sin x]\end{array}$

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Problem 2211

Find the characteristic polynomial and the eigenvalues of the matrix. $\left[\begin{array}{rr} 9 & 4 \\ -4 & 3 \end{array}\right]$
The characteristic polynomial is $\square$ $\square$ . (Type an expression using $\lambda$ as the variable. Type an exact answer, using radicals as needed.)

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Problem 2212

1. Write a balanced chemical equation, including physical state symbols, for the combustion of liquid nonane into gaseous carbon dioxide and gaseous water. $\mathrm{C}_{9} \mathrm{H}_{20}(l)+14 \mathrm{O}_{2}(g) \rightarrow 9 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)$
2. Suppose 0.340 kg of nonane are burned in air at a pressure of exactly 1 atm and a temperature of $15.0^{\circ} \mathrm{C}$ . Calculate the volume of carbon dioxide gas that is produced. Round your answer to 3 significant digits. $\square$ L

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Problem 2213

Clever | Portal Big Ideas Math:Assessment bigideasmath.com/BIM/student/assignment?studentAssignmentId=cda1057e-bdb8-45d7-80f1-8 몸ㅁㅁㅁㅣ 煰品 Play Kahootl-Enter. 0 Classroom Learn to Type I Type. BIG IDEAS MATH Course 3: CA > Chapter 3: Angles of Polygons > Section Exercises 3.3 > Exercise 36
Solve the proportion. $\frac{9}{x}=\frac{6}{2}$ $x=18 x$ x $\qquad$ $\qquad$ 36

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Problem 2214

Given $\sqrt[3]{27}=k$ , where $k$ is an integer, what is the value of $k$ ?

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Problem 2215

3. $\frac{10-(-3)^{2}-(-4-9)}{-3+5}$

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Problem 2216

8. $g+\frac{1}{2}=-\frac{3}{2}$

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Problem 2217

Determine if the following vectors are orthogonal. $\mathbf{u}=\left[\begin{array}{r} 10 \\ 5 \\ 1 \end{array}\right], \mathbf{v}=\left[\begin{array}{r} 2 \\ -5 \\ 5 \end{array}\right]$
Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a simplified fraction.) A. The vectors $\mathbf{u}$ and $\mathbf{v}$ are orthogonal because $\mathbf{u}+\mathbf{v}=$ $\square$ . B. The vectors $\mathbf{u}$ and $\mathbf{v}$ are not orthogonal because $\mathbf{u}+\mathbf{v}=$ $\square$ . C. The vectors $\mathbf{u}$ and $\mathbf{v}$ are not orthogonal because $\mathbf{u} \cdot \mathbf{v}=$ $\square$ $\square$ . D. The vectors $\mathbf{u}$ and $\mathbf{v}$ are orthogonal because $\mathbf{u} \cdot \mathbf{v}=$ $\square$ .

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Problem 2218

$\frac{2^{n+1}-2^{n+2}}{2^{n-1}-2^{n-2}}$

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Problem 2219

13. Assume A and B are $5 \times 5$ matrices. Which of the following might be invalid? a. $(7 A)^{T}=7 A^{T}$ b. $(A B)^{T}=A^{T} B^{T}$ c. $(A+B)^{T}=B^{T}+A^{T}$ d. $(A-B)^{T}=A^{T}-B^{T}$
14. Given the matrices: $A$ is $3 \times 5, B$ is $3 \times 1, C$ is $2 \times 1, D$ is $2 \times 2, E$ is $3 \times 3, F$ is $1 \times 4, G$ is $4 \times 1$ . Which matrix operation is defined? a. $\mathrm{A}+\mathrm{B}$ b. C-D c. $\mathrm{D}+\mathrm{E}$ d. FG
15. The matrix $\left[\begin{array}{cccc}1 & 3 & 1 & 4 \\ 0 & -5 & 7 & 2 \\ 0 & 0 & 0 & 5 \\ 0 & 0 & 0 & 6\end{array}\right]$ is in reduced row-echolon form a. true b. false
16. Given that $A$ is invertible, $A^{-1} A B$ is not equal to a. $\mathrm{ABA}^{-1}$ b. $\mathrm{AA}^{-1} \mathrm{~B}$ c. B d. $\mathrm{BB}^{-1} \mathrm{~B}$
17. If $A$ is an $5 \times 10$ matrix and $B$ is an $10 \times 3$ matrix, then the matrix products $A B$ and $A^{T} B^{T}$ are defined. a. true b. false
18. The determinant of the matrix $\left[\begin{array}{lll}1 & 1 & 1 \\ 0 & 8 & 0 \\ 9 & 4 & 6\end{array}\right]$ is $\begin{array}{lll}\text { a. }-24 & 4.24 & \text { c. } 48\end{array}$ c. 48 d. 0
19. If $A$ is a square matrix then $\operatorname{det}(A)=\operatorname{det}\left(A^{T}\right)$ a. true b. false
20. Given 2 different vectors $u$ and $v$ in 3-space, which of the following vectors is always orthogonal to $u$ ? a. $u+v$ b. u-v c. u.v d. uxv
21. The trancformation $T(x, y)=(2 x+1,3 y+2)$ is linear. false $\begin{aligned} & \text { matrix } A=\left[\begin{array}{l}1 \\ 1 \\ 2 \\ \\ \\ -1\end{array}=\left[\begin{array}{llr}-4 / 3 & 1 / 3 & 1 \\ 1 / 3 & -1 / 3 & 0 \\ 5 / 3 & 1 / 3 & -1\end{array}\right] .\right.\end{aligned}$ a. true b. false
23. The vector component of $v \mathrm{l}=(3,4)$ in the direction of $v 2=(1,1)$ is a. $(3.5,3.5)$ b. $(3,3)$ c. $(4,5)$ d. $(2,2)$
24. The number of different Eigen values of the matrix $\left[\begin{array}{lll}0 & 4 & 3 \\ 0 & 0 & 6 \\ 0 & 0 & 9\end{array}\right]$ is $\begin{array}{llll}\text { a. } 1 & \text { b. } 2 & \text { c. } 3 & \text { d. } 4\end{array}$ 2

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Problem 2220

1. You have a right rectangular prism and you're required to find the perimeter, area of the base, and the volume. The measurement of the given prism is as follows: $\begin{array}{l} \text { Length }=60 \mathrm{~cm} \\ \text { Width }=10 \mathrm{~cm} \\ \text { Height }=5 \mathrm{~cm} \end{array}$

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Problem 2221

The derivative of $y=e^{\tan ^{-1} x}$ is:

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Problem 2222

Using an appropriate substitution (Inverse trigonometric): $\int \frac{d x}{x^{2}+6 x+90}=$

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Problem 2223

Esercizio 1. Rispondere al più a uno dei seguenti quesiti. i) Calcolare, al variare del parametro $\alpha \in[0,+\infty)$ , il limite per $n \rightarrow+\infty$ della successione $\left(a_{n}\right)_{n}$ tale che $a_{n}=\frac{\sin \frac{\sqrt{6}}{n}}{\exp \left(\frac{2 \log n}{n^{\frac{3}{2}}}\right)-1}\left[1-\cos \left(\frac{1}{n^{\alpha}}\right)\right], \quad n \geq 1$

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Problem 2224

2. Вычислить интеграл: $\int_{l}\left(i z^{3}+3\right) d z$ , где $l$ - отрезок прямой от точки $z_{1}=1$ до точки $z_{2}=i$ .

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Problem 2225

2. Solve the following set of linear equations by the matrix method: a) $\begin{array}{l} x_{1}+3 x_{2}+2 x_{3}=3 \\ 2 x_{1}-x_{2}-3 x_{3}=-8 \\ 5 x_{1}+2 x_{2}+x_{3}=9 \end{array}$ A Self-regulated Learning Module

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Problem 2226

Упражнения
1. Представить в виде многочлена:
1. $\left(\frac{1}{5}-m\right)^{2}$
2. $\left(2+\frac{1}{8} x\right)^{2}$
3. $\left(-7 y+\frac{1}{7} x\right)^{2}$
4. $\left(x-\frac{3}{4}\right)\left(\frac{3}{4}+x\right)$
5. $(4 x+2 y)^{3}$ II. Разложить на множители:
1. $9 x^{2}-6 x+1$
2. $16 m^{2}+24 m n+9 n^{2}$
3. $0,09 m^{2}-64 n^{2}$
4. $7,29 x^{6}-7,84 y^{6}$
5. $27 a^{3}-64 b^{3}$
6. $(2-x)^{2}-(3 x+5)^{2}$
7. $(3 m+5)^{2}-64$
8. $x^{2}-2 x-3$
9. $7 x^{2}-5 x+3$ III. Сократить дробь
1. $\frac{4 a-4 b}{a^{2}-b^{2}}$
2. $\frac{14 c-8 b}{49 c^{2}-16 b^{2}}$ $\frac{4 x^{2}+20 x+25}{4 x^{2}-25}$ IV. Упростить выражение
1. $\sqrt[3]{2 a b^{2}} \cdot \sqrt[3]{4 a^{2} b}$
2. $\sqrt[4]{\frac{a b}{c}} \cdot \sqrt[4]{\frac{a^{3} c}{b}}$
3. $\frac{\sqrt[5]{a^{6} \cdot b^{7}}}{\sqrt[5]{a \cdot b^{2}}}$
4. $\frac{\sqrt[3]{\frac{3 x}{y^{2}}}}{\sqrt[3]{\frac{y}{9 x^{2}}}}$
5. $\left(\sqrt[6]{x^{4}}\right)^{-3}$
6. $\sqrt{\sqrt[3]{729}}$
7. $\sqrt[3]{\sqrt[3]{9}} \cdot \sqrt[9]{3^{7}}$
8. $\left(\sqrt{\sqrt[3]{a^{2} b}}\right)^{6}$
9. $\left(x^{3 / 4}\right)^{4 / 5}$
10. $\frac{\left(\mathrm{a}^{-3}\right)^{-2} \cdot\left(\mathrm{a}^{3}\right)^{-3}}{\left(\mathrm{a}^{-1}\right)^{-2}:\left(\mathrm{a}^{2}\right)^{-4}}$
11. $\left(\frac{2}{5} a^{-3} b^{2}\right)^{-2}:\left(3 \frac{1}{3} a^{-4} b^{3}\right)^{2}$

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Problem 2227

Having that $\operatorname{gcd}(a, b)=1$ , prove the following- (i) $\operatorname{gcd}(2 a+b, a+2 b)=1$ or 3 . (ii) $\operatorname{god}\left(a+b, a^{2}+b^{2}\right)=1$ or 2 .

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Problem 2228

5. Найти разложение функции в ряд Лорана в точке $z_{0}$ по степеням $z-z_{0}$ . Указать главную и правильную части ряда и его область сходимости. $\frac{z+2 i}{(z-1)^{2}}, z_{0}=1$

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Problem 2229

Example: Differentiate the following functions.
1. $f(x)=\left(x^{4}+3\right)^{50}$
2. $g(t)=\sqrt{t^{3} \sin t}$

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Problem 2230

If $f(x)=\frac{3 x-1}{x-2}$ then $f^{-1}(x)=$ A) $\frac{x-2}{x-3}$ B) $\frac{2 x-1}{x-3}$ C) $\frac{2 x+1}{x-3}$ D) $\frac{x-3}{2 x-1}$

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Problem 2231

If $f^{-1}(x)=\frac{1}{x-9}$ then $D_{f}=$ A) $\mathbb{R}-\{9\}$ B) $\mathbb{R}-\{1\}$ C) $\mathbb{R}$ D) $\mathbb{R}-\{0\}$

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Problem 2232

Graph the following. Identify the Amplitude and Period of each. 1.) $y=7 \sin x$ 2.) $y=-3 \cos x$ 3.) $y=\frac{1}{2} \cos x$ 4.) $y=\frac{2}{3} \sin x$
5. $y=\sin (2 x)$ 6.) $y=\cos \left(\frac{1}{3} x\right)$ 7.) $y=\sin (-x)$ 8.) $y=\cos (\pi x)$ 9.) $y=4 \sin (2 x)$ 10.) $y=-2 \cos \left(\frac{1}{4} x\right)$

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Problem 2233

• Problem 3: (9 points) Find the local maximum and minimum values and saddle points of the function f(x, y) = x³- xy + y³

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Problem 2234

1. $\begin{array}{l} \frac{1}{2} z^{2}+3 \frac{1}{2}+5 z-3+6 z-\frac{1}{2} z^{2} \\ =\left(\square z^{2}-\square z+\left(\square z+\left(\square z^{2}\right)+\square\right.\right. \\ =\square z^{2}+\square \\ \square\end{array}$

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Problem 2235

2. $4 y+9 y$

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Problem 2236

$3 \times \frac{4}{10}$

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Problem 2237

6. $\frac{1}{2} x+\frac{1}{2}+\frac{1}{2} x+\frac{1}{2}$

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Problem 2238

13. $z^{4}+z^{4}+z^{4}+z^{4}$

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Problem 2239

$=\left(1 \frac{1}{2} z^{2}-\left[\frac{1}{2} z^{2}\right)\right.$

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Problem 2240

2 A medicine manufacturer produces pain relieving tablets. Each tablet is in the shape of a solid circular cylinder with base radius $x \mathrm{~mm}$ and height $h$ mm , whose surface area is $A=2 \pi x^{2}+\frac{120}{x}$ where $A$ is measured in $\mathrm{mm}^{2}$ . If the manufacturer wishes to minimize the surface area of each tablet, find the value of $x$ for which $A$ is a minimum, to 2 decimal places. A. 2.21 B. 2.12 C. 1.23 D. 1.32

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Problem 2241

8 70 Г9gs 9

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Problem 2242

8 70 Г9gs 9

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Problem 2243

$\frac{3}{8} \div \frac{1}{4}=$

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Problem 2244

$2 \div 3 \frac{2}{3}=$
Sulmity

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Problem 2245

10. Given that $x^{2}-2 b x+225$ is a perfect square, find the possible values of $b$ .

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Problem 2246

Differentiate the function. $y=\left(9 x^{4}-x+4\right)\left(-x^{5}+3\right)$

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Problem 2247

Use the quotient rule to find the derivative of the following. $y=\frac{x^{2}-3 x+1}{x^{2}+5}$

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Problem 2248

3) $f(x)=2(5 x+1)$ $\begin{array}{l} f(0)= \\ f(-2)= \\ f(2)= \end{array}$

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Problem 2249

Solve for $x$ . $y=(7+x) m$

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Problem 2250

What is the formula for the volume of a right cone with base area $B$ and height $h$ ? A. $V=\frac{1}{3} B h$ B. $v=B h$ C. $V=2 B h^{2}$ D. $v=-\frac{1}{3} B h$

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Problem 2251

Create the $n$ th Taylor's Polynomial for $\ln (x)$ about $x=1$ .

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Problem 2252

If $f(x)=\sqrt{-x^{2}+5 x-6}$ , then what is $\operatorname{dom}(f)$ ? (A) $(-\infty, 2] \cup[3, \infty)$ (B) $[2,3]$ (C) $(-\infty, 2) \cup(3, \infty)$ (D) $(-\infty,-2) \cup(3, \infty)$ (E) $(-\infty,-2] \cup(3, \infty)$

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Problem 2253

\#49) $\left\{\begin{array}{c}-3 x-18, \quad \text { for } x<-5, \\ 1, \quad \text { for }-5 \leq x<1, \\ x+2, \quad \text { for } x \geq 1\end{array}\right.$ a) b) \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-5 \\ \hline-3 \\ \hline 0 & \\ \hline \end{tabular}

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Problem 2254

The graph of $y=\ln x$ after reflecting it about the $x$ -axis then shifting it 2 units to the left is the graph of (A) $y=-\ln (x+2)$ (B) $y=-\ln (x-2)$ (C) $y=\ln (2-x)$ (D) $y=\ln (-x-2)$ (E) $y=-\ln (2-x)$

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Problem 2255

The graph of $y=\ln x$ after reflecting it about the $x$ -axis then shifting it 2 units to the left is the graph of (A) $y=-\ln (x+2)$ (B) $y=-\ln (x-2)$ (C) $y=\ln (2-x)$ (D) $y=\ln (-x-2)$ (E) $y=-\ln (2-x)$

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Problem 2256

The equation of the following conic section is (A) $9 x^{2}-y^{2}=36$ (B) $x^{2}-9 y^{2}=36$ (C) $x^{2}+3 y^{2}=6$ (D) $9 x^{2}+y^{2}=36$ (E) $x^{2}+9 y^{2}=36$

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Problem 2257

$\angle T U W \cong \angle V U W .$
Which term describes $\overline{U W}$ ? perpendicular bisector altitude angle bisector median

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Problem 2258

If $f(x)=2-3^{x-1}$ , then what is range of $f$ ? (A) $(-\infty, 2)$ (B) $(-\infty, 2]$ (C) $(2, \infty)$ (D) $[2, \infty)$ (E) $(-\infty, 0)$

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Problem 2259

ewrite $f(x)=(a x+b) /(x+c)$ in $f(x)=a+d /(x+c)$ form. 5) $f(x)=\frac{x-3}{x-4}$

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Problem 2260

et is launched from a platform 20 feet above the ground with an initial velocity of 60 feet per second. Its height is given by $h(t)=-16 t 2+60 t+20 h(t)=-16 t^{\wedge} 2$ $+60 \mathrm{t}+20 \mathrm{~h}(\mathrm{t})=-16 \mathrm{t} 2+60 \mathrm{t}+20$ . Find the time it takes to reach maximum height.

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Problem 2261

Solve the rational inequality. 7) $\frac{-4 x+7}{5 x^{2}+6}>0$

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Problem 2262

$\begin{array}{l} \frac{4}{x}+5 y=7 \\ \text { Let } \frac{1}{x} b e \\ 4 a+5 y=7 \rightarrow \text { (1) } \\ \frac{3}{x}+4 y=5 \\ 3 a+4 y=5 \rightarrow \text { (2) } \end{array}$

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Problem 2263

The weekly revenue from the sale of $x$ units of a service is given by $R(x)=110 x-5 x^{2}$ thousand dollars, where $0 \leq x \leq 19$ . How many units should be sold to maximize the revenue?

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Problem 2264

Simple cless - work $\begin{array}{l} \frac{(x+4)^{8}}{x^{-3}} \\ \frac{5^{x} \times 25^{x-1}}{125^{x+1}} \\ \frac{163 / 4-8 \frac{1}{3}}{2^{2} \times 3} \end{array}$
Solution

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Problem 2265

$\begin{array}{r}x+y+z=5 \\ x-y+4 z=2 \\ 5 x+y+z=9\end{array}$

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Problem 2266

$1 = 3x + 2x^2y^2$ Implicit differentiation

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Problem 2267

(15 points) Use an analytic method to solve $\sqrt{4 x-3}=2 x-3$

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Problem 2268

Find the average rate of change of the function $f(x) = x^3 + 2x^2 - 5x + 3$ over the interval $[1, 5]$ .

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Problem 2269

PROBLEM 2: GRAPHING A LINE USING INTERCEPTS Graph each equation using the $x$ - and $y$ -intercepts.
9. $x-2 y=-2$
10. $2 x+5 y=20$
11. $2 x-3 y=12$
12. $-x+3 y=6$
13. $6 x-2 y=18$
14. $-4 x+3 y=18$
PROBLEM 3: GRAPHING HORIZONTAL AND VERTICAL LINES If $A=0$ in the standard form $A x+B y=C$ , then you can write the equation in the form $y=b$ , where $b$ is a constant. If $B=0$ , you can write the equation in the form $x=a$ , where $a$ is a constant. The graph of $y=b$ is a horizontal line, and the graph of $x=a$ is a vertical line.

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Problem 2270

8) $2 x-3 y=6$

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Problem 2271

$-12 y^{3}(2 x y)$
Answer Attempt 1 out of 2

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Problem 2272

$\left\{\begin{array}{l}x+y=-8 \\ x-y=-4\end{array}\right.$

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Problem 2273

$\text{Find the average rate of change of the function } f(x) = \frac{2x-1}{x+4} \text{ over the interval } [-3, 8].$

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Problem 2274

(1 point)
The total cost (in hundreds of dollars) of producing $x$ slide rules per day is $C(x)=12+\sqrt{2 x+20}$
Find the marginal cost at each production level $x$ given below: $\begin{array}{l} x=25 \square \\ x=40 \square \end{array}$

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Problem 2275

27. Niech $\mathcal{A}=\{(2,1),(1,1)\}, \mathcal{B}=\{(1,3),(0,1)\}, \mathcal{C}=\{(0,1),(1,4)\}$ i niech $\varphi: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ będzie takim przekształceniem liniowym, że $M(\varphi)_{\mathcal{A}}^{\mathcal{B}}=\left(\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right)$ . Znaleźć $M(\varphi)_{\mathcal{A}}^{\mathcal{C}}$ .

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Problem 2276

Consider the following function: $f(x)=e^{e^{e^{e^{x}}}}$ . $f^{\prime}(x)=$

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Problem 2277

3. A regression was run to determine if there is a relationship between the diameter ( $x$ ,ininches) of a silver maple silver and the tree's age ( $y$ ,ininches). The results of the regression are below. Use this to predict the age of a silver maple tree with diameter 22 inches. Round your answer to three decimal places. $\begin{array}{l} y=a x+b \\ a=3.679 \\ b=-0.54 \\ r=0.967 \end{array}$ age of tree: $\qquad$ $y=80.936$

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Problem 2278

13. Graph $f(x)=-2 x(x-1)(2 x-4)(x+2)$
Left behavior: Right behavior:

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Problem 2279

Simplify. Express your answer as a single fraction in simplest form. $\frac{w}{w+2}-9$

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Problem 2280

$\sqrt{x-4}=7$

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Problem 2281

2. (i) $\frac{x}{2}=5+\frac{x}{3}$

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Problem 2282

Factor the expression completely. $35 x^{2}+63 x^{4}$
Answer Attempt 1 out of 2

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Problem 2283

1. $\frac{2}{5}+\frac{3}{6}+\frac{1}{4}$
7. $\frac{2}{3} \times \frac{25}{34}$
2. $\left(\frac{3}{4}+\frac{7}{5}\right)-\frac{9}{10}$
8. $\frac{2}{5} \times \frac{7}{6} \times \frac{10}{3}$
3. $\frac{12}{13} \times \frac{3}{4}$
9. $\frac{9}{20}+\frac{17}{10}+\frac{21}{100}$
4. $\frac{1}{3} \times \frac{1}{5}$
10. $\frac{9}{5}-\frac{3}{6}-\frac{1}{4}$
5. $\left(\frac{7}{5} \div \frac{6}{8}\right)+\frac{4}{10}$
11. $\frac{56}{19} \div \frac{26}{38}$
6. $\left(\frac{7}{8}+\frac{9}{4}\right)+\frac{3}{11}$
12. $\frac{9}{10} \div \frac{1}{10}$

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Problem 2284

3. (i) $7(x-2)=2(2 x-4)$

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Problem 2285

4) Determine the exact value for each: a) $\cos ^{2} \frac{7 \pi}{6}-\sin ^{2} \frac{11 \pi}{2}$ b) $2-\csc ^{2} \frac{11 \pi}{6}$

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Problem 2286

Find the derivative of the function $f(x) = x^5$ .

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Problem 2287

$f(x) = \frac{4}{\sqrt[4]{x}}$ Encuentra la derivada de $f(x)$ .

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Problem 2288

$\frac{1}{9 z^{2}+31 z-4}-4$

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Problem 2289

What is the value of $c$ in the system below? $\begin{array}{l} -2 a+3 b+2 c=7 \\ 2 a+3 b=29 \\ 5 a=20 \end{array}$

See Solution

Problem 2290

$12^{x}=4^{x+3}$

See Solution

Problem 2291

2. $96 \div(9-7)^{3}$

See Solution

Problem 2292

3. $4^{3}+36 \div(3+1) \cdot 2$

See Solution

Problem 2293

1. $27-2 \cdot 4^{2}$

See Solution

Problem 2294

What is the solution to $\log _{2}(9 x)-\log _{2} 3=3$ ? $x=\frac{3}{8}$ $x=\frac{8}{3}$ $x=3$ $x=9$

See Solution

Problem 2295

(1) Let $A=\left[\begin{array}{lll}2 & 1 & 0 \\ 0 & 4 & 2 \\ 6 & 3 & 5\end{array}\right]$ . (a) Carry A to an upper triangular $U$ by a series of elementary row operations. (b) Find a matrix $E$ such that $E A=U$ . (c) Multiply by $E^{-1}=L$ to factor $A$ into $L U$ .

See Solution

Problem 2296

Find the derivative of the function $f(x)=\frac{73}{x^{-2}}+\frac{5}{x^{3}}$ .

See Solution

Problem 2297

11 a Calculate $\frac{d y}{d x}$ when $y=x^{2}-6 x+1$ . b Solve the equation $\frac{d y}{d x}=0$ . c Find the coordinates of the turning point of this curve.

See Solution

Problem 2298

Do Now Practice
Calculate the slope of the line containing the points: i) $(1,1)$ and $(2,2)$ ii) (1, 2) and (2, 1) iii) $(5,1)$ and $(2,1)$

See Solution

Problem 2299

$\frac{\sec x+\tan x}{\sin x}=\frac{\csc x}{\sec x-\tan x}$

See Solution

Problem 2300

$\frac{3x}{x-5} - \frac{x+3}{6x-30} \cdot \frac{450}{x^2+3x}$

See Solution

1 ...20 21 22 23 24 25 26 ...269

Math Statement

Problem 2201

Follow the instructions below.Write b3⋅b2b^{3} \cdot b^{2}b3⋅b2 without exponents. b3⋅b2=b^{3} \cdot b^{2}=b3⋅b2= □\square□Fill in the blank. b3⋅b2=b[b^{3} \cdot b^{2}=b^{[ }b3⋅b2=b[

Problem 2202

Simplify. (u4)5\left(u^{4}\right)^{5}(u4)5Write your answer without parentheses.

Problem 2203

Find the differential of y=cos⁡(−6πx)y=\cos (-6 \pi x)y=cos(−6πx).

Problem 2204

Problem 2205

Compute (a) Δy\Delta yΔy and (b) dy for the given values of xxx and dx=Δx\mathrm{dx}=\Delta xdx=Δx. y=7−x2,x=−2,Δx=.4y=7-x^{2}, \quad x=-2, \quad \Delta x=.4y=7−x2,x=−2,Δx=.4 (a) Δy=\Delta y=Δy= □\square□ (b) dy=d y=dy= 16 □\square□

Problem 2206

Solve the inequality for uuu. 1−5u≤−91-5 u \leq-91−5u≤−9Simplify your answer as much as possible.

Problem 2207

Problem 2208

Problem 2209

1. Find the derivatives of the following functions: a) y=x3sinh⁡xy=\frac{x^{3}}{\sinh x}y=sinhxx3​ b) y=tanh⁡32xy=\tanh ^{3} 2 xy=tanh32x c) y=ecosh⁡4x2y=e^{\cosh 4 x^{2}}y=ecosh4x2

Problem 2210

Problem 2211

Problem 2212

Problem 2213

Problem 2214

Given 273=k\sqrt[3]{27}=k327​=k, where kkk is an integer, what is the value of kkk ?

Problem 2215

3. 10−(−3)2−(−4−9)−3+5\frac{10-(-3)^{2}-(-4-9)}{-3+5}−3+510−(−3)2−(−4−9)​

Problem 2216

8. g+12=−32g+\frac{1}{2}=-\frac{3}{2}g+21​=−23​

Problem 2217

Problem 2218

2n+1−2n+22n−1−2n−2\frac{2^{n+1}-2^{n+2}}{2^{n-1}-2^{n-2}}2n−1−2n−22n+1−2n+2​

Problem 2219

Problem 2220

Problem 2221

The derivative of y=etan⁡−1xy=e^{\tan ^{-1} x}y=etan−1x is:

Problem 2222

Using an appropriate substitution (Inverse trigonometric): ∫dxx2+6x+90=\int \frac{d x}{x^{2}+6 x+90}=∫x2+6x+90dx​=

Problem 2223

Problem 2224

2. Вычислить интеграл: ∫l(iz3+3)dz\int_{l}\left(i z^{3}+3\right) d z∫l​(iz3+3)dz, где lll - отрезок прямой от точки z1=1z_{1}=1z1​=1 до точки z2=iz_{2}=iz2​=i.

Problem 2225

Problem 2226

Problem 2227

Having that gcd⁡(a,b)=1\operatorname{gcd}(a, b)=1gcd(a,b)=1, prove the following- (i) gcd⁡(2a+b,a+2b)=1\operatorname{gcd}(2 a+b, a+2 b)=1gcd(2a+b,a+2b)=1 or 3 . (ii) god⁡(a+b,a2+b2)=1\operatorname{god}\left(a+b, a^{2}+b^{2}\right)=1god(a+b,a2+b2)=1 or 2 .

Problem 2228

Problem 2229

Example: Differentiate the following functions.1. f(x)=(x4+3)50f(x)=\left(x^{4}+3\right)^{50}f(x)=(x4+3)502. g(t)=t3sin⁡tg(t)=\sqrt{t^{3} \sin t}g(t)=t3sint​

Problem 2230

If f(x)=3x−1x−2f(x)=\frac{3 x-1}{x-2}f(x)=x−23x−1​ then f−1(x)=f^{-1}(x)=f−1(x)= A) x−2x−3\frac{x-2}{x-3}x−3x−2​ B) 2x−1x−3\frac{2 x-1}{x-3}x−32x−1​ C) 2x+1x−3\frac{2 x+1}{x-3}x−32x+1​ D) x−32x−1\frac{x-3}{2 x-1}2x−1x−3​

Problem 2231

If f−1(x)=1x−9f^{-1}(x)=\frac{1}{x-9}f−1(x)=x−91​ then Df=D_{f}=Df​= A) R−{9}\mathbb{R}-\{9\}R−{9} B) R−{1}\mathbb{R}-\{1\}R−{1} C) R\mathbb{R}R D) R−{0}\mathbb{R}-\{0\}R−{0}

Problem 2232

Problem 2233

• Problem 3: (9 points) Find the local maximum and minimum values and saddle points of the function f(x, y) = x³- xy + y³

Problem 2234

Problem 2235

2. 4y+9y4 y+9 y4y+9y

Problem 2236

3×4103 \times \frac{4}{10}3×104​

Problem 2237

6. 12x+12+12x+12\frac{1}{2} x+\frac{1}{2}+\frac{1}{2} x+\frac{1}{2}21​x+21​+21​x+21​

Problem 2238

13. z4+z4+z4+z4z^{4}+z^{4}+z^{4}+z^{4}z4+z4+z4+z4

Problem 2239

=(112z2−[12z2)=\left(1 \frac{1}{2} z^{2}-\left[\frac{1}{2} z^{2}\right)\right.=(121​z2−[21​z2)

Problem 2240

Problem 2241

8 70 Г9gs 9

Problem 2242

8 70 Г9gs 9

Problem 2243

38÷14=\frac{3}{8} \div \frac{1}{4}=83​÷41​=

Problem 2244

2÷323=2 \div 3 \frac{2}{3}=2÷332​=Sulmity

Problem 2245

10. Given that x2−2bx+225x^{2}-2 b x+225x2−2bx+225 is a perfect square, find the possible values of bbb.

Problem 2246

Differentiate the function. y=(9x4−x+4)(−x5+3)y=\left(9 x^{4}-x+4\right)\left(-x^{5}+3\right)y=(9x4−x+4)(−x5+3)

Problem 2247

Use the quotient rule to find the derivative of the following. y=x2−3x+1x2+5y=\frac{x^{2}-3 x+1}{x^{2}+5}y=x2+5x2−3x+1​

Problem 2248

3) f(x)=2(5x+1)f(x)=2(5 x+1)f(x)=2(5x+1) f(0)=f(−2)=f(2)=\begin{array}{l} f(0)= \\ f(-2)= \\ f(2)= \end{array}f(0)=f(−2)=f(2)=​

Follow the instructions below.
Write $b^{3} \cdot b^{2}$ without exponents. $b^{3} \cdot b^{2}=$ $\square$
Fill in the blank. $b^{3} \cdot b^{2}=b^{[ }$

Simplify. $\left(u^{4}\right)^{5}$
Write your answer without parentheses.

Find the differential of $y=\cos (-6 \pi x)$ .

Compute (a) $\Delta y$ and (b) dy for the given values of $x$ and $\mathrm{dx}=\Delta x$ . $y=7-x^{2}, \quad x=-2, \quad \Delta x=.4$ (a) $\Delta y=$ $\square$ (b) $d y=$ 16 $\square$

Solve the inequality for $u$ . $1-5 u \leq-9$
Simplify your answer as much as possible.

1. Find the derivatives of the following functions: a) $y=\frac{x^{3}}{\sinh x}$ b) $y=\tanh ^{3} 2 x$ c) $y=e^{\cosh 4 x^{2}}$

Given $\sqrt[3]{27}=k$ , where $k$ is an integer, what is the value of $k$ ?

3. $\frac{10-(-3)^{2}-(-4-9)}{-3+5}$

8. $g+\frac{1}{2}=-\frac{3}{2}$

$\frac{2^{n+1}-2^{n+2}}{2^{n-1}-2^{n-2}}$

The derivative of $y=e^{\tan ^{-1} x}$ is:

Using an appropriate substitution (Inverse trigonometric): $\int \frac{d x}{x^{2}+6 x+90}=$

2. Вычислить интеграл: $\int_{l}\left(i z^{3}+3\right) d z$ , где $l$ - отрезок прямой от точки $z_{1}=1$ до точки $z_{2}=i$ .

Having that $\operatorname{gcd}(a, b)=1$ , prove the following- (i) $\operatorname{gcd}(2 a+b, a+2 b)=1$ or 3 . (ii) $\operatorname{god}\left(a+b, a^{2}+b^{2}\right)=1$ or 2 .

Example: Differentiate the following functions.
1. $f(x)=\left(x^{4}+3\right)^{50}$
2. $g(t)=\sqrt{t^{3} \sin t}$

If $f(x)=\frac{3 x-1}{x-2}$ then $f^{-1}(x)=$ A) $\frac{x-2}{x-3}$ B) $\frac{2 x-1}{x-3}$ C) $\frac{2 x+1}{x-3}$ D) $\frac{x-3}{2 x-1}$

If $f^{-1}(x)=\frac{1}{x-9}$ then $D_{f}=$ A) $\mathbb{R}-\{9\}$ B) $\mathbb{R}-\{1\}$ C) $\mathbb{R}$ D) $\mathbb{R}-\{0\}$

2. $4 y+9 y$

$3 \times \frac{4}{10}$

6. $\frac{1}{2} x+\frac{1}{2}+\frac{1}{2} x+\frac{1}{2}$

13. $z^{4}+z^{4}+z^{4}+z^{4}$

$=\left(1 \frac{1}{2} z^{2}-\left[\frac{1}{2} z^{2}\right)\right.$

$\frac{3}{8} \div \frac{1}{4}=$

$2 \div 3 \frac{2}{3}=$
Sulmity

10. Given that $x^{2}-2 b x+225$ is a perfect square, find the possible values of $b$ .

Differentiate the function. $y=\left(9 x^{4}-x+4\right)\left(-x^{5}+3\right)$

Use the quotient rule to find the derivative of the following. $y=\frac{x^{2}-3 x+1}{x^{2}+5}$

3) $f(x)=2(5 x+1)$ $\begin{array}{l} f(0)= \\ f(-2)= \\ f(2)= \end{array}$

Solve for $x$ . $y=(7+x) m$

What is the formula for the volume of a right cone with base area $B$ and height $h$ ? A. $V=\frac{1}{3} B h$ B. $v=B h$ C. $V=2 B h^{2}$ D. $v=-\frac{1}{3} B h$

Create the $n$ th Taylor's Polynomial for $\ln (x)$ about $x=1$ .

The equation of the following conic section is (A) $9 x^{2}-y^{2}=36$ (B) $x^{2}-9 y^{2}=36$ (C) $x^{2}+3 y^{2}=6$ (D) $9 x^{2}+y^{2}=36$ (E) $x^{2}+9 y^{2}=36$

$\angle T U W \cong \angle V U W .$
Which term describes $\overline{U W}$ ? perpendicular bisector altitude angle bisector median

If $f(x)=2-3^{x-1}$ , then what is range of $f$ ? (A) $(-\infty, 2)$ (B) $(-\infty, 2]$ (C) $(2, \infty)$ (D) $[2, \infty)$ (E) $(-\infty, 0)$

ewrite $f(x)=(a x+b) /(x+c)$ in $f(x)=a+d /(x+c)$ form. 5) $f(x)=\frac{x-3}{x-4}$

Solve the rational inequality. 7) $\frac{-4 x+7}{5 x^{2}+6}>0$

$\begin{array}{l} \frac{4}{x}+5 y=7 \\ \text { Let } \frac{1}{x} b e \\ 4 a+5 y=7 \rightarrow \text { (1) } \\ \frac{3}{x}+4 y=5 \\ 3 a+4 y=5 \rightarrow \text { (2) } \end{array}$

The weekly revenue from the sale of $x$ units of a service is given by $R(x)=110 x-5 x^{2}$ thousand dollars, where $0 \leq x \leq 19$ . How many units should be sold to maximize the revenue?

Simple cless - work $\begin{array}{l} \frac{(x+4)^{8}}{x^{-3}} \\ \frac{5^{x} \times 25^{x-1}}{125^{x+1}} \\ \frac{163 / 4-8 \frac{1}{3}}{2^{2} \times 3} \end{array}$
Solution

$\begin{array}{r}x+y+z=5 \\ x-y+4 z=2 \\ 5 x+y+z=9\end{array}$

$1 = 3x + 2x^2y^2$ Implicit differentiation

(15 points) Use an analytic method to solve $\sqrt{4 x-3}=2 x-3$

Find the average rate of change of the function $f(x) = x^3 + 2x^2 - 5x + 3$ over the interval $[1, 5]$ .

8) $2 x-3 y=6$

$-12 y^{3}(2 x y)$
Answer Attempt 1 out of 2

$\left\{\begin{array}{l}x+y=-8 \\ x-y=-4\end{array}\right.$

$\text{Find the average rate of change of the function } f(x) = \frac{2x-1}{x+4} \text{ over the interval } [-3, 8].$

(1 point)
The total cost (in hundreds of dollars) of producing $x$ slide rules per day is $C(x)=12+\sqrt{2 x+20}$
Find the marginal cost at each production level $x$ given below: $\begin{array}{l} x=25 \square \\ x=40 \square \end{array}$