Math Statement

Problem 18901

Самостоятельная работа по теме: «Свойства степеней» ВАРИАНТ 2 o 1. Представьте в виде степени произведение: 1) $x^{9} x^{2}$ ; 2) $7^{11} \cdot 7^{3}$ 3) $(a+b)(a+b)^{7}$ 4) $a a^{7}$ ; 5) $m^{4} m^{5} m^{11}$

See Solution

Problem 18902

$I=\int \frac{x+1}{\left(x^{2}+9\right)^{2}} d x$

See Solution

Problem 18903

Exercice 1 (C) -35 min 07 pt
On considère les polynômes $P$ et $Q$ définis par: $P(x)=-x^{3}-6 x^{2}+9 x+14 \text { et } Q(x)=x^{4}-5 x^{2}+4$
1. a) Vérifier que $(-1)$ est une racine de $P$ . b) Factoriser alors $P(x)$ . c) Résoudre dans $\mathbb{R}$ l'équation $P(x)=0$
En déduire l'ensemble des solutions dans IR de l'équation $x \sqrt{x}-6 x-9 \sqrt{x}+14=0$ b) a) Factoriser le trinôme $T(x)=x^{2}-5 x+4$ . c) En déduire une factorisation du polynôme $Q(x)$ . b) Résoudre dans $\mathbb{R}$ l'équation $\sqrt{Q(x)}=2$ d) Soit $f(x)=\frac{P(x)-Q(x)}{x^{2}+2 x+5}$ a/ Déterminer le domaine de définition de $f$ . b/ Montrer que $f(x)=-x^{2}+x+2$ et vérifier que $f(x)-f(x+1)=2 x$ c/ En déduire la somme $S_{n}=1+2+3+\cdots+n$ où n est un entier naturel supérieur à 2 .

See Solution

Problem 18904

7. The largest interval in which a solution of the IVP $y^{\prime}+(\ln t) y=\tan t, \quad y\left(\frac{\pi}{4}\right)=1$ is certain to exist is (a) $\left(0, \frac{\pi}{2}\right)$ (b) $(0, \pi)$ (c) $(0,1)$ . (d) $(1, \infty)$

See Solution

Problem 18905

2. The integral $\int \sin (x) \sin (3 x) d x$ can be solved by trigonometric identity: a. $\frac{\sin (-2 x)+\sin (4 x)}{2}$ b. $\frac{\cos (2 x)-\cos (4 x)}{2}$ c. $\frac{\sin (-2 x)-\sin (4 x)}{2}$ d. None

See Solution

Problem 18906

3. If $y=\left(\cosh ^{2}(3 x)-\sinh ^{2}(3 x)\right)^{4}$ then $\frac{d y}{d x}$ at $x=0$ is: a. 1 b. 0 c. 2 d. -1

See Solution

Problem 18907

For the probability mass function $\mathrm{f}(\mathrm{x}, \mathrm{y})=\frac{x+y}{250}$ for $x=3,4,5,6,7$ and $y=3,4,5,6,7$
Find $P(X=3 \mid Y=7)$ (Write in the form of an integer)

See Solution

Problem 18908

$h(x) = x \tan(2 \sqrt{x}) + 7$

See Solution

Problem 18909

For the probability mass function $f(x)=\frac{x}{155}$ for $x=10,11, \ldots, 20$ Find F(15) (Write in the form of an integer or decimal)
Answer:

See Solution

Problem 18910

For the joint probability density function $f(x, y)=$ $\frac{2 x+2 y}{90}$ for $1 \leq \mathrm{x} \leq 4 \& 1 \leq \mathrm{y} \leq 4$ , and $\mathrm{f}(\mathrm{x}, \mathrm{y})=0$ elsewhere
Find $P(1<X<2,3<Y<4)$ (Write in the form of an integer or decimal)
Answer: $\square$

See Solution

Problem 18911

3) $I=\int x^{2} \cosh x d x$ (5 points)

See Solution

Problem 18912

For the joint probability density function $f(x, y)=\frac{2 x+2 y}{90}$ for $1 \leq x \leq 4 \& 1 \leq y \leq 4$ , and $f(x, y)=0$ elsewhere
Find $P(3<X<4,3<Y<4)$ (Write in the form of an integer or decimal)
Answer: $\square$

See Solution

Problem 18913

9. Find the zeros of $f(x)=x(x+2)^{3} .$
List them in order of least to greatest, separated by commas. If the multiplicity is more than one, only list the zero once.

See Solution

Problem 18914

Вариант 2 1) Выполните умножение одночленов a) $\frac{3}{4} x y^{2} \cdot 16 y$ б) $1,6 a^{2} c \cdot\left(-2 a c^{2}\right)$ в) $-x^{3} y^{4} \cdot 1,4 x^{6} y^{5}$ 2) Возведите одночлен в указанную степень a) $\left(-10 x^{2} y^{6}\right)^{3}$ б) $\left(-\frac{1}{3} x y\right)^{4}$ в) $-\left(3 a^{2} b\right)^{3}$ 3) Выполните действия a) $35 a \cdot(2 a)^{2}$ в) $\left(-\frac{1}{8} x^{2} y^{3}\right) \cdot\left(2 x^{6} y\right)^{4}$

See Solution

Problem 18915

Find the equation of the axis of symmetry of the function $y=2 x^{2}-7 x+5$

See Solution

Problem 18916

Вариант 1 1) Выполните умножение одночленов a) $\frac{2}{3} a \cdot 12 a b^{2}$ б) $0,5 x^{2} y \cdot(-x y)$ в) $-0,4 x^{4} y^{2} \cdot 2,5 x^{2} y^{4}$ 2) Возведите одночлен в указанную степен а) $\left(-\frac{1}{2} a b\right)^{3}$ б) $-\left(2 k x^{2}\right)^{2}$ B) $\left(-10 s^{3} b^{2}\right)^{4}$ 3) Выполните действия a) $20 a^{3} \cdot(5 a)^{2}$ б) $-0,4 x^{5}$ $\left(2 x^{3}\right)^{4}$ в) $\left(3 x^{6} y^{3}\right)^{4} \cdot\left(-\frac{1}{81} x y^{2}\right)$

See Solution

Problem 18917

INDEPENDENT Use the eliminatio 1 $\begin{array}{l} 3 x-y=9 \\ 2 x-y=7 \end{array}$

See Solution

Problem 18918

Let $S=\left\{E_{1}, E_{2}, E_{3}, E_{4}\right\}$ be the sample space of an experiment. Event $A=\left\{E_{1}, E_{2}\right\}$ . Event $B=\left\{E_{3}\right\}$ . Event $C=\left\{E_{2}, E_{3}\right\}$ . The probàbilities of the sample points are assigned as follows: \begin{tabular}{cc} \hline Sample point & Probability \\ \hline $E_{1}$ & 0.1496 \\ $E_{2}$ & 0.1852 \\ $E_{3}$ & 0.2457 \\ $E_{4}$ & 0.4195 \\ \hline \end{tabular}
Then, $P(A \cup B)$ is equal to
Select one: a. 0.3953 b. 0.0000 c. 0.1496 d. 0.2457 e. 0.4309 f. 0.3348 g. 0.5805 h. 1.0000 i. 0.1852

See Solution

Problem 18919

6. Evaluate $\lim _{x \rightarrow \frac{\pi}{2}}(\sin x-\cos x)^{\tan x}$ [5 pts]

See Solution

Problem 18920

16. The Euler differential equation $x^{2} y^{\prime \prime}+5 x y^{\prime}+3 y=0, \quad y(1)=1, \quad y^{\prime}(1)=0$ has a solution (a) $y(t)=-\frac{1}{2} x^{-3}+\frac{3}{2} x^{-1}$ (b) $y(t)=x^{-1} \ln x$ (c) $y(t)=x^{-3}(1+2 \ln x)$ (d) $y(t)=x^{-3}+2 \ln x$

See Solution

Problem 18921

On considère la suite $\left(U_{n}\right)_{n \in I N} U_{0}=3, U_{n+1}=\frac{3 U_{n}+2}{U_{n}+2}$ 1) Montrer que $\forall n \in I N \quad U_{n}>2$ 2) Montrer que $\left(U_{n}\right)$ est décroissante. En déduire que $\left(U_{n}\right)$ est convergente 3) a-Montrer $\forall n \in I N U_{n+1}-2 \leq \frac{1}{4}\left(U_{n}-2\right)$ $b$ - En déduire $\forall n \in I N \quad U_{n}-2 \leq\left(\frac{1}{4}\right)^{n}$ c - Calculer $\lim _{x \rightarrow+\infty} U_{n}$

See Solution

Problem 18922

b. $\lim _{x \rightarrow 0}\left(\frac{\sin x}{x}\right)^{\frac{1}{x^{3}}}$

See Solution

Problem 18923

(4) $\begin{array}{l}(3 m-n=7) 7 \\ 21 m+6 n=-29\end{array}$

See Solution

Problem 18924

Write the following equation in its equivalent logarithmic form. $\sqrt[3]{64}=4$
The equation in logarithmic form is $\square$ (Type an equation.)

See Solution

Problem 18925

Find the $1^{\text {st }}$ and $2^{\text {nd }}$ derivative of y with respect to x from the given parametric equations a. $\quad x=\ln \left(\frac{1+e^{-2 t}}{1-e^{-2 t}}\right), y=\arctan (2 t)$

See Solution

Problem 18926

Упростите выражение: $2 \log _{4} k-3 \log _{4} 6$

See Solution

Problem 18927

In Exercises 1-4, find the domain of the function $f$ . Use limits to describe the behavior of $f$ at value(s) of $x$ not in its domain.
1. $f(x)=\frac{1}{x+3}$
2. $f(x)=\frac{-3}{x-1}$
3. $f(x)=\frac{-1}{x^{2}-4}$
4. $f(x)=\frac{2}{x^{2}-1}$

See Solution

Problem 18928

السؤال الاول : ( 25 علامة ) جد التكامل اكتب خطوات الحل )

See Solution

Problem 18929

$\lim _{x \rightarrow 1^{+}}-\ln x-1$

See Solution

Problem 18930

Find the domain of the function $f(x) = \sqrt{1-x} + \sqrt{x-1}$ .

See Solution

Problem 18931

السؤال الاول : ( 25 علامة ) جد التكامل اكتب خطوات الحل )

See Solution

Problem 18932

3. $x+5=\frac{14}{x}$
5. $x+\frac{4 x}{x-3}=\frac{12}{x-3}$

See Solution

Problem 18933

10. $11 k+2=24$

See Solution

Problem 18934

7. Calculate the value of the following limit: $\lim _{n \rightarrow \infty}\left(1+\frac{21}{\ln \left(n^{7}\right)}\right)^{\ln (10 n)}$
ANS:

See Solution

Problem 18935

10. $x+\frac{6}{x}=-7$
12. $2-\frac{3}{x+4}=\frac{12}{x^{2}+4 x}$

See Solution

Problem 18936

Q1: For some event $A$ with $P(A)=0.1$ then $P(A \mid \Omega)+P(\phi \mid \Omega)+P(\Omega \mid A)=$ A) 0.1 B) 1.2 C) 2.3 D) 1.1 E) None
Q2: Let $X$ be a random variable with $E(X)=1$ and $E\left(X^{10}+X\right)=2$ Then $E\left(X^{10}\right)=$ A) 0 B) 1 C) 2 D) 3 E) None
Q3: For $x>0$ we have $u(x)+3 \delta(y)=$ A) 1 B) 2 C) 3 D) 4 E) None
Q4: For $R_{X Y}=\{(0,0),(1,1)\}$ , if $f(0,0)=0.2$ and $f(1,1)=0.8$ . Then $E(X Y)=$ A) 1 B) 0.2 C) 0.8 D) 0.7 E) None
Q5: For some disjoint events $A, B$ with $P(A)=0.2$ and $P(B)=0.4$ , we have $P(A \cup B)=$ A) 0.2 B) 0.3 C) 0.4 D) 0.6 E) None
Q6: If $P(A)=0.2$ and $P(\bar{A} \cap B)=P(\bar{B} \cap A)$ , then $P(B)=$ A) 0.1 B) 0.2 C) 0.4 D) 0.6 E) None
Q7: $\int_{-\infty}^{\infty} x^{3} \delta(x+1) d x=$ A) -1 B) 8 C) -8 D) 1 E) None

See Solution

Problem 18937

6. Find the positive value of $x$ that solves the following equation: $x^{60}=\sum_{k=0}^{30}\binom{30}{k} 20^{30-k}$
ANS:

See Solution

Problem 18938

8. Calculate the value of the following limit: $\lim _{n \rightarrow \infty} \sqrt{n^{4}+n^{2}}-\sqrt{n^{4}-5 n^{2}+n}$
ANS:

See Solution

Problem 18939

9. Calculate the value of the following limit: $\lim _{n \rightarrow \infty}\left(\sin ^{n}(\pi / 6)+\sin ^{n}(\pi / 3)+\sin ^{n}(\pi / 2)\right)^{1 / n}$
ANS:

See Solution

Problem 18940

10. Calculate the value of the following series: $\sum_{k=2}^{\infty} \frac{1}{(3 k+1)(3 k+4)}$
ANS:

See Solution

Problem 18941

(12) Let $y_{1}$ and $y_{2}$ be two solutions of the DE $t^{2} y^{\prime \prime}-t(t+1) y^{\prime}+y=0, \quad t>0 .$
If $W\left(y_{1}, y_{2}\right)(2)=2 \mathrm{e}^{2}$ , then $W\left(y_{1}, y_{2}\right)(-1)=$ (a) -e (b) $\mathrm{e}^{-1}$ (c) $e^{2}$ (d) $-\mathrm{e}^{-1}$ (e) $e$

See Solution

Problem 18942

Factor the expression: $3c^3 + 24$ .

See Solution

Problem 18943

1. Let $a_{n}=-n^{2}+18 n-56$ where $n \in \mathbb{N}$ . What is the smallest $n_{0} \in \mathbb{N}$ such that $a_{n}$ is decreasing for all $n \geqslant n_{0}$ .
ANS:

See Solution

Problem 18944

3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right) .$
ANS: $\qquad$

See Solution

Problem 18945

4. Solve the equation $\sin (8 x)=\sin (7 x) \cos (x)$ for $x \in(0, \pi)$ .
ANS:

See Solution

Problem 18946

Identify the coefficient and degree of the term: $-10 x^{4} b^{4}$ The coefficient is $\square$ and the degree is $\square$ Question Help: Video Written Example

See Solution

Problem 18947

$(-4)+(-5)=-9$

See Solution

Problem 18948

Consider the line with the equation: $y=x+10$ Give the equation of the line parallel to Line 1 which passes through $(8,6)$ : $\square$ Give the equation of the line perpendicular to Line 1 which passes through $(8,6)$ : $\square$

See Solution

Problem 18949

ANS: $x \in(1,5) \cup 18 ;+$
3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right)$
ANS: $N=10$

See Solution

Problem 18950

5p 2. Fie expresia $E(x)=\left(\frac{1}{x-3}+\frac{x}{9-x^{2}}\right): \frac{3}{(x-3)(x+3)}$ , unde $x \in \mathbb{R} \backslash\{ \pm 3\}$ . (2p) a) Arată că $E(-1)=1$ . (3p) b) Calculează numărul $z=E(1)+2 E(2)+3 E(3)+\ldots+2022 E(2022)$ .

See Solution

Problem 18951

7. $\frac{d}{d x}\left[x^{2}\left(x^{3}+7\right)\right]$
8. $\frac{d}{d x}(2 x-3)^{2}$
9. $\frac{d}{d x}\left[\frac{x^{5}+6 x^{4}+5 x^{3}}{x^{2}}\right]$
10. $\frac{d}{d x}\left[\left(3 x^{4}+7\right)\left(x^{3}-5 x\right)\right]$
11. $\frac{d}{d x}\left[\frac{5 x+6}{3 x-7}\right]$
12. $\frac{d}{d x}\left[(7 x+4)\left(x^{2}+8\right)\right]$

See Solution

Problem 18952

Q14: For a random variable $X$ with CDF $F(x)=1-e^{-x}, x>0$ , find the pdf $f(x)$ and $P(X=0.2)$

See Solution

Problem 18953

Q15: For $X \sim B(n, p)$ we have $\operatorname{Var}(X)=0.8 E(X)$ . Find $p$

See Solution

Problem 18954

$5 \frac{17}{18}-2 \frac{2}{3}$

See Solution

Problem 18955

(iii) Evaluate the following without using log tables: $2 \log 5+\log 3+3 \log 2-\frac{1}{2} \log 36-2 \log 10$

See Solution

Problem 18956

Represent the function $\frac{10}{(1-7 x)}$ as a power series $f(x)=\sum_{n=0}^{\infty} c_{n} x^{n}$ $\begin{array}{l} c_{0}=\square \\ c_{1}=\square \\ c_{2}=\square \\ c_{3}=\square \\ c_{4}=\square \end{array}$
Find the radius of convergence $R=$ $\square$ .

See Solution

Problem 18957

Aufgabe $5 \quad$ Bilden Sie hier auch $f^{\prime \prime}(x)$ $f(x)=\frac{4 x^{2}}{\left(x^{2}+1\right)^{3}}$

See Solution

Problem 18958

$\int \frac{1}{1+2 x} d x$

See Solution

Problem 18959

$\tan \left(\tan ^{-1} \frac{52 \pi}{7}\right)$

See Solution

Problem 18960

2. 4. What is the conductance of a $39 \Omega$ resistor? Ans. 25,6 mS.

See Solution

Problem 18961

Multiply: $-20 \times-12=$ $\square$
Save answer

See Solution

Problem 18962

What is $\left|-6 \frac{3}{4}\right| ?$ $5 \frac{3}{4}$ 1 $6 \frac{3}{4}$ $-5$
Save answer

See Solution

Problem 18963

Quiz Review: Factor each completely. 1) $50 b^{2}-40 b+8$ 2) $45 x^{2}-80$ 3) $75 r^{2}-27$ 4) $75 a^{2}-30 a+3$ 5) $64 u^{4}-125 u$ 6) $27+x^{3}$ 7) $u^{4}+64 u$ 8) $x-125 x^{4}$ 9) $14 n^{3}+6 n^{2}+21 n+9$ 10) $30 r^{3}+35 r^{2}-6 r-7$

See Solution

Problem 18964

Graph each equation. 5) $y=x^{2}-2 x-3$
Identify the $\min / \max$ value of each. Th

See Solution

Problem 18965

Multiply. $-3 \times 1.7=$

See Solution

Problem 18966

Найдите $d^{8} f(1,0)$ для функции $f(x, y)=x^{2} e^{2 y}$ .

See Solution

Problem 18967

Graph the given function. State the period, amplitude, phase shift, and vertical shift of the function. $y=-\sin \left(x+\frac{\pi}{6}\right)$

See Solution

Problem 18968

Дараалж буруу бодсон тоо
Еренхий шинж чанартай, ялгаатай юмсын цуглуулгыг олонлог гэня. Тэгвэл дараах зуитлуудзсс аль нь бухэл тоОн олонлогт 6artax B9? $2.3,-4,8 \sqrt{7}, 2.8,2,8$

See Solution

Problem 18969

6. $\angle 1$ and $\angle 2$ form a linear pair. If $m \angle 1=(5 x+9)^{\circ}$ and $m \angle 2=(3 x+11)^{\circ}$ , find the measure of each angle.

See Solution

Problem 18970

Question
Round 7.698 to the nearest tenth.

See Solution

Problem 18971

For each pair of functions $f$ and $g$ below, find $f(g(x))$ and $g(f(x))$ . Then, determine whether $f$ and $g$ are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all $x$ in the domain of the composition. You do not have to indicate the domain.) (a) $f(x)=-\frac{2}{x}, x \neq 0$ (b) $f(x)=3 x+5$ $\begin{array}{l} g(x)=-\frac{2}{x}, x \neq 0 \\ f(g(x))=\square \\ g(f(x))=\square \end{array}$ $f$ and $g$ are inverses of each other $f$ and $g$ are inverses of each other $f$ and $g$ are not inverses of each other $f$ and $g$ are not inverses of each other

See Solution

Problem 18972

3. $\begin{aligned} x+y & =8 \\ -x+2 y & =7\end{aligned}$

See Solution

Problem 18973

Which of the following is true about the expression $c^{5}+\left(-9 c^{2}\right)+40 c+7 d^{7} e^{3}-5 c^{3}+4 d ?$ The coefficient of the third term is $c$ . The coefficient of the fourth term is 7. The coefficient of the first term is 0 . There are no negative coefficients.

See Solution

Problem 18974

Determine algebraically whether the given function is even, odd, or neither. $f(x)=2 x+|-5 x|$
Choose the correct answer. Even Neither

See Solution

Problem 18975

Which expression has the greatest value? $\frac{1}{5}\left(\frac{5^{3}}{5^{2}}\right)^{2}$ $\frac{5^{8}}{\left(5^{2}\right)^{4}}$ $\left(\frac{5^{3}}{5^{4}}\right)^{3}$ $\frac{\left(5^{2}\right)^{3}}{5^{4}}$ sUbmit all

See Solution

Problem 18976

Question 15 of 40 What are the center and radius of the circle defined by the equation $x^{2}+y^{2}-6 x+10 y+25=0$ ? A. Center $(-3,5)$ ; radius 9 B. Center $(3,-5)$ ; radius 3 C. Center $(3,-5)$ ; radius 9 D. Center $(-3,5)$ ; radius 3 SUBMIT

See Solution

Problem 18977

If $f(x)=\left\{\begin{array}{ll}3 x-2 & \text { if }-3 \leq x \leq 4 \\ x^{3}-4 & \text { if } 4<x \leq 5\end{array}\right.$ , find: (a) $f(0)$ , (b) $f(1)$ , (c) $f(4)$ , and (d) $f(5)$ .

See Solution

Problem 18978

Write the expression $\cos 4 \theta \sin \theta-\sin 4 \theta \cos \theta$ as a single sine or cosine.

See Solution

Problem 18979

Which expression is equivalent to $(8 a-3 b+7)-(2 a+b-4)$ ? $6 a-2 b+11$ $6 a-4 b+3$ $6 a-2 b+3$ $6 a-4 b+11$

See Solution

Problem 18980

For the quadratic function $f(x)=x^{2}+6 x$ , answer parts (a) through ( $f$ ). concave up (b) Find the $y$ -intercept and the $x$ -intercepts, if any.
What is the $y$ -intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept is 0 . $\square$ (Type an integer or a simplified fraction.) B. There is no y-intercept.
What is the x-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $x$ -intercept(s) is/are $0,-6$ . $\square$ (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no x-intercepts. (c) Use parts (a) and (b) to graph the function.
Use the graphing tool to graph the function.
Click to enlarge graph (d) Find the domain and the range of the quadratic function.
The domain of $f$ is $(-\infty, \infty)$ . (Type your answer in interval notation.) The range of $f$ is $[-9, \infty)$ . (Type your answer in interval notation.) (e) Determine where the quadratic function is increasing and where it is decreasing.
The function is increasing on the interval $(-3, \infty)$ . (Type your answer in interval notation.) The function is decreasing on the interval $(-\infty,-3)$ . (Type your answer in interval notation.) (f) Determine where $f(x)>0$ and where $f(x)<0$ . Select the correct choice below and fill in the answer box(es) within your choice. (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) A. $f(x)<0$ on $\square$ , and $f(x)$ is never positive B. $f(x)>0$ on $\square$ , and $f(x)$ is never negative C. $f(x)>0$ on $\square$ , and $\mathrm{f}(\mathrm{x})<0$ on $\square$

See Solution

Problem 18981

Evaluate the definite integral. $\int_{1}^{2}\left(e^{3 u}-\frac{1}{(u+2)^{2}}\right) d u$

See Solution

Problem 18982

Question
Evaluate the following integral using the Fundamental Theorem of Calculus. $\begin{array}{l} \int_{-5 \pi / 2}^{5 \pi / 2}(\cos x-4) d x \\ \int_{-5 \pi / 2}^{5 \pi / 2}(\cos x-4) d x=\square \end{array}$ $\square$ (Type an exact answer.)

See Solution

Problem 18983

Name:
Ai $\qquad$ $\qquad$ -
Writing Equations of Lines $\qquad$ Exit Ticket 1) 13 marks] $A$ line passes through the points $(3,2)$ and $(5,-1)$ .
Find the equation of this line in the form $y=m x+b$ . 2) 13 marks/ Find the equation of the line with gradient $\frac{2}{3}$ that passes through the point $(-2,-1)$ in the form $a x+b y+d=0$ .

See Solution

Problem 18984

2 $\begin{array}{l} \text { 2.) }-5 x+10=10 \\ -5 x+10-10=10-10 \\ -5 x=0 \end{array}$

See Solution

Problem 18985

4. [-/0.32 Points]
DETAILS MY NOTES SCOLALG7 4.4.014. 0/100 Submissions
Use the Laws of Logarithms to evaluate the expression. $-\frac{1}{3} \log _{5}(125)$ $\square$ Need Helo?

See Solution

Problem 18986

Given the equation $x / 3=-12$ , the value of $x=-4$ .
A True B False Find the value of $x$ if the answer is false: $\qquad$

See Solution

Problem 18987

a. $\quad \log (14)$ b. $\log (35)$

See Solution

Problem 18988

Calculate c. $\log (72)$ d. $\log (121)$

See Solution

Problem 18989

6.) $7-4 x=x=53$

See Solution

Problem 18990

5. Find the phase relations for the following pairs of sinusoids: a) $u=6 \sin \left(30 t-40^{\circ}\right) V$ and $i=10 \sin (30 t-\pi / 3) \mathrm{mA}$ b) $u_{1}=-8 \sin \left(40 t-80^{\circ}\right) \mathrm{V}$ and $u_{2}=-10 \sin \left(40 t-50^{\circ}\right) \mathrm{V}$ c) $i_{1}=4 \cos \left(70 t-40^{\circ}\right) \mathrm{mA}$ and $i_{2}=-6 \cos \left(70 t+80^{\circ}\right) \mathrm{mA}$ d) $u=-4 \sin \left(45 t+5^{\circ}\right) V$ and $i=7 \cos \left(45 t+80^{\circ}\right) \mathrm{mA}$
Ans. a) $u$ leads $i$ by $20^{\circ}$ ; b) $u_{1}$ lags $u_{2}$ by $30^{\circ}$ ; c) $i_{1}$ leads $i_{2}$ by $60^{\circ}$ ; d) $u$ leads $i$ by $15^{\circ}$

See Solution

Problem 18991

Use the quadratic formula to solve. Express your answer in simplest form. $4 w^{2}+20 w+25=0$

See Solution

Problem 18992

6.02 EXAM REVIEW_UNIT 2 XEM OZ6 Q Find une value of X In the equarinn novow. Question o 6/16 $1 / 6(36 x-12)-5 x=10$
A $x=-2$ B $x=8$ C $\mathrm{x}=12$ D $x=22$

See Solution

Problem 18993

Use the quadratic formula to solve. Express your answer in simplest form. $4 x^{2}-5 x-6=0$

See Solution

Problem 18994

A. Given the equation: $3 \sqrt[4]{m}(5 \sqrt{m})=15 \sqrt[x]{m^{3}}$
Find the value of $x$ .

See Solution

Problem 18995

Write the logarithmic expression as a single logarithm with coefficient 1 , and simplify as much as possible. Assume that the variables represent positive real numbers. $\ln y+\ln 3=$

See Solution

Problem 18996

Question
Use the properties of exponents to determine the value of $a$ for the equation: $\left(x^{\frac{1}{2}}\right)^{3} \sqrt{x}=x^{a}$

See Solution

Problem 18997

Part: 1 / 3
Part 2 of 3 (b) Approximate the logarithm to 4 decimal places. If necessary, round intermediate steps to 9 decimal places. $\log _{5} 28 \approx$ $\square$

See Solution

Problem 18998

4. Find the periods of a) $4+3 \sin \left(800 \pi t-15^{\circ}\right)$ ; b) $8,1 \cos ^{2} 9 \pi t$ .
Ans. a) 2,5 ms; b) 111 ms .

See Solution

Problem 18999

Subtract. Your answer should be a polynomial in standard form. $\left(d^{2}+6 d+9\right)-\left(d^{3}+6 d+9\right)=$ $\square$

See Solution

Problem 19000

Calculate the value of the following series: $\sum_{k=2}^{\infty} \frac{1}{(3 k+1)(3 k+4)}$

See Solution

1 ...187 188 189 190 191 192 193 ...269

Math Statement

Problem 18901

Problem 18902

I=∫x+1(x2+9)2dxI=\int \frac{x+1}{\left(x^{2}+9\right)^{2}} d xI=∫(x2+9)2x+1​dx

Problem 18903

Problem 18904

Problem 18905

Problem 18906

3. If y=(cosh⁡2(3x)−sinh⁡2(3x))4y=\left(\cosh ^{2}(3 x)-\sinh ^{2}(3 x)\right)^{4}y=(cosh2(3x)−sinh2(3x))4 then dydx\frac{d y}{d x}dxdy​ at x=0x=0x=0 is: a. 1 b. 0 c. 2 d. -1

Problem 18907

For the probability mass function f(x,y)=x+y250\mathrm{f}(\mathrm{x}, \mathrm{y})=\frac{x+y}{250}f(x,y)=250x+y​ for x=3,4,5,6,7x=3,4,5,6,7x=3,4,5,6,7 and y=3,4,5,6,7y=3,4,5,6,7y=3,4,5,6,7Find P(X=3∣Y=7)P(X=3 \mid Y=7)P(X=3∣Y=7) (Write in the form of an integer)

Problem 18908

h(x)=xtan⁡(2x)+7h(x) = x \tan(2 \sqrt{x}) + 7h(x)=xtan(2x​)+7

Problem 18909

For the probability mass function f(x)=x155f(x)=\frac{x}{155}f(x)=155x​ for x=10,11,…,20x=10,11, \ldots, 20x=10,11,…,20 Find F(15) (Write in the form of an integer or decimal)Answer:

Problem 18910

Problem 18911

3) I=∫x2cosh⁡xdxI=\int x^{2} \cosh x d xI=∫x2coshxdx (5 points)

Problem 18912

Problem 18913

9. Find the zeros of f(x)=x(x+2)3.f(x)=x(x+2)^{3} .f(x)=x(x+2)3.List them in order of least to greatest, separated by commas. If the multiplicity is more than one, only list the zero once.

Problem 18914

Problem 18915

Find the equation of the axis of symmetry of the function y=2x2−7x+5y=2 x^{2}-7 x+5y=2x2−7x+5

Problem 18916

Problem 18917

INDEPENDENT Use the eliminatio 1 3x−y=92x−y=7\begin{array}{l} 3 x-y=9 \\ 2 x-y=7 \end{array}3x−y=92x−y=7​

Problem 18918

Problem 18919

6. Evaluate lim⁡x→π2(sin⁡x−cos⁡x)tan⁡x\lim _{x \rightarrow \frac{\pi}{2}}(\sin x-\cos x)^{\tan x}limx→2π​​(sinx−cosx)tanx [5 pts]

Problem 18920

Problem 18921

Problem 18922

b. lim⁡x→0(sin⁡xx)1x3\lim _{x \rightarrow 0}\left(\frac{\sin x}{x}\right)^{\frac{1}{x^{3}}}limx→0​(xsinx​)x31​

Problem 18923

(4) (3m−n=7)721m+6n=−29\begin{array}{l}(3 m-n=7) 7 \\ 21 m+6 n=-29\end{array}(3m−n=7)721m+6n=−29​

Problem 18924

Write the following equation in its equivalent logarithmic form. 643=4\sqrt[3]{64}=4364​=4The equation in logarithmic form is □\square□ (Type an equation.)

Problem 18925

Find the 1st 1^{\text {st }}1st and 2nd 2^{\text {nd }}2nd derivative of y with respect to x from the given parametric equations a. x=ln⁡(1+e−2t1−e−2t),y=arctan⁡(2t)\quad x=\ln \left(\frac{1+e^{-2 t}}{1-e^{-2 t}}\right), y=\arctan (2 t)x=ln(1−e−2t1+e−2t​),y=arctan(2t)

Problem 18926

Упростите выражение: 2log⁡4k−3log⁡462 \log _{4} k-3 \log _{4} 62log4​k−3log4​6

Problem 18927

Problem 18928

السؤال الاول : ( 25 علامة ) جد التكامل اكتب خطوات الحل )

Problem 18929

lim⁡x→1+−ln⁡x−1\lim _{x \rightarrow 1^{+}}-\ln x-1limx→1+​−lnx−1

Problem 18930

Find the domain of the function f(x)=1−x+x−1 f(x) = \sqrt{1-x} + \sqrt{x-1} f(x)=1−x​+x−1​.

Problem 18931

السؤال الاول : ( 25 علامة ) جد التكامل اكتب خطوات الحل )

Problem 18932

3. x+5=14xx+5=\frac{14}{x}x+5=x14​5. x+4xx−3=12x−3x+\frac{4 x}{x-3}=\frac{12}{x-3}x+x−34x​=x−312​

Problem 18933

10. 11k+2=2411 k+2=2411k+2=24

Problem 18934

7. Calculate the value of the following limit: lim⁡n→∞(1+21ln⁡(n7))ln⁡(10n)\lim _{n \rightarrow \infty}\left(1+\frac{21}{\ln \left(n^{7}\right)}\right)^{\ln (10 n)}n→∞lim​(1+ln(n7)21​)ln(10n)ANS:

Problem 18935

10. x+6x=−7x+\frac{6}{x}=-7x+x6​=−712. 2−3x+4=12x2+4x2-\frac{3}{x+4}=\frac{12}{x^{2}+4 x}2−x+43​=x2+4x12​

Problem 18936

Problem 18937

6. Find the positive value of xxx that solves the following equation: x60=∑k=030(30k)2030−kx^{60}=\sum_{k=0}^{30}\binom{30}{k} 20^{30-k}x60=k=0∑30​(k30​)2030−kANS:

Problem 18938

8. Calculate the value of the following limit: lim⁡n→∞n4+n2−n4−5n2+n\lim _{n \rightarrow \infty} \sqrt{n^{4}+n^{2}}-\sqrt{n^{4}-5 n^{2}+n}n→∞lim​n4+n2​−n4−5n2+n​ANS:

Problem 18939

9. Calculate the value of the following limit: lim⁡n→∞(sin⁡n(π/6)+sin⁡n(π/3)+sin⁡n(π/2))1/n\lim _{n \rightarrow \infty}\left(\sin ^{n}(\pi / 6)+\sin ^{n}(\pi / 3)+\sin ^{n}(\pi / 2)\right)^{1 / n}n→∞lim​(sinn(π/6)+sinn(π/3)+sinn(π/2))1/nANS:

Problem 18940

10. Calculate the value of the following series: ∑k=2∞1(3k+1)(3k+4)\sum_{k=2}^{\infty} \frac{1}{(3 k+1)(3 k+4)}k=2∑∞​(3k+1)(3k+4)1​ANS:

Problem 18941

Problem 18942

Factor the expression: 3c3+243c^3 + 243c3+24.

Problem 18943

1. Let an=−n2+18n−56a_{n}=-n^{2}+18 n-56an​=−n2+18n−56 where n∈Nn \in \mathbb{N}n∈N. What is the smallest n0∈Nn_{0} \in \mathbb{N}n0​∈N such that ana_{n}an​ is decreasing for all n⩾n0n \geqslant n_{0}n⩾n0​.ANS:

Problem 18944

3. If S(N)=∑k=1NkS(N)=\sum_{k=1}^{N} kS(N)=∑k=1N​k then which value of NNN solves the following equation? ∑n=1S(N)4n=43(455−1).\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right) .n=1∑S(N)​4n=34​(455−1).ANS: \qquad

Problem 18945

4. Solve the equation sin⁡(8x)=sin⁡(7x)cos⁡(x)\sin (8 x)=\sin (7 x) \cos (x)sin(8x)=sin(7x)cos(x) for x∈(0,π)x \in(0, \pi)x∈(0,π).ANS:

Problem 18946

Identify the coefficient and degree of the term: −10x4b4-10 x^{4} b^{4}−10x4b4 The coefficient is □\square□ and the degree is □\square□ Question Help: Video Written Example

Problem 18947

$I=\int \frac{x+1}{\left(x^{2}+9\right)^{2}} d x$

3. If $y=\left(\cosh ^{2}(3 x)-\sinh ^{2}(3 x)\right)^{4}$ then $\frac{d y}{d x}$ at $x=0$ is: a. 1 b. 0 c. 2 d. -1

For the probability mass function $\mathrm{f}(\mathrm{x}, \mathrm{y})=\frac{x+y}{250}$ for $x=3,4,5,6,7$ and $y=3,4,5,6,7$
Find $P(X=3 \mid Y=7)$ (Write in the form of an integer)

$h(x) = x \tan(2 \sqrt{x}) + 7$

For the probability mass function $f(x)=\frac{x}{155}$ for $x=10,11, \ldots, 20$ Find F(15) (Write in the form of an integer or decimal)
Answer:

3) $I=\int x^{2} \cosh x d x$ (5 points)

9. Find the zeros of $f(x)=x(x+2)^{3} .$
List them in order of least to greatest, separated by commas. If the multiplicity is more than one, only list the zero once.

Find the equation of the axis of symmetry of the function $y=2 x^{2}-7 x+5$

INDEPENDENT Use the eliminatio 1 $\begin{array}{l} 3 x-y=9 \\ 2 x-y=7 \end{array}$

6. Evaluate $\lim _{x \rightarrow \frac{\pi}{2}}(\sin x-\cos x)^{\tan x}$ [5 pts]

b. $\lim _{x \rightarrow 0}\left(\frac{\sin x}{x}\right)^{\frac{1}{x^{3}}}$

(4) $\begin{array}{l}(3 m-n=7) 7 \\ 21 m+6 n=-29\end{array}$

Write the following equation in its equivalent logarithmic form. $\sqrt[3]{64}=4$
The equation in logarithmic form is $\square$ (Type an equation.)

Find the $1^{\text {st }}$ and $2^{\text {nd }}$ derivative of y with respect to x from the given parametric equations a. $\quad x=\ln \left(\frac{1+e^{-2 t}}{1-e^{-2 t}}\right), y=\arctan (2 t)$

Упростите выражение: $2 \log _{4} k-3 \log _{4} 6$

$\lim _{x \rightarrow 1^{+}}-\ln x-1$

Find the domain of the function $f(x) = \sqrt{1-x} + \sqrt{x-1}$ .

3. $x+5=\frac{14}{x}$
5. $x+\frac{4 x}{x-3}=\frac{12}{x-3}$

10. $11 k+2=24$

7. Calculate the value of the following limit: $\lim _{n \rightarrow \infty}\left(1+\frac{21}{\ln \left(n^{7}\right)}\right)^{\ln (10 n)}$
ANS:

10. $x+\frac{6}{x}=-7$
12. $2-\frac{3}{x+4}=\frac{12}{x^{2}+4 x}$

6. Find the positive value of $x$ that solves the following equation: $x^{60}=\sum_{k=0}^{30}\binom{30}{k} 20^{30-k}$
ANS:

8. Calculate the value of the following limit: $\lim _{n \rightarrow \infty} \sqrt{n^{4}+n^{2}}-\sqrt{n^{4}-5 n^{2}+n}$
ANS:

9. Calculate the value of the following limit: $\lim _{n \rightarrow \infty}\left(\sin ^{n}(\pi / 6)+\sin ^{n}(\pi / 3)+\sin ^{n}(\pi / 2)\right)^{1 / n}$
ANS:

10. Calculate the value of the following series: $\sum_{k=2}^{\infty} \frac{1}{(3 k+1)(3 k+4)}$
ANS:

Factor the expression: $3c^3 + 24$ .

1. Let $a_{n}=-n^{2}+18 n-56$ where $n \in \mathbb{N}$ . What is the smallest $n_{0} \in \mathbb{N}$ such that $a_{n}$ is decreasing for all $n \geqslant n_{0}$ .
ANS:

3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right) .$
ANS: $\qquad$

4. Solve the equation $\sin (8 x)=\sin (7 x) \cos (x)$ for $x \in(0, \pi)$ .
ANS:

Identify the coefficient and degree of the term: $-10 x^{4} b^{4}$ The coefficient is $\square$ and the degree is $\square$ Question Help: Video Written Example

$(-4)+(-5)=-9$

Consider the line with the equation: $y=x+10$ Give the equation of the line parallel to Line 1 which passes through $(8,6)$ : $\square$ Give the equation of the line perpendicular to Line 1 which passes through $(8,6)$ : $\square$

ANS: $x \in(1,5) \cup 18 ;+$
3. If $S(N)=\sum_{k=1}^{N} k$ then which value of $N$ solves the following equation? $\sum_{n=1}^{S(N)} 4^{n}=\frac{4}{3}\left(4^{55}-1\right)$
ANS: $N=10$

Q14: For a random variable $X$ with CDF $F(x)=1-e^{-x}, x>0$ , find the pdf $f(x)$ and $P(X=0.2)$

Q15: For $X \sim B(n, p)$ we have $\operatorname{Var}(X)=0.8 E(X)$ . Find $p$

$5 \frac{17}{18}-2 \frac{2}{3}$

(iii) Evaluate the following without using log tables: $2 \log 5+\log 3+3 \log 2-\frac{1}{2} \log 36-2 \log 10$

Aufgabe $5 \quad$ Bilden Sie hier auch $f^{\prime \prime}(x)$ $f(x)=\frac{4 x^{2}}{\left(x^{2}+1\right)^{3}}$

$\int \frac{1}{1+2 x} d x$

$\tan \left(\tan ^{-1} \frac{52 \pi}{7}\right)$

2. 4. What is the conductance of a $39 \Omega$ resistor? Ans. 25,6 mS.

Multiply: $-20 \times-12=$ $\square$
Save answer

What is $\left|-6 \frac{3}{4}\right| ?$ $5 \frac{3}{4}$ 1 $6 \frac{3}{4}$ $-5$
Save answer

Graph each equation. 5) $y=x^{2}-2 x-3$
Identify the $\min / \max$ value of each. Th

Multiply. $-3 \times 1.7=$

Найдите $d^{8} f(1,0)$ для функции $f(x, y)=x^{2} e^{2 y}$ .

Graph the given function. State the period, amplitude, phase shift, and vertical shift of the function. $y=-\sin \left(x+\frac{\pi}{6}\right)$

6. $\angle 1$ and $\angle 2$ form a linear pair. If $m \angle 1=(5 x+9)^{\circ}$ and $m \angle 2=(3 x+11)^{\circ}$ , find the measure of each angle.

Question
Round 7.698 to the nearest tenth.

3. $\begin{aligned} x+y & =8 \\ -x+2 y & =7\end{aligned}$

Determine algebraically whether the given function is even, odd, or neither. $f(x)=2 x+|-5 x|$
Choose the correct answer. Even Neither