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Problem 22301

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Find the numerical value of $\left[\sum n^{2} \delta[n+1]\right]$ : Note: The sum is from 0 to 5 a. 5 b. 1 c. 0

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Problem 22302

Solve the system of equations. If the system has no solution, say that it is inconsistent. $\begin{cases} x + 4y = 8 \\ 6x + 24y = 48 \end{cases}$ Select the correct choice below and, if necessary, fill in any answer boxes within your choice.
A. The solution is $x =$ and $y =$ . (Type integers or simplified fractions.)
B. There are infinitely many solutions. Using ordered pairs, they can be expressed as $\{(x,y) | x =$ , y any real number\}. (Simplify your answer. Type an expression using $y$ as the variable as needed.)
C. The system is inconsistent.

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Problem 22303

Solve the following inequality algebraically. $-3 x^{2}+5 x>-3 x-3$
Answer Attempt 1 out of 3 $\square$

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Problem 22304

$\frac{2\sin^2\theta - 8\sin\theta + 6}{6\cos\theta - 2\sin\theta\cos\theta} = \frac{1 - \sin\theta}{\cos\theta}$
$LS = \frac{2\sin^2\theta - 8\sin\theta + 6}{6\cos\theta - 2\sin\theta\cos\theta}$
$RS = \frac{1 - \sin\theta}{\cos\theta}$
$= \frac{2(\sin^2\theta - 4\sin\theta + 3)}{2\cos\theta(3 - \sin\theta)}$
$= \frac{(\sin\theta - 3)(\sin\theta - 1)}{-\cos\theta(\sin\theta - 3)}$
$= \frac{-(\sin\theta - 1)}{\cos\theta}$
$= \frac{1 - \sin\theta}{\cos\theta}$
$LS = RS$

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Problem 22305

Решите уравнение: $\cos(\frac{6\pi x}{5}) = 2\sqrt{x^2 + 2x - 35}$

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Problem 22306

Solve the given system of equations. If the system has no solution, say that it is inconsistent.
$x - 3y + 4z = 5$ $2x + y + z = -4$ $-2x + 3y - 3z = -2$
Select the correct choice below and fill in any answer boxes within your choice.
A. The solution is $x =$ _, $y =$ _, and $z =$ _. (Type integers or simplified fractions.)
B. There are infinitely many solutions. Using ordered triplets, they can be expressed as $\{(x,y,z) | x =$ _, $y =$ _, $z$ any real number\}. (Simplify your answers. Type expressions using $z$ as the variable as needed.)
C. There are infinitely many solutions. Using ordered triplets, they can be expressed as $\{(x,y,z) | x =$ _, $y$ any real number, $z$ any real number\}. (Simplify your answer. Type an expression using $y$ and $z$ as the variables as needed.)
D. The system is inconsistent.

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Problem 22307

Sketch the graph of $y = \frac{2}{3}x$

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Problem 22308

Solve the given system of equations. If the system has no solution, say that it is inconsistent.
$x - 3y + 4z = 5$
$2x + y + z = -4$
$-2x + 3y - 3z = -2$

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Problem 22309

Determine whether the following statement is true or false.
The matrix $\begin{bmatrix} 1 & 3 & -2 \\ 0 & 1 & 5 \\ 0 & 0 & 0 \end{bmatrix}$ is in row echelon form.
Choose the correct answer below. True False

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Problem 22310

What are the zeros, the degree, and the $y$ -intercept of the polynomial $f(x) = 3x(x + 1)^2(x - 2)^2$ Degree: Zeros: Y-intercept:

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Problem 22311

Write the augmented matrix of the given system of equations. $\begin{cases} x - 7y = 3 \\ 7x + 6y = 9 \end{cases}$ The augmented matrix is $\begin{bmatrix} \Box & \Box & \Box \\ \Box & \Box & \Box \end{bmatrix}$ .

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Problem 22312

14) $10 x y-15 x^{2} y^{2}$

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Problem 22313

Diberi $6^{3 x-2}=1296$ , cari nilai $x$ . Given $6^{3 x-2}=1296$ , find the value of $x$ .

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Problem 22314

Solve by completing the square: $z^{2}=12 z+1$

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Problem 22315

Determine if the subset of $\mathbb{R}^{3}$ consisting of vectors of the form $\left[\begin{array}{l}a \\ b \\ c\end{array}\right]$ , where $a \geq 0, b \geq 0$ , and $c \geq 0$ is a subspace. Select true or false for each statement.
True $\square$ 1. The set contains the zero vector
True 2. This set is closed under vector addition $\square$ 3. This set is a subspace
False $\square$ 4. This set is closed under scalar multiplications

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Problem 22316

Find the value of $x$ for $3^{x-2}=81^{x}$ . Jawapan / Answer:

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Problem 22317

Solve for $x$ : $\begin{array}{l} \log _{6} x+\log _{6}(x+4)=5 \\ x= \end{array}$

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Problem 22318

Use the given function and the given interval to complete parts $\mathbf{a}$ and $\mathbf{b}$ . $f(x)=2 x^{3}-27 x^{2}+108 x \text { on }[2,7]$ a. Determine the absolute extreme values of $f$ on the given interval when they exist. b. Use a graphing utility to confirm your conclusions. a. What is/are the absolute maximum/maxima of $f$ on the given interval? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The absolute maximum/maxima is/are $\square$ at $x=$ $\square$ . (Use a comma to separate answers as needed. Type exact answers, using radicals as needed.) B. There is no absolute maximum of $f$ on the given interval.

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Problem 22319

$x^2 + y^2 - 6x + 8y + 16 = 0$

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Problem 22320

Find the exact values of the following. a) $\sin\frac{7\pi}{6} =$ b) $\sin\left(\frac{4\pi}{3}\right)$ c) $\cos\frac{3\pi}{4}$

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Problem 22321

Note: You may need to assume the fact that $\lim_{M \to +\infty} M^n e^{-M} = 0$ for all $n$ .
Decide whether or not the given integral converges.
$\int_{-\infty}^{-8} \frac{1}{x^2} dx$
The integral converges. The integral diverges.
If the integral converges, compute its value. (If the integral diverges, enter DNE.)

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Problem 22322

4. Find the measure of each angle, to the nearest degree.
a) $\tan \theta = 1.5$ b) $\tan A = \frac{3}{4}$ c) $\tan B = 0.6000$ d) $\tan W = \frac{4}{5}$ e) $\tan C = 0.8333$ f) $\tan \theta = \frac{6}{7}$ g) $\tan X = 3.0250$ h) $\tan \theta = \frac{15}{9}$

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Problem 22323

(c) Estimate $\int_0^6 (x^2 + 1) dx$ using a right-hand sum with $n = 3$ (i.e. $R_3$ ).
Round your answer to two decimal places.
$R_3 =$

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Problem 22324

5.12: Let the random variable $Y_n$ have distribution that is $b(n, p)$ a) Prove that $\frac{X_n}{n}$ converges in probability to $p$ . This result is one form of the weak law of large numbers. b) Prove that $1 - \frac{X_n}{n}$ converges in probability to $1 - p$ c) Prove that $(\frac{X_n}{n})(1 - \frac{Y_n}{n})$ converges in probability to $p(1 - p)$ let $z_n =$ $= \lim_{n \to \infty} p(|z|$

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Problem 22325

5.12: Let the random variable $Y_n$ have distribution that is $b(n, p)$ a) Prove that $\frac{X_n}{n}$ converges in probability to $p$ . This result is one form of the weak law of large numbers. b) Prove that $1 - \frac{X_n}{n}$ converges in probability to $1 - p$ c) Prove that $(\frac{X_n}{n})(1 - \frac{Y_n}{n})$ converges in probability to $p(1 - p)$

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Problem 22326

$-6(2 r-2)=-8 r+40$

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Problem 22327

$2 \log_{a}(8x^3) - \frac{1}{7} \log_{a}(4x+11) = \square$ (Simplify your answer.)

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Problem 22328

Use Euler's Method with $\mathrm{h}=0.1$ to approximate the solution to the following initial value problem on the interval $1 \leq x \leq 2$ . Compare these approximations with the actual solution $y=-\frac{1}{x}$ by graphing the polygonal-line approximation and the actual solution on the same coordinate system. $y^{\prime}=\frac{1}{x^{2}}-\frac{y}{x}-y^{2}, y(1)=-1$
Complete the table. \begin{tabular}{|c|c|c|} \hline $\boldsymbol{n}$ & $\mathbf{x}_{\mathbf{n}}$ & \begin{tabular}{c} Euler's Method \\ approximate solution \end{tabular} \\ \hline 0 & 1 & -1 \\ \hline 1 & 1.1 & -0.90000 \\ \hline 2 & 1.2 & -0.81654 \\ \hline 3 & 1.3 & -0.74572 \\ \hline 4 & 1.4 & -0.68480 \\ \hline 5 & 1.5 & -0.63176 \\ \hline 6 & 1.6 & -0.58511 \\ \hline 7 & 1.7 & -0.54371 \\ \hline 8 & 1.8 & -0.50669 \\ \hline 9 & 1.9 & -0.47335 \\ \hline 10 & 2.0 & 0.44314 \\ \hline \end{tabular} (Round to five decimal places as needed.)

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Problem 22329

Select the correct answer.
What is the completely factored form of this expression? $3 x^{2}-17 x-28$ A. $(3 x+4)(x+7)$ B. $(3 x+4)(x-7)$ C. $3 x^{2}-17 x-28$ D. $\left(3 x^{2}+4\right)(x-7)$

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Problem 22330

Consider the following function: $f(x) = -3x^3 - \frac{45}{2}x^2 - 54x - 14$
Step 2 of 4: Determine where the function is increasing and decreasing. Enter your answers in interval notation.
Answer 2 Points
Separate multiple intervals with a comma.
Selecting a radio button will replace the entered answer value(s) with the radio button value. If the radio button is not selected, the entered answer is used.
Increasing on:
Decreasing on:
Never increasing
Never decreasing
Next

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Problem 22331

Determine the following indefinite integral. Check your work by differentiation. $\begin{array}{c} \int \sqrt[13]{r^{7}} d r \\ \int \sqrt[13]{r^{7}} d r=\square \end{array}$ $\square$

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Problem 22332

Use integration by substitution to solve the integral below. Use C for the constant of integration.
$\int e^{x^6+3} \cdot 6x^5 dx$
Answer 4 Points
Choose the correct answer from the options below.
$e^{x^6+3} + C$
$36e^{x^6+3}x^{10} + 30e^{x^6+3}x^4 + C$
$e^{6x^5} + C$
$e^{\frac{1}{7}x^7+3x} + C$

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Problem 22333

Rewrite each equation as requested. (a) Rewrite as a logarithmic equation. $e^{y}=3$ (b) Rewrite as an exponential equation. $\ln x=6$ (a) $\square$ (b) $\square$ $\square 109$ $9{ }^{9}$ ■In $\square$ $\square$ $\square$

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Problem 22334

Show that the value of $\oint_C xy^2 dx + (x^2 y + 2x) dy$ around any square depends only on the area of the square and not on its location in the plane.
$\oint_C Mdx + Ndy = \iint_R (\frac{\partial N}{\partial x} - \frac{\partial M}{\partial y})dxdy$
What part of the function should be substituted for $M$ ? $M = xy^2$ (Type an expression using x and y as the variables.)
What part of the function should be substituted for $N$ ? $N = x^2y + 2x$ (Type an expression using x and y as the variables.)
Differentiate $M$ with respect to $y$ . $\frac{\partial M}{\partial y} = 2xy$
Differentiate $N$ with respect to $x$ . $\frac{\partial N}{\partial x} =$

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Problem 22335

Solve the following pair of simultaneous equations: $\begin{aligned} 3 x+y & =19 \\ x-y & =1 \end{aligned}$

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Problem 22336

Solve $\begin{aligned} 4 y+x & =27 \\ y-x & =3 \end{aligned}$

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Problem 22337

c. $4x^2 + 24x + 36$

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Problem 22338

Consider the following. $f(x)=x^{4}-3 x^{2}-4$
Find all the zeros of the function. (Enter your answers as a comma-separated li $x=$ $\square$

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Problem 22339

Factor the binomial completely. $27-m^{3}$

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Problem 22340

2) $\lim_{x \to 1} \frac{\ln{x^2}}{x^2 - 1}$

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Problem 22341

$3)\ \log{(x^2+1)}-x=0$

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Problem 22342

Area under a Curve
30. Find the first-quadrant area bounded by the curve $y=x^{2}+1$ , the $y$ -axis, and the lines $y$ $=3$ and $y=6$ .

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Problem 22343

Question 3
Find the average rate of change of the function $f(x)=\frac{7}{3 x+6}$ , on the interval $x \in[3,5]$ . Average rate of change $=$ $\square$ Give an exact answer. Submit Question

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Problem 22344

$\frac{1}{\sqrt{3} - 2} \times \frac{\sqrt{3} + 2}{\sqrt{3} + 2}$

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Problem 22345

10. $(7x + 3) - (x + 9)$

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Problem 22346

11. [5 marks] Find the absolute extrema of $f(x) = x^3 - 12x$ on $[-1, 3]$ . $f'(x) = 3x^2 - 12$ $3(x^2 - 4)$ $(x-2)(x+2)$ 2 $f(2)$ $f(-1)$ $f(3)$

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Problem 22347

65) $f(x) = \frac{x^2 - 6x + 2}{x+8}$
A) $x = y + 6$ B) $y = x - 14$ Objective: (4.5) Find Oblique Asymptote of Rational Function
Solve.
66) $x^2 - 9x + 20 > 0$
A) $(5, \infty)$ B) $(-\infty, 4) \cup (5, \infty)$ Objective: (4.6) Solve Quadratic Polynomial Inequality
List the critical values of the related function. Then solve the inequality.
67) $\frac{1}{x+6} > 0$
A) No critical values; $\emptyset$ B) $-6; (-\infty, -6)$ Objective: (4.6) Solve Rational Inequality I

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Problem 22348

8. Factor completely. (a) $3x^2 - x - 14$ (b) $20x^2 + 11x - 3$ (c) $6x^2 + 17x + 12$ (d) $12x^2 - 11x + 2$

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Problem 22349

Solve the following system of equations. $-3x+y=17$ $7x+y=-23$ $x=$ $y=$

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Problem 22350

14. The graph of which function has the same axis of symmetry as the graph of $y=2 x^{2}-8 x+3$ ? Explain your reasoning. A. $y=-4 x^{2}+16 x-5$ B. $y=2 x^{2}+8 x+7$ C. $y=3 x^{2}-6 x+7$ D. $y=-6 x^{2}+10 x-1$

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Problem 22351

13. $\begin{aligned} -60 & =x-16 \\ -60+\square & =x-16+ \end{aligned}$

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Problem 22352

$x^{2}-14 x+49$ $a^{2}+28 a+19 b$
For \#30 \& 31, (a) Write the third term for "Completing the Square" of the perfect square trinomial. (b) Write the perfect square trinomial as a binomial squared. 30) $\mathrm{x}^{2}+18 \mathrm{x}+$ $\qquad$ 31) $a^{2}+11 a+$ $\qquad$

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Problem 22353

1 Fill in the Blank 1 point An equation is shown. $(\frac{27}{8})^{-\frac{2}{3}} = \frac{a}{b}$ Find the value of each variable. a = type your answer... b = type your answer...

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Problem 22354

Exer. 21-24: Use polar coordinates to find the limit, if it exists. $21 \lim _{(x, y) \rightarrow(0,0)} \frac{x y^{2}}{x^{2}+y^{2}}$ $22 \lim _{(x, y) \rightarrow(0,0)} \frac{x^{3}-y^{3}}{x^{2}+y^{2}}$ $23 \lim _{(x, y) \rightarrow(0,0)} \frac{x^{2}+y^{2}}{\sin \left(x^{2}+y^{2}\right)}$ $24 \lim _{(4, y) \rightarrow(0,0)} \frac{\sinh \left(x^{2}+y^{2}\right)}{x^{2}+y^{2}}$

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Problem 22355

$= \tan^2{x} \cdot \csc{x}$ Rule ?
$= \frac{\sin^2{x}}{\cos^2{x}} \cdot \csc{x}$ Rule ?
$= \frac{\sin^2{x}}{\cos^2{x}} \cdot \left( \frac{1}{\sin{x}} \right)$ Rule ?
$= \frac{\sin{x}}{\cos{x}} \cdot \left( \frac{1}{\cos{x}} \right)$ Rule ?
$= \tan{x} \cdot \left( \frac{1}{\cos{x}} \right)$ Rule ?
$= \tan{x} \cdot \sec{x}$ Rule ?
Rule Algebra Reciprocal Quotient Pythagorean Odd/Even

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Problem 22356

Suppose that the functions $f$ and $g$ are defined as follows. $f(x) = x-5$ $g(x) = \sqrt{3x-4}$
Find $\frac{f}{g}$ and $f+g$ . Then, give their domains using interval notation.

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Problem 22357

a) $\frac{7}{q-2} \cdot \frac{2 q-4}{q+4}$

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Problem 22358

For the region formed by the functions $f(x)=x^{2}-2 x-2$ and $g(x)=5$ on the interval $[-1,2]$ , use definite integrals to find the area of the region. Answer: The area is $\square$ Hint: Follow Example 2.

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Problem 22359

Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions. $\begin{array}{r} -10 x-3 y=17 \\ 4 x-9 y=8 \end{array}$

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Problem 22360

15. $(2 x-7)(x+5)=0$

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Problem 22361

Write the Maclaurin series for $f(x) = 5x^2 e^{-2x}$ as $\sum_{n=0}^{\infty} c_n x^n$ .
Find the first six coefficients.
$c_0 =$ $c_1 =$ $c_2 =$ $c_3 =$ $c_4 =$ $c_5 =$

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Problem 22362

This is Section 4.4 Problem 46: For the function $f(x)=x^{2}-2 x+1$ on the interval $[0,2]$ , the average value of $f$ is is $\square$ . (Use a fraction.)
Hint: Follow Exämple 6. $\square$

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Problem 22363

In Exercises 1-4, decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient.
1. $f(x)=4 x^{2}-3 x+5 x^{3}-7$
2. $h(x)=5 x^{3}-7 x^{-2}+x-1$
3. $g(x)=x^{4}-\frac{1}{3} x^{2}+10-4 x^{3}+2 x$
4. $f(x)=8 x^{2}-\sqrt{3} x+2$
In Exercises 5-7, evaluate the function for the given value of $x$ .
5. $f(x)=-2 x^{4}+x^{3}+5 x^{2}-3 x-7 ; x=-1$
6. $g(x)=5 x^{4}-2 x^{3}+9 x-10 ; x=-6$
7. $h(x)=x^{5}-4 x^{3}+3 x^{2}+11 x-8 x=7$
In Exercises 8 and 9 , describe the end behavior of the graph of the function.
8. $g(x)=6 x^{4}-3 x^{3}+12 x^{2}+8 x+2$
9. $h(x)=-5 x^{3}+6 x^{2}-5 x^{4}+x^{2}-1$
In Exercises 10-13, graph the polynomial function.
10. $q(x)=x^{4}-2$
11. $h(x)=x^{3}-2 x+3$
12. $k(x)=2 x^{2}+3=x^{3}$
13. $f(x)=x^{3}-2 x^{3}+1$
In Exercises 14 and 16, describe the x-values for which $f$ is inereasing, decreasing, positive, and negative. 14. 16.
16. Suppose $f(x) \rightarrow-\infty$ as $x \rightarrow-\infty$ and $f(x) \Rightarrow-\infty$ as $x \rightarrow+\infty$ . Describe the degree and leading coefficient of the function.

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Problem 22364

Your answer was A. Wrong. Consider the function $f(x) = \frac{x - 6}{x^2 - 36}$ . Which of the following statements is true about this function?
A The function has infinite discontinuity at $x = 6$ . B The function has removable discontinuity at $x = 0$ . C The function has an infinite discontinuity at $x = -6$ . D The function has no points of discontinuity. E The function has a removable discontinuity at $x = -6$ . F None of the above.

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Problem 22365

Graph: $\begin{cases} y > \frac{1}{2}x - 2 \\ y < -4x + 1 \end{cases}$

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Problem 22366

Write an equivalent expression by expanding $-5(-2d+6)$ .
$-5(-2d+6) = \boxed{\phantom{10}}d - \boxed{\phantom{30}}$

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Problem 22367

Write an equivalent expression by expanding $-5(-2d+6)$ .
$-5(-2d+6) = \boxed{\phantom{10}}d - \boxed{?}$

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Problem 22368

Consider the following limit of Riemann sums of a function $f$ on $[a, b]$ . Identify $f$ and express the limit as a definite integral. $\lim _{\Delta \rightarrow 0} \sum_{k=1}^{n} x_{k}^{} \tan ^{2} x_{k}^{} \Delta x_{k} ;[2,3]$
The limit, expressed as a definite integral, is $\square$ $\square$ $\square$

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Problem 22369

In Exercises 8-11, find the product.
8. $5 x^{2}\left(3 x^{2}+7 x+6\right)$
9. $-2 x^{4}\left(10 x^{3}-9 x^{2}-7 x+4\right)$ $15 x^{4}+35^{3}+30 x^{2}$
10. $\left(8 x^{2}-3 x+1\right)(-3 x+2)$
11. $(-x-6)\left(3 x^{2}+2 x+9\right)$

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Problem 22370

What is the standard enthalpy of formation of $PCl_3(g)$ in kJ mol $^{-1}$ ? (Note that $P_4(s)$ is the standard state of phosphorus)
$P_4(s) + 10 Cl_2(g) \rightarrow 4 PCl_5(s)$ $\Delta H^{\circ} = -1774.0$ kJ $PCl_3(g) + Cl_2(g) \rightarrow PCl_5(s)$ $\Delta H^{\circ} = -156.5$ kJ
-287.0 +1517.5 +287.0 -1517.5 +474.0

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Problem 22371

Perform the indicated operation 14.) $(1+5 i)+(6-i)$

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Problem 22372

For exercises 1-6, write each percent as a fraction in simplest form and as a decimal.
1. $60\%$
2. $22\%$
3. $88\%$
4. $55\%$
5. $90\%$
6. $14\%$

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Problem 22373

For the equation $y=-\frac{x}{5}+2$ a) Complete the table: \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-5 & $\square$ \\ \hline 0 & $\square$ \\ \hline 5 & $\square$ \\ \hline \end{tabular} b) Use the appropriate tool to graph the given equation.

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Problem 22374

$-4x + 2x^2 - 5x^4$
$20x^7 + 7 + 18x^6$
$-18x^{24} - 18x^{18} + 9x^{17}$
25 points possible 16/25 answered
Question 17
For the following polynomials, identify the degree, the leading term, and the leading coefficient.
degree leading term leading coefficient
Add Work
Next Question

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Problem 22375

$f(x) = \frac{x^2 - 1}{-x^3 - x^2}$
If there is more than one answer, enter your answers as a comma separated list. If there is no solution, enter NONE. Do not leave a blank empty.
(a) The function has x-intercept(s) at $x =$
(b) The function has y-intercept(s) at $y =$
(c) The function has vertical asymptote(s) when $x =$
(d) The function has horizontal asymptote(s) when $y =$
Note: You can earn partial credit on this problem.

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Problem 22376

Find all zeros of $f(x)=x^{3}-4 x^{2}-5 x+14$ . Enter the zeros separated by commas. Enter exact value, not decimal approximations.

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Problem 22377

c. $y = -2|x - 2| + 4$ $(2, 4)$ Domain: $(-\infty, \infty)$ Range: $(-\infty, 4]$

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Problem 22378

Simplify: $\frac{x^{2}-x-12}{9-x} \div \frac{x+3}{x+4}$
0:00
Select one: a. $\frac{x^{2}-16}{9-x}$ b. $9-x$ c. $\frac{-x^{2}-6 x+9}{9-x}$ d. $\frac{9-x}{x^{2}-16}$

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Problem 22379

This is similar to Section 4.5 Problem 18:
Determine the indefinite integral $\int \frac{12 x^{2}}{\left(x^{3}+4\right)^{2}} d x$ by substitution. (It is recommended that you check your results by differentiation.) Use capital C for the free constant.
Answer: $\square$
Hint: Follow Example 6.

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Problem 22380

Get a similar question You can retry this question below
Simplify $\frac{\sec (x) \cos (x)}{\sin (x)}$ to a single trigonometric function. $\tan (x)$

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Problem 22381

Determine the indefinite integral $\int \frac{36 x^{5}}{x^{6}+5} d x$ by substitution. (It is recommended that you check your results by differentiation.) Use capital C for the free constant.
Answer: $\square$
Hint: Follow Example 6.

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Problem 22382

e for x : $3125^{x+3}=25^{3 x-1}$ Attempt 1 out of 2

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Problem 22383

tion list restion 14 vestion 15
Find the zerrs of the function aloworracally. $f(x)=3 x^{2}-x+2$
The zeros are $\square$ . (Sinclly your answer: Type an exact answer, using radicals and ias needed. Use inte

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Problem 22384

for x : $\left(\frac{1}{125}\right)^{-5 x+1}=\left(\frac{1}{25}\right)^{-x-5}$ Attempt 1 out of 2

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Problem 22385

(c) $14m \div (-2m)=$

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Problem 22386

Determine the indefinite integral $\int \frac{4}{7 x-8} d x$ by substitution. Assume $u>0$ when $\ln (u)$ appears. (It is recommended that you check your results by differentiation.) Use capital C for the f
Answer: $\square$
Hint: Follow Examples 5 and 6. Submit Answer

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Problem 22387

9. $\tan \left(\frac{7 \pi}{12}\right)$

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Problem 22388

This is Section 4.5 Problem 58: Evaluate the definite integral $\int_{0}^{1} 3 r^{2} e^{r^{3}} d r$ by the following: (a) Determine the indefinite integral $\int 3 r^{2} e^{r^{3}} d r$ by substitution. (It is recommended that you check your results by differentiation.) Use capital C for the free constant.
Answer: $\square$ (b) The exact value of the definite integral is $\square$ .

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Problem 22389

This is Section 4.5 Problem 66: Evaluate the definite integral $\int_{2}^{10} \frac{1}{\sqrt{5 x-1}} d x$ by the following: (a) Determine the indefinite integral $\int \frac{1}{\sqrt{5 x-1}} d x$ by substitution. (It is recommended that you check your results by differentiation.) Use capital C for the free constant.
Answer: $\square$ (b) The exact value of the definite integral is $\square$

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Problem 22390

Evaluate the integral by making the given substitution. (Use $C$ for the constant of integration.) $\int e^{-5 x} d x, \quad u=-5 x$

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Problem 22391

If $u=f(x)$ , then $d u=f^{\prime}(x) d x$ , and so it is helpful to look for some expression in $\int e^{x} \sqrt{36+e^{x}} d x$ for which the derivative is also present.
We see that $36+e^{x}$ is part of this integral, and the derivative of $36+e^{x}$ is $\square$ , which is also present. Submit Skip (you cannot come back)

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Problem 22392

Question Compute the exact value of $\tan\left(\frac{19\pi}{12}\right)$ .
Provide your answer below:
Content attribution FEEDBACK MORE INSTRUCTION

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Problem 22393

Convert to a logarithmic equation. $10^5 = 100,000$

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Problem 22394

n make on paper.) PM ractionaı
Fractions / Fractions
Fractional
Question Watch Video Show Examples
If the expression $4 x^{-3} y^{-1} \sqrt{x y^{5}}$ is written in the form $a x^{b} y^{c}$ , then what is the product of $a, b$ and $c$ ?
Answer Attempt 1 out of 2 $\square$ Submit Answer

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Problem 22395

$\text{Given that } u = 36 + e^x, \text{ convert the expression } \frac{2}{3} u^{3/2} + C \text{ back to an expression in terms of } x.$

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Problem 22396

Question Watch Video Show Examples
If $f(x)$ is an exponential function of the form of $y=a b^{x}$ where $f(5)=5$ and $f(14)=35$ , then find the value of $f(18)$ , to the nearest hundredth.
Answer Attempt 2 out of 2 $27.74$ Submit Answer

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Problem 22397

Determine the indefinite integral $\int-6 x^{2} e^{4 x^{3}+5} d x$ by substitution. (It is recommended that you check your result rentiation.) Use capital C for the free constant.
Answer: $\square$
Hint: Follow Example 7. Submit Answer

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Problem 22398

Question Watch Video Show Examples
If $f(x)$ is an exponential function of the form of $y=a b^{x}$ where $f(-4.5)=20$ and $f(1.5)=11$ , then find the value of $f(-4)$ , to the nearest hundredth.
Answer Attempt 2 out of 2 $16.35$ Submit Answer

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Problem 22399

For numbers 1-4 evaluate the expression and round your answer to two decimal places. 1) $27^{\frac{4}{3}}$ 2) $(\sqrt[4]{45})^{5}$
3. $14^{\frac{2}{3}}$ 4) $(\sqrt[3]{8})^{5}$
For numbers 4-9 simplify the expressions 5) $\sqrt[4]{80}$ 6) $\sqrt[3]{81}$ 7) $\frac{1}{1+\sqrt{5}}$ 8) $\sqrt[3]{x^{9} y^{8} z^{16}}$ 9) $\sqrt{16 x^{5} y^{6} z}$ 10) $\sqrt{14}+5 \sqrt{14}$ 11) $4 \sqrt[3]{5 x}-7 \sqrt[3]{5 x}$

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Problem 22400

lomework: Practice Final Exam - Homework Question $32,4.5 .27$ lode stion list question 31
Question 32
Question 33
Determine the oblique asymptote of the graph of the function. $g(x)=\frac{x^{2}+5 x-2}{x+3}$
The equation of the oblique asymptote is $\square$ .

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Math Statement

Problem 22301

Scanned with CamScannerFind the numerical value of [∑n2δ[n+1]]\left[\sum n^{2} \delta[n+1]\right][∑n2δ[n+1]] : Note: The sum is from 0 to 5 a. 5 b. 1 c. 0

Problem 22302

Problem 22303

Solve the following inequality algebraically. −3x2+5x>−3x−3-3 x^{2}+5 x>-3 x-3−3x2+5x>−3x−3Answer Attempt 1 out of 3 □\square□

Problem 22304

Problem 22305

Решите уравнение: cos⁡(6πx5)=2x2+2x−35\cos(\frac{6\pi x}{5}) = 2\sqrt{x^2 + 2x - 35}cos(56πx​)=2x2+2x−35​

Problem 22306

Problem 22307

Sketch the graph of y=23xy = \frac{2}{3}xy=32​x

Problem 22308

Solve the given system of equations. If the system has no solution, say that it is inconsistent.x−3y+4z=5x - 3y + 4z = 5x−3y+4z=52x+y+z=−42x + y + z = -42x+y+z=−4−2x+3y−3z=−2-2x + 3y - 3z = -2−2x+3y−3z=−2

Problem 22309

Determine whether the following statement is true or false.The matrix [13−2015000] \begin{bmatrix} 1 & 3 & -2 \\ 0 & 1 & 5 \\ 0 & 0 & 0 \end{bmatrix} ⎣⎡​100​310​−250​⎦⎤​ is in row echelon form.Choose the correct answer below. True False

Problem 22310

What are the zeros, the degree, and the yyy-intercept of the polynomial f(x)=3x(x+1)2(x−2)2f(x) = 3x(x + 1)^2(x - 2)^2f(x)=3x(x+1)2(x−2)2 Degree: Zeros: Y-intercept:

Problem 22311

Write the augmented matrix of the given system of equations. {x−7y=37x+6y=9 \begin{cases} x - 7y = 3 \\ 7x + 6y = 9 \end{cases} {x−7y=37x+6y=9​ The augmented matrix is [□□□□□□] \begin{bmatrix} \Box & \Box & \Box \\ \Box & \Box & \Box \end{bmatrix} [□□​□□​□□​].

Problem 22312

14) 10xy−15x2y210 x y-15 x^{2} y^{2}10xy−15x2y2

Problem 22313

Diberi 63x−2=12966^{3 x-2}=129663x−2=1296, cari nilai xxx. Given 63x−2=12966^{3 x-2}=129663x−2=1296, find the value of xxx.

Problem 22314

Solve by completing the square: z2=12z+1z^{2}=12 z+1z2=12z+1

Problem 22315

Problem 22316

Find the value of xxx for 3x−2=81x3^{x-2}=81^{x}3x−2=81x. Jawapan / Answer:

Problem 22317

Solve for xxx : log⁡6x+log⁡6(x+4)=5x=\begin{array}{l} \log _{6} x+\log _{6}(x+4)=5 \\ x= \end{array}log6​x+log6​(x+4)=5x=​

Problem 22318

Problem 22319

x2+y2−6x+8y+16=0x^2 + y^2 - 6x + 8y + 16 = 0x2+y2−6x+8y+16=0

Problem 22320

Find the exact values of the following. a) sin⁡7π6=\sin\frac{7\pi}{6} =sin67π​= b) sin⁡(4π3)\sin\left(\frac{4\pi}{3}\right)sin(34π​) c) cos⁡3π4\cos\frac{3\pi}{4}cos43π​

Problem 22321

Problem 22322

Problem 22323

(c) Estimate ∫06(x2+1)dx\int_0^6 (x^2 + 1) dx∫06​(x2+1)dx using a right-hand sum with n=3n = 3n=3 (i.e. R3R_3R3​).Round your answer to two decimal places.R3=R_3 =R3​=

Problem 22324

Problem 22325

Problem 22326

−6(2r−2)=−8r+40-6(2 r-2)=-8 r+40−6(2r−2)=−8r+40

Problem 22327

2log⁡a(8x3)−17log⁡a(4x+11)=□2 \log_{a}(8x^3) - \frac{1}{7} \log_{a}(4x+11) = \square2loga​(8x3)−71​loga​(4x+11)=□ (Simplify your answer.)

Problem 22328

Problem 22329

Problem 22330

Problem 22331

Determine the following indefinite integral. Check your work by differentiation. ∫r713dr∫r713dr=□\begin{array}{c} \int \sqrt[13]{r^{7}} d r \\ \int \sqrt[13]{r^{7}} d r=\square \end{array}∫13r7​dr∫13r7​dr=□​ □\square□

Problem 22332

Problem 22333

Rewrite each equation as requested. (a) Rewrite as a logarithmic equation. ey=3e^{y}=3ey=3 (b) Rewrite as an exponential equation. ln⁡x=6\ln x=6lnx=6 (a) □\square□ (b) □\square□ □109\square 109□109 999{ }^{9}99 ■In □\square□ □\square□ □\square□

Problem 22334

Problem 22335

Solve the following pair of simultaneous equations: 3x+y=19x−y=1\begin{aligned} 3 x+y & =19 \\ x-y & =1 \end{aligned}3x+yx−y​=19=1​

Problem 22336

Solve 4y+x=27y−x=3\begin{aligned} 4 y+x & =27 \\ y-x & =3 \end{aligned}4y+xy−x​=27=3​

Problem 22337

c. 4x2+24x+364x^2 + 24x + 364x2+24x+36

Problem 22338

Consider the following. f(x)=x4−3x2−4f(x)=x^{4}-3 x^{2}-4f(x)=x4−3x2−4Find all the zeros of the function. (Enter your answers as a comma-separated li x=x=x= □\square□

Problem 22339

Factor the binomial completely. 27−m327-m^{3}27−m3

Problem 22340

2) lim⁡x→1ln⁡x2x2−1\lim_{x \to 1} \frac{\ln{x^2}}{x^2 - 1}limx→1​x2−1lnx2​

Problem 22341

3) log⁡(x2+1)−x=03)\ \log{(x^2+1)}-x=03) log(x2+1)−x=0

Problem 22342

Area under a Curve30. Find the first-quadrant area bounded by the curve y=x2+1y=x^{2}+1y=x2+1, the yyy-axis, and the lines yyy =3=3=3 and y=6y=6y=6.

Problem 22343

Question 3Find the average rate of change of the function f(x)=73x+6f(x)=\frac{7}{3 x+6}f(x)=3x+67​, on the interval x∈[3,5]x \in[3,5]x∈[3,5]. Average rate of change === □\square□ Give an exact answer. Submit Question

Problem 22344

13−2×3+23+2\frac{1}{\sqrt{3} - 2} \times \frac{\sqrt{3} + 2}{\sqrt{3} + 2}3​−21​×3​+23​+2​

Problem 22345

10. (7x+3)−(x+9) (7x + 3) - (x + 9) (7x+3)−(x+9)

Problem 22346

11. [5 marks] Find the absolute extrema of f(x)=x3−12xf(x) = x^3 - 12xf(x)=x3−12x on [−1,3][-1, 3][−1,3]. f′(x)=3x2−12f'(x) = 3x^2 - 12f′(x)=3x2−12 3(x2−4)3(x^2 - 4)3(x2−4) (x−2)(x+2)(x-2)(x+2)(x−2)(x+2) 2 f(2)f(2)f(2) f(−1)f(-1)f(−1) f(3)f(3)f(3)

Problem 22347

Scanned with CamScanner
Find the numerical value of $\left[\sum n^{2} \delta[n+1]\right]$ : Note: The sum is from 0 to 5 a. 5 b. 1 c. 0

Solve the following inequality algebraically. $-3 x^{2}+5 x>-3 x-3$
Answer Attempt 1 out of 3 $\square$

Решите уравнение: $\cos(\frac{6\pi x}{5}) = 2\sqrt{x^2 + 2x - 35}$

Sketch the graph of $y = \frac{2}{3}x$

Solve the given system of equations. If the system has no solution, say that it is inconsistent.
$x - 3y + 4z = 5$
$2x + y + z = -4$
$-2x + 3y - 3z = -2$

Determine whether the following statement is true or false.
The matrix $\begin{bmatrix} 1 & 3 & -2 \\ 0 & 1 & 5 \\ 0 & 0 & 0 \end{bmatrix}$ is in row echelon form.
Choose the correct answer below. True False

What are the zeros, the degree, and the $y$ -intercept of the polynomial $f(x) = 3x(x + 1)^2(x - 2)^2$ Degree: Zeros: Y-intercept:

Write the augmented matrix of the given system of equations. $\begin{cases} x - 7y = 3 \\ 7x + 6y = 9 \end{cases}$ The augmented matrix is $\begin{bmatrix} \Box & \Box & \Box \\ \Box & \Box & \Box \end{bmatrix}$ .

14) $10 x y-15 x^{2} y^{2}$

Diberi $6^{3 x-2}=1296$ , cari nilai $x$ . Given $6^{3 x-2}=1296$ , find the value of $x$ .

Solve by completing the square: $z^{2}=12 z+1$

Find the value of $x$ for $3^{x-2}=81^{x}$ . Jawapan / Answer:

Solve for $x$ : $\begin{array}{l} \log _{6} x+\log _{6}(x+4)=5 \\ x= \end{array}$

$x^2 + y^2 - 6x + 8y + 16 = 0$

Find the exact values of the following. a) $\sin\frac{7\pi}{6} =$ b) $\sin\left(\frac{4\pi}{3}\right)$ c) $\cos\frac{3\pi}{4}$

(c) Estimate $\int_0^6 (x^2 + 1) dx$ using a right-hand sum with $n = 3$ (i.e. $R_3$ ).
Round your answer to two decimal places.
$R_3 =$

$-6(2 r-2)=-8 r+40$

$2 \log_{a}(8x^3) - \frac{1}{7} \log_{a}(4x+11) = \square$ (Simplify your answer.)

Determine the following indefinite integral. Check your work by differentiation. $\begin{array}{c} \int \sqrt[13]{r^{7}} d r \\ \int \sqrt[13]{r^{7}} d r=\square \end{array}$ $\square$

Rewrite each equation as requested. (a) Rewrite as a logarithmic equation. $e^{y}=3$ (b) Rewrite as an exponential equation. $\ln x=6$ (a) $\square$ (b) $\square$ $\square 109$ $9{ }^{9}$ ■In $\square$ $\square$ $\square$

Solve the following pair of simultaneous equations: $\begin{aligned} 3 x+y & =19 \\ x-y & =1 \end{aligned}$

Solve $\begin{aligned} 4 y+x & =27 \\ y-x & =3 \end{aligned}$

c. $4x^2 + 24x + 36$

Consider the following. $f(x)=x^{4}-3 x^{2}-4$
Find all the zeros of the function. (Enter your answers as a comma-separated li $x=$ $\square$

Factor the binomial completely. $27-m^{3}$

2) $\lim_{x \to 1} \frac{\ln{x^2}}{x^2 - 1}$

$3)\ \log{(x^2+1)}-x=0$

Area under a Curve
30. Find the first-quadrant area bounded by the curve $y=x^{2}+1$ , the $y$ -axis, and the lines $y$ $=3$ and $y=6$ .

Question 3
Find the average rate of change of the function $f(x)=\frac{7}{3 x+6}$ , on the interval $x \in[3,5]$ . Average rate of change $=$ $\square$ Give an exact answer. Submit Question

$\frac{1}{\sqrt{3} - 2} \times \frac{\sqrt{3} + 2}{\sqrt{3} + 2}$

10. $(7x + 3) - (x + 9)$

11. [5 marks] Find the absolute extrema of $f(x) = x^3 - 12x$ on $[-1, 3]$ . $f'(x) = 3x^2 - 12$ $3(x^2 - 4)$ $(x-2)(x+2)$ 2 $f(2)$ $f(-1)$ $f(3)$

8. Factor completely. (a) $3x^2 - x - 14$ (b) $20x^2 + 11x - 3$ (c) $6x^2 + 17x + 12$ (d) $12x^2 - 11x + 2$

Solve the following system of equations. $-3x+y=17$ $7x+y=-23$ $x=$ $y=$

13. $\begin{aligned} -60 & =x-16 \\ -60+\square & =x-16+ \end{aligned}$

1 Fill in the Blank 1 point An equation is shown. $(\frac{27}{8})^{-\frac{2}{3}} = \frac{a}{b}$ Find the value of each variable. a = type your answer... b = type your answer...

Suppose that the functions $f$ and $g$ are defined as follows. $f(x) = x-5$ $g(x) = \sqrt{3x-4}$
Find $\frac{f}{g}$ and $f+g$ . Then, give their domains using interval notation.

a) $\frac{7}{q-2} \cdot \frac{2 q-4}{q+4}$

For the region formed by the functions $f(x)=x^{2}-2 x-2$ and $g(x)=5$ on the interval $[-1,2]$ , use definite integrals to find the area of the region. Answer: The area is $\square$ Hint: Follow Example 2.

Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions. $\begin{array}{r} -10 x-3 y=17 \\ 4 x-9 y=8 \end{array}$

15. $(2 x-7)(x+5)=0$

Write the Maclaurin series for $f(x) = 5x^2 e^{-2x}$ as $\sum_{n=0}^{\infty} c_n x^n$ .
Find the first six coefficients.
$c_0 =$ $c_1 =$ $c_2 =$ $c_3 =$ $c_4 =$ $c_5 =$

This is Section 4.4 Problem 46: For the function $f(x)=x^{2}-2 x+1$ on the interval $[0,2]$ , the average value of $f$ is is $\square$ . (Use a fraction.)
Hint: Follow Exämple 6. $\square$

Graph: $\begin{cases} y > \frac{1}{2}x - 2 \\ y < -4x + 1 \end{cases}$

Write an equivalent expression by expanding $-5(-2d+6)$ .
$-5(-2d+6) = \boxed{\phantom{10}}d - \boxed{\phantom{30}}$

Write an equivalent expression by expanding $-5(-2d+6)$ .
$-5(-2d+6) = \boxed{\phantom{10}}d - \boxed{?}$

Perform the indicated operation 14.) $(1+5 i)+(6-i)$

For exercises 1-6, write each percent as a fraction in simplest form and as a decimal.
1. $60\%$
2. $22\%$
3. $88\%$
4. $55\%$
5. $90\%$
6. $14\%$

For the equation $y=-\frac{x}{5}+2$ a) Complete the table: \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline-5 & $\square$ \\ \hline 0 & $\square$ \\ \hline 5 & $\square$ \\ \hline \end{tabular} b) Use the appropriate tool to graph the given equation.