Math Statement

Problem 22401

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 22402

Express $\log_5 10Z$ as a sum of logarithms.

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Problem 22403

$x^2 + 8x + 12 = 0$

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Problem 22404

For number 10 and 11 graph the function and identify the domain and range. 10) $f(x)=\sqrt{x-3}$ 11) $g(x)=\sqrt{x+4}$
For number 12-13 solve the equation and check your answer. 12) $3 \sqrt[3]{5 x+6}=18$

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Problem 22405

Solve the inequality $9 - 3x \leq -(1 + 5x)$ and graph the solution set.

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Problem 22406

Rewrite $\sqrt[7]{c}$ as a power.

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Problem 22407

Calculate the product of 6.1 cm and 1.6 cm.

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Problem 22408

Find the value of $\sqrt[8]{x^{9}}$ .

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Problem 22409

A rocket starts from rest with mass $m_0$ and burns fuel at rate $k$ . Find $v(t)$ from $m = m_0 - kt$ and $m \frac{dv}{dt} = ck - mg$ .
(a) $v(t) = \, \mathrm{m/sec}$
(b) If fuel is 80% of $m_0$ and lasts 110s, find $v(110)$ with $g=9.8 \, \mathrm{m/s}^2$ and $c=2500 \, \mathrm{m/s}$ .
$v(110) = \, \mathrm{m/sec}$ [Round to nearest whole number]

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Problem 22410

What is the value of $\frac{1}{\sqrt{e}}$ ?

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Problem 22411

Analyze the function $F(x)=\frac{x^{2}-5 x-6}{x+4}$ . Find its domain, vertical asymptote, and horizontal/oblique asymptote.

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Problem 22412

Find the value of $\frac{1}{\sqrt[8]{x^{7}}}$ .

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Problem 22413

Analyze the function $F(x)=\frac{x^{2}-3x-4}{x+14}$ for domain, vertical, and horizontal asymptotes.

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Problem 22414

Simplify $\sqrt[3]{(4 a^{2})^{6}} = I a$ .

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Problem 22415

Which expression converts 100 inches/min to feet/min? Consider the options involving unit conversions.

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Problem 22416

Find the missing factor $D$ in the equation $-15 y^{4}=(D)(3 y^{2})$ .

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Problem 22417

Calculate the following: $36^{\frac{3}{2}}$ , $\left(\frac{1}{81}\right)^{\frac{-1}{2}}$ , $\left(\frac{1}{125}\right)^{\frac{-2}{3}}$ .

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Problem 22418

Find the domain of $H(x)=\frac{5 x-30}{36-x^{2}}$ and its vertical asymptote(s). Choices included.

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Problem 22419

Find the derivative of $e^{x} \cos x$ .

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Problem 22420

Prove that $\vdash_{\text {tot }}\{x \geq 0\} \operatorname{Fac1}(x)\{y=x !\}$ is valid. Find a suitable loop invariant.

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Problem 22421

Simplify these expressions:
$\sqrt[3]{(4 a^{2})^{6}} = I^{a}, \quad \sqrt[3]{(b^{\frac{2}{5}})^{6}} = b^{-}, \quad \sqrt[4]{\frac{c^{18}}{c^{6}}} = c, \quad \sqrt[4]{81 d^{5} \times 16 d^{-6}} = d$

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Problem 22422

Find the horizontal asymptote of the drug concentration function $C(t)=\frac{t}{7t^{2}+8}$ . What is $C=\square$ ?

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Problem 22423

Which formula converts 80 USD to AUD using the rates: 1 USD = 1.0343 AUD, 1 AUD = 0.9668 USD?

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Problem 22424

Calculate the sum: $-82 + (-14) =$

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Problem 22425

Find the product and express it as $a + b i$ : simplify $(2 + 5 i)^{2}$ .

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Problem 22426

Find the horizontal asymptote of $C(t)=\frac{t}{7t^{2}+8}$ . What does $C(t)$ approach as $t$ increases?

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Problem 22427

Find the difference and express it as $a + b i$ : $(-3 + 2 i) - (4 - 3 i)$

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Problem 22428

Find the horizontal asymptote of $C(t)=\frac{t}{7 t^{2}+8}$ , identify the graph, and determine when concentration is highest.

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Problem 22429

Solve the equation $x^{2}+8 x+17=0$ and express solutions as $a+b i$ .

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Problem 22430

Find the displacement of a mass on a spring from $t=0$ to $t=\pi$ given $v(t)=6 \sin(t)-6 \cos(t)$ . Evaluate $\int_{0}^{\pi}(6 \sin(t)-6 \cos(t)) dt$ .

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Problem 22431

Calculate $-12 + (-12)$ .

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Problem 22432

Solve for real values of $x$ in the equation $(x+9)^{2}-7(x+9)-18=0$ .

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Problem 22433

Solve for $x$ given $y=87.5$ in the equation $300 x+\frac{500}{7} y=10000$ .

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Problem 22434

Calculate the work done by the force $F(x)=x^{-1}+4x$ from $x=3$ to $x=5$ : $W=\int_{3}^{5}(x^{-1}+4x)dx$

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Problem 22435

Find the distance a wave travels from $t=1$ to $t=4$ given $v=\sqrt{\frac{8}{x}}$ . Evaluate the integral $\int_{1}^{4} \sqrt{\frac{8}{x}} d x$ .

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Problem 22436

Solve for all real values of $y$ in the equation $y^{5}-18 y^{4}+6 y^{3}=0$ .

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Problem 22437

A car's velocity is given by $v(t)=2 t^{1/2}+5$ . Find the displacement (in m) from $t=2$ to $t=8$ .

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Problem 22438

Solve for $x$ in the equation $\sqrt{6x - 1} = 3$ . What are the real solutions?

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Problem 22439

Simplify $7^{5} \cdot 7^{2}$ using the Product Rule of Exponents.

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Problem 22440

Find the displacement and total distance traveled by a particle with velocity $v(t)=4-2t$ from $t=0$ to $t=6$ .

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Problem 22441

Find all real solutions for the equation: $y^{5}-16 y^{4}+52 y^{3}=0$ . What are the values of $y$ ?

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Problem 22442

Identify the expression that applies the Product Rule of Exponents: $6^{2} \cdot 7^{3}$ , $10^{8} \cdot 10^{8}$ , $\left(5^{2}\right)^{9}$ , or $32^{7}$ ?

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Problem 22443

Calculate the value of $10^{2} \cdot 10^{3}$ . Options: 100,000, 10, 1,100, $10^{5}$ .

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Problem 22444

Choose the right symbol for the fractions: $\frac{3}{7}(-) \frac{6}{13}$ . Options: $<$ , $=$ , $>$ .

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Problem 22445

Choose a symbol for the fractions: $\frac{1}{3}$ ? $-\frac{2}{7}$ . Options: $<$ , $=$ , $>$ .

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Problem 22446

Calculate the total oil leaked in the first 5 hours after the tanker breaks apart using $R(t)=\frac{0.9}{1+t^{2}}$ .

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Problem 22447

Choose the right symbol for the fractions: $\frac{17}{34}() \frac{1}{2}$ from =, <, >.

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Problem 22448

What is $\frac{3}{4} \div 4$ ?

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Problem 22449

Solve the equation: $-10 x + 1 + 7 x = 37$ . Find the value of $x$ . Options: $-15$ , $-12$ , $12$ , $15$ .

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Problem 22450

Find the displacement and total distance traveled by a particle with velocity $v(t)=4-2t$ from $t=0$ to $t=6$ .

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Problem 22451

Place a symbol between the fractions: $\frac{13}{15}()_{-} \frac{5}{6}$ from $<, =, >$ .

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Problem 22452

Solve the equation: $(0.9 / 2) * \ln (26) - \ln (5) = (0.45) * \ln (26) - \ln (5)$ .

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Problem 22453

Calculate $-1 \frac{7}{8} \div \frac{3}{4}$ .

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Problem 22454

Solve for $g$ in the equation: $5(2-g)=0$ .

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Problem 22455

Find $f$ for the integral $\int \frac{x}{\sqrt{3 x^{2}+2}} d x$ using the substitution $u=3 x^{2}+2$ .

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Problem 22456

Find $f$ for the integral $\int x \sqrt{x+4} dx$ using the substitution $u=x+4$ , so $\int f(u) du$ . $f(u)=$

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Problem 22457

Evaluate the integral using substitution: $\int \frac{x^{6}}{\sqrt{x^{7}-4}} d x = C$ .

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Problem 22458

Graph the line represented by the equation $-3x + y = -9$ .

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Problem 22459

Evaluate the integral using substitution: $\int 7 x^{3} \cos(4 x^{4}) \, dx = C$ .

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Problem 22460

Find $\frac{\partial f}{\partial x}$ , $\frac{\partial f}{\partial y}$ , and evaluate at (1,-1) for $f(x, y)=6 x e^{5 x y}$ .

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Problem 22461

Solve for t in the equation: $1 = p r t$

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Problem 22462

Evaluate the integral using substitution: $\int -x(5-8x)^{5} dx =$

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Problem 22463

Evaluate the integral: $\int \frac{x^{6}}{(x^{7}+5)^{7}} \, dx =$

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Problem 22464

Evaluate the integral from 0 to 1: $\int_{0}^{1} 6 x^{4}\left(1-x^{5}\right)^{3} d x=$

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Problem 22465

Evaluate the integral: $\int -3 \sin(x) \sqrt{\cos(x)} \, dx =$

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Problem 22466

Evaluate the integral using substitution: $\int \cos (x)(13-\cos (x))^{8} \sin (x) d x =$

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Problem 22467

Solve for $x$ in the equation $\frac{x-2}{2}=m+n$ .

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Problem 22468

Find the second partial derivatives $f_{xx}(x, y), f_{yy}(x, y), f_{xy}(x, y), f_{yx}(x, y)$ for $f(x, y)=7x^2y$ and evaluate at $(1,-1)$ .

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Problem 22469

Find the $x$ and $y$ intercepts of the line given by the equation $2x - 4y = 8$ .

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Problem 22470

Evaluate the integral: $\int_{-\pi / 2}^{\pi / 2} \sin ^{6}(x) \cos (x) d x.$

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Problem 22471

Find the $x$ -intercept and $y$ -intercept of the line defined by $x + 2y = 8$ .

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Problem 22472

Evaluate the integral using substitution: $\int 7 \sin ^{2}(4 x) \cos ^{3}(4 x) d x.$

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Problem 22473

Solve for $r_{2}$ in the equation $R(r_{1}+r_{2})=r_{1} r_{2}$ .

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Problem 22474

Find the $y$ -intercept and $x$ -intercept of the line given by $6x - 5y = -30$ .

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Problem 22475

Evaluate the integral using substitution: $\int 5 t \sin(t^{2}) \cos(t^{2}) \, dt =$

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Problem 22476

Find the slope-intercept form of a line with slope -2 and $y$ -intercept -3.

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Problem 22477

Find the partial derivatives $\frac{\partial f}{\partial x}$ , $\frac{\partial f}{\partial y}$ , and evaluate at $(1,-1)$ for $f(x, y)=13,000-30 x+20 y+8 x y$ .

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Problem 22478

Find the general antiderivative of $\frac{d y}{d x}=7 e^{x}+4$ . Antiderivative $=$ $+C$ .

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Problem 22479

Find the antiderivative for $\frac{d x}{d t}=2 e^{t}-3$ with the condition $x(0)=4$ . What is $x$ ?

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Problem 22480

Find the antiderivatives of $\frac{d x}{d t}=2 t^{-1}+5$ . What is $x$ ? Include the constant $C$ .

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Problem 22481

Find the function $f(x)$ given $f^{\prime \prime \prime}(x)=e^{x}$ , $f^{\prime \prime}(0)=6$ , $f^{\prime}(0)=10$ .

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Problem 22482

Find an antiderivative of $f(x)=\frac{2}{x}-10 e^{x}$ .

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Problem 22483

Graph the line given by the equation $y = -4x$ .

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Problem 22484

Find the function $f(x)$ where $f'(x)=9^{x}$ and $f(4)=-5$ . What is $f(x)$ ?

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Problem 22485

Evaluate the integral $\int_{-2}^{8} f(x) dx$ where $f(x)=x$ for $x<1$ and $f(x)=\frac{1}{x}$ for $x \geq 1$ .

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Problem 22486

Graph the line represented by the equation $y = 2x$ .

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Problem 22487

Calculate the area between $f(x)=3^{-x}$ and $f(x)=0$ for $x$ in $[2,7]$ using integration. Provide the exact value.

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Problem 22488

Calculate the area between $f(x)=3^{-x}$ and $f(x)=0$ from $x=2$ to $x=7$ using integration. Provide the exact answer.

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Problem 22489

Find the circumference of a circle with radius $r=6.9 \mathrm{ft}$ .

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Problem 22490

What level of differences in the sequence $1, 2, \ldots, n$ is constant based on the sum formula $\frac{n(n+1)}{2}$ ?

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Problem 22491

Find the product of the polynomials $(2 x^{3}+3 x^{2})(4 x^{4}-5 x^{3}-6 x^{2})$ .

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Problem 22492

Calculate the product of $(2q^9 + 3q^7)(-6q^2 + 9)$ . What is the result?

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Problem 22493

What is the simplified form of $\frac{-10 x^{2}+20 x+80}{x+2}$ ? Choices: $-10 x+40$ , $x-4$ , $x+4$ , $10 x-40$ .

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Problem 22494

Find the circumference of a circle with diameter $d=8.2 \mathrm{ft}$ .

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Problem 22495

Calculate the slope of the line through the points (-3, -2) and (1, 2) using the formula $\frac{y_2 - y_1}{x_2 - x_1}$ .

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Problem 22496

Solve the inequality and graph the solution: $-18 - 5y \geq 52$ .

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Problem 22497

Find the circumference of a circle with diameter $d=7 \mathrm{~m}$ .

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Problem 22498

Evaluate the integral of $y=7xe^{-x}$ from $x=2$ to $x$ .

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Problem 22499

Calculate the circumference of a circle with diameter $d=6.8 \mathrm{~mm}$ .

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Problem 22500

Find the area of a circle with a radius of $r=7.1$ yd.

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Math Statement

Problem 22401

8) x9y8z163\sqrt[3]{x^{9} y^{8} z^{16}}3x9y8z16​ 9) 16x5y6z\sqrt{16 x^{5} y^{6} z}16x5y6z​ 10) 14+514\sqrt{14}+5 \sqrt{14}14​+514​ 11) 45x3−75x34 \sqrt[3]{5 x}-7 \sqrt[3]{5 x}435x​−735x​

Problem 22402

Express log⁡510Z\log_5 10Zlog5​10Z as a sum of logarithms.

Problem 22403

x2+8x+12=0x^2 + 8x + 12 = 0x2+8x+12=0

Problem 22404

For number 10 and 11 graph the function and identify the domain and range. 10) f(x)=x−3f(x)=\sqrt{x-3}f(x)=x−3​ 11) g(x)=x+4g(x)=\sqrt{x+4}g(x)=x+4​For number 12-13 solve the equation and check your answer. 12) 35x+63=183 \sqrt[3]{5 x+6}=18335x+6​=18

Problem 22405

Solve the inequality 9−3x≤−(1+5x)9 - 3x \leq -(1 + 5x)9−3x≤−(1+5x) and graph the solution set.

Problem 22406

Rewrite c7\sqrt[7]{c}7c​ as a power.

Problem 22407

Calculate the product of 6.1 cm and 1.6 cm.

Problem 22408

Find the value of x98\sqrt[8]{x^{9}}8x9​.

Problem 22409

Problem 22410

What is the value of 1e\frac{1}{\sqrt{e}}e​1​?

Problem 22411

Analyze the function F(x)=x2−5x−6x+4F(x)=\frac{x^{2}-5 x-6}{x+4}F(x)=x+4x2−5x−6​. Find its domain, vertical asymptote, and horizontal/oblique asymptote.

Problem 22412

Find the value of 1x78\frac{1}{\sqrt[8]{x^{7}}}8x7​1​.

Problem 22413

Analyze the function F(x)=x2−3x−4x+14F(x)=\frac{x^{2}-3x-4}{x+14}F(x)=x+14x2−3x−4​ for domain, vertical, and horizontal asymptotes.

Problem 22414

Simplify (4a2)63=Ia\sqrt[3]{(4 a^{2})^{6}} = I a3(4a2)6​=Ia.

Problem 22415

Which expression converts 100 inches/min to feet/min? Consider the options involving unit conversions.

Problem 22416

Find the missing factor DDD in the equation −15y4=(D)(3y2)-15 y^{4}=(D)(3 y^{2})−15y4=(D)(3y2).

Problem 22417

Calculate the following: 363236^{\frac{3}{2}}3623​, (181)−12\left(\frac{1}{81}\right)^{\frac{-1}{2}}(811​)2−1​, (1125)−23\left(\frac{1}{125}\right)^{\frac{-2}{3}}(1251​)3−2​.

Problem 22418

Find the domain of H(x)=5x−3036−x2H(x)=\frac{5 x-30}{36-x^{2}}H(x)=36−x25x−30​ and its vertical asymptote(s). Choices included.

Problem 22419

Find the derivative of excos⁡xe^{x} \cos xexcosx.

Problem 22420

Prove that ⊢tot {x≥0}Fac1⁡(x){y=x!}\vdash_{\text {tot }}\{x \geq 0\} \operatorname{Fac1}(x)\{y=x !\}⊢tot ​{x≥0}Fac1(x){y=x!} is valid. Find a suitable loop invariant.

Problem 22421

Problem 22422

Find the horizontal asymptote of the drug concentration function C(t)=t7t2+8C(t)=\frac{t}{7t^{2}+8}C(t)=7t2+8t​. What is C=□C=\squareC=□?

Problem 22423

Which formula converts 80 USD to AUD using the rates: 1 USD = 1.0343 AUD, 1 AUD = 0.9668 USD?

Problem 22424

Calculate the sum: −82+(−14)=-82 + (-14) = −82+(−14)=

Problem 22425

Find the product and express it as a+bia + b ia+bi: simplify (2+5i)2(2 + 5 i)^{2}(2+5i)2.

Problem 22426

Find the horizontal asymptote of C(t)=t7t2+8C(t)=\frac{t}{7t^{2}+8}C(t)=7t2+8t​. What does C(t)C(t)C(t) approach as ttt increases?

Problem 22427

Find the difference and express it as a+bia + b ia+bi: (−3+2i)−(4−3i)(-3 + 2 i) - (4 - 3 i)(−3+2i)−(4−3i)

Problem 22428

Find the horizontal asymptote of C(t)=t7t2+8C(t)=\frac{t}{7 t^{2}+8}C(t)=7t2+8t​, identify the graph, and determine when concentration is highest.

Problem 22429

Solve the equation x2+8x+17=0x^{2}+8 x+17=0x2+8x+17=0 and express solutions as a+bia+b ia+bi.

Problem 22430

Find the displacement of a mass on a spring from t=0t=0t=0 to t=πt=\pit=π given v(t)=6sin⁡(t)−6cos⁡(t)v(t)=6 \sin(t)-6 \cos(t)v(t)=6sin(t)−6cos(t). Evaluate ∫0π(6sin⁡(t)−6cos⁡(t))dt\int_{0}^{\pi}(6 \sin(t)-6 \cos(t)) dt∫0π​(6sin(t)−6cos(t))dt.

Problem 22431

Calculate −12+(−12)-12 + (-12)−12+(−12).

Problem 22432

Solve for real values of xxx in the equation (x+9)2−7(x+9)−18=0(x+9)^{2}-7(x+9)-18=0(x+9)2−7(x+9)−18=0.

Problem 22433

Solve for xxx given y=87.5y=87.5y=87.5 in the equation 300x+5007y=10000300 x+\frac{500}{7} y=10000300x+7500​y=10000.

Problem 22434

Calculate the work done by the force F(x)=x−1+4xF(x)=x^{-1}+4xF(x)=x−1+4x from x=3x=3x=3 to x=5x=5x=5: W=∫35(x−1+4x)dxW=\int_{3}^{5}(x^{-1}+4x)dxW=∫35​(x−1+4x)dx

Problem 22435

Find the distance a wave travels from t=1t=1t=1 to t=4t=4t=4 given v=8xv=\sqrt{\frac{8}{x}}v=x8​​. Evaluate the integral ∫148xdx\int_{1}^{4} \sqrt{\frac{8}{x}} d x∫14​x8​​dx.

Problem 22436

Solve for all real values of yyy in the equation y5−18y4+6y3=0y^{5}-18 y^{4}+6 y^{3}=0y5−18y4+6y3=0.

Problem 22437

A car's velocity is given by v(t)=2t1/2+5v(t)=2 t^{1/2}+5v(t)=2t1/2+5. Find the displacement (in m) from t=2t=2t=2 to t=8t=8t=8.

Problem 22438

Solve for xxx in the equation 6x−1=3\sqrt{6x - 1} = 36x−1​=3. What are the real solutions?

Problem 22439

Simplify 75⋅727^{5} \cdot 7^{2}75⋅72 using the Product Rule of Exponents.

Problem 22440

Find the displacement and total distance traveled by a particle with velocity v(t)=4−2tv(t)=4-2tv(t)=4−2t from t=0t=0t=0 to t=6t=6t=6.

Problem 22441

8) $\sqrt[3]{x^{9} y^{8} z^{16}}$ 9) $\sqrt{16 x^{5} y^{6} z}$ 10) $\sqrt{14}+5 \sqrt{14}$ 11) $4 \sqrt[3]{5 x}-7 \sqrt[3]{5 x}$

Express $\log_5 10Z$ as a sum of logarithms.

$x^2 + 8x + 12 = 0$

For number 10 and 11 graph the function and identify the domain and range. 10) $f(x)=\sqrt{x-3}$ 11) $g(x)=\sqrt{x+4}$
For number 12-13 solve the equation and check your answer. 12) $3 \sqrt[3]{5 x+6}=18$

Solve the inequality $9 - 3x \leq -(1 + 5x)$ and graph the solution set.

Rewrite $\sqrt[7]{c}$ as a power.

Find the value of $\sqrt[8]{x^{9}}$ .

What is the value of $\frac{1}{\sqrt{e}}$ ?

Analyze the function $F(x)=\frac{x^{2}-5 x-6}{x+4}$ . Find its domain, vertical asymptote, and horizontal/oblique asymptote.

Find the value of $\frac{1}{\sqrt[8]{x^{7}}}$ .

Analyze the function $F(x)=\frac{x^{2}-3x-4}{x+14}$ for domain, vertical, and horizontal asymptotes.

Simplify $\sqrt[3]{(4 a^{2})^{6}} = I a$ .

Find the missing factor $D$ in the equation $-15 y^{4}=(D)(3 y^{2})$ .

Calculate the following: $36^{\frac{3}{2}}$ , $\left(\frac{1}{81}\right)^{\frac{-1}{2}}$ , $\left(\frac{1}{125}\right)^{\frac{-2}{3}}$ .

Find the domain of $H(x)=\frac{5 x-30}{36-x^{2}}$ and its vertical asymptote(s). Choices included.

Find the derivative of $e^{x} \cos x$ .

Prove that $\vdash_{\text {tot }}\{x \geq 0\} \operatorname{Fac1}(x)\{y=x !\}$ is valid. Find a suitable loop invariant.

Find the horizontal asymptote of the drug concentration function $C(t)=\frac{t}{7t^{2}+8}$ . What is $C=\square$ ?

Calculate the sum: $-82 + (-14) =$

Find the product and express it as $a + b i$ : simplify $(2 + 5 i)^{2}$ .

Find the horizontal asymptote of $C(t)=\frac{t}{7t^{2}+8}$ . What does $C(t)$ approach as $t$ increases?

Find the difference and express it as $a + b i$ : $(-3 + 2 i) - (4 - 3 i)$

Find the horizontal asymptote of $C(t)=\frac{t}{7 t^{2}+8}$ , identify the graph, and determine when concentration is highest.

Solve the equation $x^{2}+8 x+17=0$ and express solutions as $a+b i$ .

Find the displacement of a mass on a spring from $t=0$ to $t=\pi$ given $v(t)=6 \sin(t)-6 \cos(t)$ . Evaluate $\int_{0}^{\pi}(6 \sin(t)-6 \cos(t)) dt$ .

Calculate $-12 + (-12)$ .

Solve for real values of $x$ in the equation $(x+9)^{2}-7(x+9)-18=0$ .

Solve for $x$ given $y=87.5$ in the equation $300 x+\frac{500}{7} y=10000$ .

Calculate the work done by the force $F(x)=x^{-1}+4x$ from $x=3$ to $x=5$ : $W=\int_{3}^{5}(x^{-1}+4x)dx$

Find the distance a wave travels from $t=1$ to $t=4$ given $v=\sqrt{\frac{8}{x}}$ . Evaluate the integral $\int_{1}^{4} \sqrt{\frac{8}{x}} d x$ .

Solve for all real values of $y$ in the equation $y^{5}-18 y^{4}+6 y^{3}=0$ .

A car's velocity is given by $v(t)=2 t^{1/2}+5$ . Find the displacement (in m) from $t=2$ to $t=8$ .

Solve for $x$ in the equation $\sqrt{6x - 1} = 3$ . What are the real solutions?

Simplify $7^{5} \cdot 7^{2}$ using the Product Rule of Exponents.

Find the displacement and total distance traveled by a particle with velocity $v(t)=4-2t$ from $t=0$ to $t=6$ .

Find all real solutions for the equation: $y^{5}-16 y^{4}+52 y^{3}=0$ . What are the values of $y$ ?

Identify the expression that applies the Product Rule of Exponents: $6^{2} \cdot 7^{3}$ , $10^{8} \cdot 10^{8}$ , $\left(5^{2}\right)^{9}$ , or $32^{7}$ ?

Calculate the value of $10^{2} \cdot 10^{3}$ . Options: 100,000, 10, 1,100, $10^{5}$ .

Choose the right symbol for the fractions: $\frac{3}{7}(-) \frac{6}{13}$ . Options: $<$ , $=$ , $>$ .

Choose a symbol for the fractions: $\frac{1}{3}$ ? $-\frac{2}{7}$ . Options: $<$ , $=$ , $>$ .

Calculate the total oil leaked in the first 5 hours after the tanker breaks apart using $R(t)=\frac{0.9}{1+t^{2}}$ .

Choose the right symbol for the fractions: $\frac{17}{34}() \frac{1}{2}$ from =, <, >.

What is $\frac{3}{4} \div 4$ ?

Solve the equation: $-10 x + 1 + 7 x = 37$ . Find the value of $x$ . Options: $-15$ , $-12$ , $12$ , $15$ .

Find the displacement and total distance traveled by a particle with velocity $v(t)=4-2t$ from $t=0$ to $t=6$ .

Place a symbol between the fractions: $\frac{13}{15}()_{-} \frac{5}{6}$ from $<, =, >$ .

Solve the equation: $(0.9 / 2) * \ln (26) - \ln (5) = (0.45) * \ln (26) - \ln (5)$ .

Calculate $-1 \frac{7}{8} \div \frac{3}{4}$ .

Solve for $g$ in the equation: $5(2-g)=0$ .

Find $f$ for the integral $\int \frac{x}{\sqrt{3 x^{2}+2}} d x$ using the substitution $u=3 x^{2}+2$ .

Find $f$ for the integral $\int x \sqrt{x+4} dx$ using the substitution $u=x+4$ , so $\int f(u) du$ . $f(u)=$

Evaluate the integral using substitution: $\int \frac{x^{6}}{\sqrt{x^{7}-4}} d x = C$ .

Graph the line represented by the equation $-3x + y = -9$ .

Evaluate the integral using substitution: $\int 7 x^{3} \cos(4 x^{4}) \, dx = C$ .

Find $\frac{\partial f}{\partial x}$ , $\frac{\partial f}{\partial y}$ , and evaluate at (1,-1) for $f(x, y)=6 x e^{5 x y}$ .

Solve for t in the equation: $1 = p r t$

Evaluate the integral using substitution: $\int -x(5-8x)^{5} dx =$

Evaluate the integral: $\int \frac{x^{6}}{(x^{7}+5)^{7}} \, dx =$

Evaluate the integral from 0 to 1: $\int_{0}^{1} 6 x^{4}\left(1-x^{5}\right)^{3} d x=$

Evaluate the integral: $\int -3 \sin(x) \sqrt{\cos(x)} \, dx =$

Evaluate the integral using substitution: $\int \cos (x)(13-\cos (x))^{8} \sin (x) d x =$

Solve for $x$ in the equation $\frac{x-2}{2}=m+n$ .

Find the second partial derivatives $f_{xx}(x, y), f_{yy}(x, y), f_{xy}(x, y), f_{yx}(x, y)$ for $f(x, y)=7x^2y$ and evaluate at $(1,-1)$ .

Find the $x$ and $y$ intercepts of the line given by the equation $2x - 4y = 8$ .

Evaluate the integral: $\int_{-\pi / 2}^{\pi / 2} \sin ^{6}(x) \cos (x) d x.$

Find the $x$ -intercept and $y$ -intercept of the line defined by $x + 2y = 8$ .

Evaluate the integral using substitution: $\int 7 \sin ^{2}(4 x) \cos ^{3}(4 x) d x.$

Solve for $r_{2}$ in the equation $R(r_{1}+r_{2})=r_{1} r_{2}$ .

Find the $y$ -intercept and $x$ -intercept of the line given by $6x - 5y = -30$ .