Math Statement

Problem 26801

Make $x$ the subject of $\frac{d x}{t}=m$

See Solution

Problem 26802

What is the $x$ -intercept of the line $6 x-3 y=24$ ? $x$ -intercept $=$ $\square$

See Solution

Problem 26803

The mgf of a random variable $X$ is given by $m(t)=\left(0,9+0.1 e^{t}\right)^{3}$ , then $p(X=1)$ is equal to a. 0.0243 b. 0.536 c. 0.027 d. 0.725 e. 0.9

See Solution

Problem 26804

Marked out of 1.00
The moment generating function of a random variable X is given by $m(t)=0.3 e^{-t}+0.4+0.3 e^{2 t}$ . Then the mean of X is given by a. 0.4 b. 0.3 c. 0.9 d. 1 e. 2.4

See Solution

Problem 26805

Дана пирамида EABCD. Её основание - параллелограмм, диагонали которого пересекаются в точке $O$ . Определи, справедливо ли равенство: $1.2 \overrightarrow{O D}-\overrightarrow{A D}+\overrightarrow{A C}=\overrightarrow{B E}$ $\square$
2. $\overrightarrow{O D}+\overrightarrow{O E}-\overrightarrow{C E}+0,5 \overrightarrow{C A}=\overrightarrow{O B}$ . $\square$
3. $\overrightarrow{A E}-\overrightarrow{O E}+0,5 \overrightarrow{B D}=\overrightarrow{D A}$ . $\square$

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Problem 26806

Exercice ( 5 pts ) On considère la suite $U$ définie par $\left\{\begin{array}{c}U_{0}=\frac{2}{3} \\ U_{n+1}=\frac{3 U_{n}+2}{2 U_{n}+3} ; \forall n \in I N\end{array}\right.$
1. Calculer $\boldsymbol{U}_{\mathbf{1}} ; \boldsymbol{U}_{\mathbf{2}}$
2. Monter que $\forall n \in I N$ on a : $0 \leq U_{n} \leq 1$
3. On pose $V_{n}=\frac{U_{n}-1^{N}}{U_{n}+1}$ a. Monter que la suite $\left(V_{n}\right)$ est une suite géométrique b. Calculer $\boldsymbol{V}_{\boldsymbol{n}}$ puis $\boldsymbol{U}_{\boldsymbol{n}}$ en fonction de $n$ c. Calculer $S_{n}=\sum_{k=0}^{n} V_{n}$ d. Calculer $\lim V_{n} ; \lim U_{n}$ et $\lim S_{n}$

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Problem 26807

Soit $\left\{U_{n}\right\}$ et $\left(V_{n}\right)$ deux suites définies par: $U_{n}=\frac{2^{n}+4 n+3}{2}$ et $V_{n}=\frac{2^{n}-4 n+3}{2}$ On pose $T_{1}=U_{n}+V_{n}$ et $T_{2}=U_{n}-V_{n}$ 1) Montrer que $T_{1}$ est géométrique et que $T_{2}$ est arithmétique ? 2) En déduire $S_{1}$ et $S_{2}$ en fonction de $n$ tels que: $S_{1}=\sum_{K=0}^{n} \boldsymbol{U}_{K}$ et $S_{2}=\sum_{K=0}^{n} V_{K}$

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Problem 26808

Find the limit $\lim _{x \rightarrow a}\left\{[h(x)]^{2}-f(x) g(x)\right\}$ given $\lim _{x \rightarrow a} f(x)=3$ , $\lim _{x \rightarrow a} g(x)=5$ , $\lim _{x \rightarrow a} h(x)=-2$ .

See Solution

Problem 26809

Find the $y$ -intercept and slope of the line given by $4 x + 2 y = -2$ . Provide answers in simplest form.

See Solution

Problem 26810

Find the value of $|-13|$ . What is your answer?

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Problem 26811

Solve the inequality $-2(4 z+5)>-2 z-22$ and express the solution in interval notation.

See Solution

Problem 26812

Determine the slope and $y$ -intercept of the line given by $2x + y = -1$ . Provide your answers in simplest form.

See Solution

Problem 26813

Find the $y$ -intercept and slope of the line given by $5x - 4y = 16$ . Provide answers in simplest form.

See Solution

Problem 26814

Determine the $y$ -intercept and slope of the line given by $-2 x + 3 y = 5$ . Provide answers in simplest form.

See Solution

Problem 26815

Simplify the expression: $(6n - 2n^4 + 7n^2) - (2n - 8n^4 - 8n^2)$ .

See Solution

Problem 26816

Simplify the expression: $(1 - 5a - 8a^2) - (8a + 2a^3 - a^2)$ .

See Solution

Problem 26817

Solve the inequality $-2(4 z+5)>-2 z-22$ and graph the solution.

See Solution

Problem 26818

Find the slope and $y$ -intercept of the line given by $-3x - 5y = -20$ . Then, graph the line.

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Problem 26819

Determine the determinant $D=\left|\begin{array}{ccc}0 & 5 & 2 \\ 4 & -3 & 0 \\ 2 & 4 & 2\end{array}\right|$
Let $\vec{u}=(3,-1,2)$ and $\vec{v}=(4,1,1)$ . Normalize the vector $\vec{u}$ . Determine the cosines of the angles between $\vec{u}$ and

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Problem 26820

3). Evaluate by changing of the ordrof integration. (a) $\int_{0}^{2} \int_{1}^{e^{x}} d y d x$ (b) $\int_{0}^{1} \int_{x^{2}}^{2-x} x y d x d y$ (c) $\int_{0}^{4 a} \int_{x / 4 a}^{2 \sqrt{a x}} d y d x$ .

See Solution

Problem 26821

目分六、(本题 20 分) $R_{D}=3 \mathrm{k} \Omega, R_{G}=10 \mathrm{M} \Omega, V_{G G}=2 \mathrm{~V}, V_{D D}=15 \mathrm{~V}, I_{D S S}=8 \mathrm{~mA}, V_{P}=4 \mathrm{~V}$ . (1) Calculate DC bias $V_{G S}, I_{D}$ , and $V_{D S}$ . (2) Draw the equivalent circuit for $A C$ analysis, and determine $\mathrm{g}_{\mathrm{m}}, \mathrm{Z}_{\mathrm{i}}, \mathrm{Z}_{0}$ and $\mathrm{A}_{\mathrm{v}}$ .

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Problem 26822

$f(x)=x e^{x}-x$ is concave up ou?

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Problem 26823

8. If $f(x)=\left\{x^{2}+3\right.$ (A) $a=1, b=3$ (B) $\frac{1}{7}$ (C) $\frac{1}{3}$ (D) $\frac{1}{3}$ (B) $\left.a=\begin{array}{c}x<0 \\ 3, b=0\end{array}\right\}$ and $f(x)$ is differentiable at $x=0$ , then: (C) $a=3, b=1$ (D) $a=0, b=3$ $\begin{array}{lll}\text { (A) } x=\ln 2 & \text { (B) } x=\ln 5 & \text { (C) } x=\ln 3\end{array}$ (D) $x=2 \ln 5$

See Solution

Problem 26824

تمسرين010: ( ش. ت. م 2011 ) (1 $A=2 x^{2}-7 x+3+(2 x-1)(3 x+2): A$ A $A$ $(2 x-1)(4 x-1)=0$ : ( 3

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Problem 26825

Q1: A) Prove that $\left[\frac{5}{3-w}-\frac{5}{3-w^{2}}\right]^{2}=-\frac{75}{169}$

See Solution

Problem 26826

B) If the function $f(x)=a x^{3}-3 x^{2}+b x+c$ has a local minimum at -5 and a local maximum at $x=\frac{-1}{2}$ and inflection point at $x=\frac{1}{4}$ find $a, b, c \in R$ .

See Solution

Problem 26827

B) If $z=\cos 2 \theta+i \sin 2 \theta$ prove that $\frac{Z+1}{Z-1}=-i \cot \theta$

See Solution

Problem 26828

$\begin{array}{r}A+B+C=0 \\ 5 A+4 B+C+D=0 \\ 10 A+6 B+D=2 \\ 6 A=1\end{array}$

See Solution

Problem 26829

Q22 Solve the linear congruence $13 x \equiv 2(\bmod 2 \cdot 3.5)$ by solving the system $\begin{array}{l} 13 x \equiv 2(\bmod 2) \\ 13 x \equiv 2(\bmod 3) \\ 13 x \equiv 2(\bmod 5) \end{array}$

See Solution

Problem 26830

$\lim _{x \rightarrow 0^{+}} x-1-\frac{2 \ln x^{2}}{\sqrt{x}}$

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Problem 26831

$\begin{array}{l}A+B=0 \\ B+C=-3 \\ A+C=0\end{array}$

See Solution

Problem 26832

$\int_{0}^{1} \int_{0}^{y^{2}} \sqrt{1+y^{3}} d x d y$

See Solution

Problem 26833

Deduce the solutions of the following equations: i. $x^{4}-5 x^{2}-6=0$ ii. $x-5 \sqrt{x}-6=0$

See Solution

Problem 26834

c.) $\frac{6}{8}=$ $\square$

See Solution

Problem 26835

Calculate $\frac{5}{4}-\frac{5}{12}$ and express the answer as a mixed number.

See Solution

Problem 26836

Solve the inequality $3x + 3 \geq x + 6$ and express the solution in interval notation.

See Solution

Problem 26837

Calculate $\frac{2}{8} - \frac{9}{2}$ and express your answer as a mixed number.

See Solution

Problem 26838

Add: $-\frac{4}{8}+\frac{5}{3}$ . Enter your answer as a mixed number (e.g., $11 / 2$ ).

See Solution

Problem 26839

What type of interval is represented by the inequality $-2 \leq x < 6$ ?

See Solution

Problem 26840

Calculate: $\frac{2}{8}-\frac{9}{2}$ without using a calculator.

See Solution

Problem 26841

Graph the solution for the inequality $x \geq -5$ .

See Solution

Problem 26842

Find the slope and $y$ -intercept of the line given by the equation: $-3x - 5y = -20$ .

See Solution

Problem 26843

Find the limit as $x$ approaches $\pi$ for $\sqrt{3+\cos 4x}$ .

See Solution

Problem 26844

Convert the following to base ten numerals: a. $5 \cdot 10^{3}+1 \cdot 10^{2}+7 \cdot 10$ b. $6 \cdot 10^{6}+4 \cdot 10+3$

See Solution

Problem 26845

Simplify the expression $-3^{3}$ using exponent properties and show only positive exponents.

See Solution

Problem 26846

Find the car's acceleration at $t=2$ seconds given $s(t)=2 t^{4}-10 t^{3}-5 t^{2}+9$ . Answer in $\mathrm{m} / \mathrm{s}^{2}$ .

See Solution

Problem 26847

Find the car's acceleration at $t=2$ seconds, given $s(t)=2 t^{4}-9 t^{3}-6 t^{2}-8$ .

See Solution

Problem 26848

Find the interval(s) where the car slows down given $s(t)=-\frac{2 t^{3}}{3}+3 t^{2}+20 t-3$ , $t \geq 0$ .

See Solution

Problem 26849

Q(3) The particular solution of the ODE $3 x(x y-2) d x+\left(x^{3}+2 y\right) d y=0, y(0)=2$ , is: (a) $x^{3} y+3 x^{2}+y^{2}=2$ b) $x^{3} y-3 x^{2}+y^{2}=2$ c) $x^{3} y-3 x^{2}+y^{2}=4$ (d) $x^{3} y-3 x^{2}-y^{2}=4$

See Solution

Problem 26850

( $O ; \vec{i}, \vec{j})$ ( $)$ (1) lim

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Problem 26851

Q5. Find $\frac{d y}{d x}$ when $2 x^{2}-y^{2}=5 x \sin (y)+2 a^{13}$

See Solution

Problem 26852

EXERCISE
1. UME 2906 Que 25 simplify (25) $\frac{1}{x} \times(27)^{\prime}+(121)^{-\frac{1}{2}} \times(625)^{-\frac{1}{4}}$

See Solution

Problem 26853

7. UME 2000 Que 9
Simplify $\frac{3\left(2^{n+1}\right)-4\left(2^{n-1}\right)}{2^{n+1}-2^{n}}$ a. $2^{n+1}$ b. $2^{n-1}$ c. 4

See Solution

Problem 26854

Find the eigenvalues and eigenvectors of $A=\left[\begin{array}{cc} 1 & -2 \\ 0 & 1 \end{array}\right]$
And then find:
1. The eigenvalues of $A^{-1}$ .
2. The eigenvalues of $A^{3}$ .
3. Spectrum and spectral radius.

See Solution

Problem 26855

الآمرين الثاني: (06 نقاط) $u_{0}+u_{1}=30 \quad, \quad u_{0} \times u_{2}=576$ . $n$ A 2

See Solution

Problem 26856

$\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1$

See Solution

Problem 26857

تمرين 1
باستعكال التُعريف اوجد مشُقة الدالة f في كل من الحالات التّالية
1. $f(x)=\sqrt{2 x+1}$ ,
2. $f(x)=\sqrt[3]{x}$ ,
3. $f(x)=\frac{-1}{x}$ .
تمرين 2
احسب مشّقة الدالة $f$ في كل من الحالات التّالية
1. $f(x)=\cos \sqrt{1-4 x}$ , 2. $f(x)=\ln \sqrt[4]{x-4}, 3$ . $f(x)=\ln \frac{x^{3}-2}{x^{2}+1}$ .
تصرين3
احسب النهايات التّلية $\lim _{x \rightarrow 0} \frac{6 x^{2}}{3 e^{x}-x^{3}-3 x-3} \quad, \quad \lim _{x \rightarrow 1} \frac{\sqrt{x+3}-2}{\sqrt{x+8}-3}$

See Solution

1 ...266 267 268 269

Math Statement

Problem 26801

Make xxx the subject of dxt=m\frac{d x}{t}=mtdx​=m

Problem 26802

What is the xxx-intercept of the line 6x−3y=246 x-3 y=246x−3y=24 ? xxx-intercept === □\square□

Problem 26803

The mgf of a random variable XXX is given by m(t)=(0,9+0.1et)3m(t)=\left(0,9+0.1 e^{t}\right)^{3}m(t)=(0,9+0.1et)3, then p(X=1)p(X=1)p(X=1) is equal to a. 0.0243 b. 0.536 c. 0.027 d. 0.725 e. 0.9

Problem 26804

Marked out of 1.00The moment generating function of a random variable X is given by m(t)=0.3e−t+0.4+0.3e2tm(t)=0.3 e^{-t}+0.4+0.3 e^{2 t}m(t)=0.3e−t+0.4+0.3e2t. Then the mean of X is given by a. 0.4 b. 0.3 c. 0.9 d. 1 e. 2.4

Problem 26805

Problem 26806

Problem 26807

Problem 26808

Problem 26809

Find the yyy-intercept and slope of the line given by 4x+2y=−24 x + 2 y = -24x+2y=−2. Provide answers in simplest form.

Problem 26810

Find the value of ∣−13∣|-13|∣−13∣. What is your answer?

Problem 26811

Solve the inequality −2(4z+5)>−2z−22-2(4 z+5)>-2 z-22−2(4z+5)>−2z−22 and express the solution in interval notation.

Problem 26812

Determine the slope and yyy-intercept of the line given by 2x+y=−12x + y = -12x+y=−1. Provide your answers in simplest form.

Problem 26813

Find the yyy-intercept and slope of the line given by 5x−4y=165x - 4y = 165x−4y=16. Provide answers in simplest form.

Problem 26814

Determine the yyy-intercept and slope of the line given by −2x+3y=5-2 x + 3 y = 5−2x+3y=5. Provide answers in simplest form.

Problem 26815

Simplify the expression: (6n−2n4+7n2)−(2n−8n4−8n2)(6n - 2n^4 + 7n^2) - (2n - 8n^4 - 8n^2)(6n−2n4+7n2)−(2n−8n4−8n2).

Problem 26816

Simplify the expression: (1−5a−8a2)−(8a+2a3−a2)(1 - 5a - 8a^2) - (8a + 2a^3 - a^2)(1−5a−8a2)−(8a+2a3−a2).

Problem 26817

Solve the inequality −2(4z+5)>−2z−22-2(4 z+5)>-2 z-22−2(4z+5)>−2z−22 and graph the solution.

Problem 26818

Find the slope and yyy-intercept of the line given by −3x−5y=−20-3x - 5y = -20−3x−5y=−20. Then, graph the line.

Problem 26819

Problem 26820

Problem 26821

Problem 26822

f(x)=xex−xf(x)=x e^{x}-xf(x)=xex−x is concave up ou?

Problem 26823

Problem 26824

تمسرين010: ( ش. ت. م 2011 ) (1 A=2x2−7x+3+(2x−1)(3x+2):AA=2 x^{2}-7 x+3+(2 x-1)(3 x+2): AA=2x2−7x+3+(2x−1)(3x+2):A A AAA (2x−1)(4x−1)=0(2 x-1)(4 x-1)=0(2x−1)(4x−1)=0 : ( 3

Problem 26825

Q1: A) Prove that [53−w−53−w2]2=−75169\left[\frac{5}{3-w}-\frac{5}{3-w^{2}}\right]^{2}=-\frac{75}{169}[3−w5​−3−w25​]2=−16975​

Problem 26826

B) If the function f(x)=ax3−3x2+bx+cf(x)=a x^{3}-3 x^{2}+b x+cf(x)=ax3−3x2+bx+c has a local minimum at -5 and a local maximum at x=−12x=\frac{-1}{2}x=2−1​ and inflection point at x=14x=\frac{1}{4}x=41​ find a,b,c∈Ra, b, c \in Ra,b,c∈R.

Problem 26827

B) If z=cos⁡2θ+isin⁡2θz=\cos 2 \theta+i \sin 2 \thetaz=cos2θ+isin2θ prove that Z+1Z−1=−icot⁡θ\frac{Z+1}{Z-1}=-i \cot \thetaZ−1Z+1​=−icotθ

Problem 26828

A+B+C=05A+4B+C+D=010A+6B+D=26A=1\begin{array}{r}A+B+C=0 \\ 5 A+4 B+C+D=0 \\ 10 A+6 B+D=2 \\ 6 A=1\end{array}A+B+C=05A+4B+C+D=010A+6B+D=26A=1​

Problem 26829

Problem 26830

lim⁡x→0+x−1−2ln⁡x2x\lim _{x \rightarrow 0^{+}} x-1-\frac{2 \ln x^{2}}{\sqrt{x}}limx→0+​x−1−x​2lnx2​

Problem 26831

A+B=0B+C=−3A+C=0\begin{array}{l}A+B=0 \\ B+C=-3 \\ A+C=0\end{array}A+B=0B+C=−3A+C=0​

Problem 26832

∫01∫0y21+y3dxdy\int_{0}^{1} \int_{0}^{y^{2}} \sqrt{1+y^{3}} d x d y∫01​∫0y2​1+y3​dxdy

Problem 26833

Deduce the solutions of the following equations: i. x4−5x2−6=0x^{4}-5 x^{2}-6=0x4−5x2−6=0 ii. x−5x−6=0x-5 \sqrt{x}-6=0x−5x​−6=0

Problem 26834

c.) 68=\frac{6}{8}=86​= □\square□

Problem 26835

Calculate 54−512\frac{5}{4}-\frac{5}{12}45​−125​ and express the answer as a mixed number.

Problem 26836

Solve the inequality 3x+3≥x+63x + 3 \geq x + 63x+3≥x+6 and express the solution in interval notation.

Problem 26837

Calculate 28−92\frac{2}{8} - \frac{9}{2}82​−29​ and express your answer as a mixed number.

Problem 26838

Add: −48+53-\frac{4}{8}+\frac{5}{3}−84​+35​. Enter your answer as a mixed number (e.g., 11/211 / 211/2).

Problem 26839

What type of interval is represented by the inequality −2≤x<6-2 \leq x < 6−2≤x<6?

Problem 26840

Calculate: 28−92\frac{2}{8}-\frac{9}{2}82​−29​ without using a calculator.

Problem 26841

Graph the solution for the inequality x≥−5x \geq -5x≥−5.

Problem 26842

Find the slope and yyy-intercept of the line given by the equation: −3x−5y=−20-3x - 5y = -20−3x−5y=−20.

Problem 26843

Find the limit as xxx approaches π\piπ for 3+cos⁡4x\sqrt{3+\cos 4x}3+cos4x​.

Problem 26844

Convert the following to base ten numerals: a. 5⋅103+1⋅102+7⋅105 \cdot 10^{3}+1 \cdot 10^{2}+7 \cdot 105⋅103+1⋅102+7⋅10 b. 6⋅106+4⋅10+36 \cdot 10^{6}+4 \cdot 10+36⋅106+4⋅10+3

Make $x$ the subject of $\frac{d x}{t}=m$

What is the $x$ -intercept of the line $6 x-3 y=24$ ? $x$ -intercept $=$ $\square$

The mgf of a random variable $X$ is given by $m(t)=\left(0,9+0.1 e^{t}\right)^{3}$ , then $p(X=1)$ is equal to a. 0.0243 b. 0.536 c. 0.027 d. 0.725 e. 0.9

Marked out of 1.00
The moment generating function of a random variable X is given by $m(t)=0.3 e^{-t}+0.4+0.3 e^{2 t}$ . Then the mean of X is given by a. 0.4 b. 0.3 c. 0.9 d. 1 e. 2.4

Find the $y$ -intercept and slope of the line given by $4 x + 2 y = -2$ . Provide answers in simplest form.

Find the value of $|-13|$ . What is your answer?

Solve the inequality $-2(4 z+5)>-2 z-22$ and express the solution in interval notation.

Determine the slope and $y$ -intercept of the line given by $2x + y = -1$ . Provide your answers in simplest form.

Find the $y$ -intercept and slope of the line given by $5x - 4y = 16$ . Provide answers in simplest form.

Determine the $y$ -intercept and slope of the line given by $-2 x + 3 y = 5$ . Provide answers in simplest form.

Simplify the expression: $(6n - 2n^4 + 7n^2) - (2n - 8n^4 - 8n^2)$ .

Simplify the expression: $(1 - 5a - 8a^2) - (8a + 2a^3 - a^2)$ .

Solve the inequality $-2(4 z+5)>-2 z-22$ and graph the solution.

Find the slope and $y$ -intercept of the line given by $-3x - 5y = -20$ . Then, graph the line.

$f(x)=x e^{x}-x$ is concave up ou?

تمسرين010: ( ش. ت. م 2011 ) (1 $A=2 x^{2}-7 x+3+(2 x-1)(3 x+2): A$ A $A$ $(2 x-1)(4 x-1)=0$ : ( 3

Q1: A) Prove that $\left[\frac{5}{3-w}-\frac{5}{3-w^{2}}\right]^{2}=-\frac{75}{169}$

B) If the function $f(x)=a x^{3}-3 x^{2}+b x+c$ has a local minimum at -5 and a local maximum at $x=\frac{-1}{2}$ and inflection point at $x=\frac{1}{4}$ find $a, b, c \in R$ .

B) If $z=\cos 2 \theta+i \sin 2 \theta$ prove that $\frac{Z+1}{Z-1}=-i \cot \theta$

$\begin{array}{r}A+B+C=0 \\ 5 A+4 B+C+D=0 \\ 10 A+6 B+D=2 \\ 6 A=1\end{array}$

$\lim _{x \rightarrow 0^{+}} x-1-\frac{2 \ln x^{2}}{\sqrt{x}}$

$\begin{array}{l}A+B=0 \\ B+C=-3 \\ A+C=0\end{array}$

$\int_{0}^{1} \int_{0}^{y^{2}} \sqrt{1+y^{3}} d x d y$

Deduce the solutions of the following equations: i. $x^{4}-5 x^{2}-6=0$ ii. $x-5 \sqrt{x}-6=0$

c.) $\frac{6}{8}=$ $\square$

Calculate $\frac{5}{4}-\frac{5}{12}$ and express the answer as a mixed number.

Solve the inequality $3x + 3 \geq x + 6$ and express the solution in interval notation.

Calculate $\frac{2}{8} - \frac{9}{2}$ and express your answer as a mixed number.

Add: $-\frac{4}{8}+\frac{5}{3}$ . Enter your answer as a mixed number (e.g., $11 / 2$ ).

What type of interval is represented by the inequality $-2 \leq x < 6$ ?

Calculate: $\frac{2}{8}-\frac{9}{2}$ without using a calculator.

Graph the solution for the inequality $x \geq -5$ .

Find the slope and $y$ -intercept of the line given by the equation: $-3x - 5y = -20$ .

Find the limit as $x$ approaches $\pi$ for $\sqrt{3+\cos 4x}$ .

Convert the following to base ten numerals: a. $5 \cdot 10^{3}+1 \cdot 10^{2}+7 \cdot 10$ b. $6 \cdot 10^{6}+4 \cdot 10+3$

Simplify the expression $-3^{3}$ using exponent properties and show only positive exponents.

Find the car's acceleration at $t=2$ seconds given $s(t)=2 t^{4}-10 t^{3}-5 t^{2}+9$ . Answer in $\mathrm{m} / \mathrm{s}^{2}$ .

Find the car's acceleration at $t=2$ seconds, given $s(t)=2 t^{4}-9 t^{3}-6 t^{2}-8$ .

Find the interval(s) where the car slows down given $s(t)=-\frac{2 t^{3}}{3}+3 t^{2}+20 t-3$ , $t \geq 0$ .

( $O ; \vec{i}, \vec{j})$ ( $)$ (1) lim

Q5. Find $\frac{d y}{d x}$ when $2 x^{2}-y^{2}=5 x \sin (y)+2 a^{13}$

EXERCISE
1. UME 2906 Que 25 simplify (25) $\frac{1}{x} \times(27)^{\prime}+(121)^{-\frac{1}{2}} \times(625)^{-\frac{1}{4}}$

7. UME 2000 Que 9
Simplify $\frac{3\left(2^{n+1}\right)-4\left(2^{n-1}\right)}{2^{n+1}-2^{n}}$ a. $2^{n+1}$ b. $2^{n-1}$ c. 4

Find the eigenvalues and eigenvectors of $A=\left[\begin{array}{cc} 1 & -2 \\ 0 & 1 \end{array}\right]$
And then find:
1. The eigenvalues of $A^{-1}$ .
2. The eigenvalues of $A^{3}$ .
3. Spectrum and spectral radius.

الآمرين الثاني: (06 نقاط) $u_{0}+u_{1}=30 \quad, \quad u_{0} \times u_{2}=576$ . $n$ A 2

$\frac{1}{1+a+b^{-1}}+\frac{1}{1+b+c^{-1}}+\frac{1}{1+c+a^{-1}}=1$