Solve

Problem 25101

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

See Solution

Problem 25102

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

See Solution

Problem 25103

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

See Solution

Problem 25104

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

See Solution

Problem 25105

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

See Solution

Problem 25106

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

See Solution

Problem 25107

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 25108

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

See Solution

Problem 25109

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

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Problem 25110

A crew built a 9 km road in $5 \frac{1}{4}$ days. How many km did they build daily? Answer as a mixed number.

See Solution

Problem 25111

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

See Solution

Problem 25112

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

See Solution

Problem 25113

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

See Solution

Problem 25114

Calculate the slope of the line through points (2,2) and (-3,4) using the formula $\frac{y_2 - y_1}{x_2 - x_1}$ .

See Solution

Problem 25115

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 25116

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

See Solution

Problem 25117

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

See Solution

Problem 25118

Find the slope of the line through (0,-2) and (1,1). Use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

See Solution

Problem 25119

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

See Solution

Problem 25120

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

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Problem 25121

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

See Solution

Problem 25122

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

See Solution

Problem 25123

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

See Solution

Problem 25124

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

See Solution

Problem 25125

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

See Solution

Problem 25126

Calculate the slope of the line through the points (-1,-4) and (-4,3) using the formula $\frac{y_2 - y_1}{x_2 - x_1}$ .

See Solution

Problem 25127

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

See Solution

Problem 25128

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

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Problem 25129

Calculate the slope of the line connecting the points $(-4, -1)$ and $(-4, 3)$ .

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Problem 25130

Calculate the volume $V$ of the solid formed by rotating the area under $y=\frac{4}{x^{2}}$ from $x=1$ to $x=\infty$ around the $\mathrm{x}$ -axis. $V=$

See Solution

Problem 25131

Calculate the slope between the points (3, -4) and (-4, -1) using the formula $\frac{y_2 - y_1}{x_2 - x_1}$ .

See Solution

Problem 25132

Find the volume $V$ of the solid formed by revolving the area under $y=10 e^{-x}$ in the first quadrant around the $y$ -axis.

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Problem 25133

A diver runs at $3.60 \mathrm{~m/s}$ and dives from a cliff, hitting the water 2.00 s later. Find the horizontal distance traveled.

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Problem 25134

Calculate the area under the curve $y=7 x e^{-x}$ for $x$ values starting from 2.

See Solution

Problem 25135

Calculate the slope of the line through the points $(-1,1)$ and $(-4,-3)$ .

See Solution

Problem 25136

A swimmer jumps out at $2.30 \mathrm{~m/s}$ and lands in 1.50s. How far from the block does he land?

See Solution

Problem 25137

Find a value of the Pythagorean triple using $x=18$ and $y=9$ with the identity $(x^{2}+y^{2})^{2}=(x^{2}-y^{2})^{2}+(2xy)^{2}$ . Options: 162, 81, 324, 729.

See Solution

Problem 25138

Find the third term in the expansion of $(a+5)^{5}$ using Pascal's Triangle.

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Problem 25139

Find the slope between points (-5,8) and (-5,-5), then between (-9,-9) and (2,-9).

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Problem 25140

Find the slope of the line through points $(-5,8)$ and $(-5,-5)$ . What is the slope?

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Problem 25141

Find a Pythagorean triple using $\left(11^{2}+4^{2}\right)^{2}=\left(11^{2}-4^{2}\right)^{2}+(2 \cdot 11 \cdot 4)^{2}$ . Which value is in the triple?

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Problem 25142

A cannonball is fired horizontally from an 80 m cliff at 80 m/s. How far does it travel horizontally before hitting the ground?

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Problem 25143

Find the second term in the expansion of $(2x - 3)^{6}$ using the Binomial Theorem.

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Problem 25144

Find the slope of the line through $(-5,1)$ and $(-5,7)$ , then through $(8,4)$ and $(8,-4)$ .

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Problem 25145

Find the slope of the line through $(4,-6)$ and $(-4,-6)$ . Then find the slope through $(-5,3)$ and $(9,3)$ .

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Problem 25146

A boulder is launched from a 60 m high cliff at 95 m/s. How far does it travel before hitting the enemy castle?

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Problem 25147

Evaluate the integral from 4 to 3 of $\frac{\cos (\arctan (5 t))}{1+(5 t)^{2}} dt$ .

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Problem 25148

Find $f(x)$ given that $f'(x)=\frac{4}{\sqrt{1-x^{2}}}$ and $f\left(\frac{1}{2}\right)=8$ .

See Solution

Problem 25149

A cannon is fired horizontally from a height of $5.0 \mathrm{~m}$ . How long until it hits the ground?

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Problem 25150

Evaluate the integral for $x>0$ : $\int \frac{1}{x \sqrt{64 x^{2}-1}} d x=$

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Problem 25151

Ashley has a \$90,500 mortgage at 3.45\% for 40 years. Find her monthly payment, total repayment, and total interest.

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Problem 25152

Evaluate the integral for $x>0$ : $\int \frac{1}{x \sqrt{64 x^{2}-1}} d x = C$ .

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Problem 25153

Find the exact values of these expressions in radians (or UNDEFINED if not defined): (a) $\sin^{-1}(-1)$ , (b) $\cos^{-1}(0)$ , (c) $\tan^{-1}\left(\frac{\sqrt{3}}{3}\right)$ .

See Solution

Problem 25154

A cannonball is shot horizontally at $50 \mathrm{~m/s}$ from an $80 \mathrm{~m}$ cliff. Find its horizontal distance before impact.

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Problem 25155

Greg borrowed \$29,000 at 7.1\% for 1 year. Find: (a) monthly payment, (b) total repayment, (c) total interest paid.

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Problem 25156

Find $f^{-1}(x)$ for $f(x)=x+2$ . What is $f^{-1}(-1)$ ?

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Problem 25157

Tad drops a cherry pit from $0.8 \mathrm{~m}$ at $18 \mathrm{~m/s}$ . How far does it land from the drop point?

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Problem 25158

Find $f^{-1}(x)$ for $f(x)=x+2$ . What is $f^{-1}(-1) ?-3$ and $f^{-1}(2) ?$

See Solution

Problem 25159

Factor and solve $4 x^{2}+12 x+5=-4$ . Find the values of $x$ .

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Problem 25160

Evaluate the matrix expression:
$2\begin{bmatrix} -5 & -8 \\ 6 & -7 \\ 4 & -1 \end{bmatrix} + \begin{bmatrix} -2 & -9 \\ 8 & -2 \\ 5 & 6 \end{bmatrix} - \begin{bmatrix} 5 & 5 \\ 2 & -1 \\ -9 & 0 \end{bmatrix}$
Simplify the resulting matrix.

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Problem 25161

A dart is thrown at 11.6 m/s and hits the board in 0.131 s. Find the distance to the board and how far below the bullseye it hit.

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Problem 25162

Evaluate the matrix expression:
$2\begin{pmatrix}-5 & -8 \\ 6 & -7 \\ 4 & -1\end{pmatrix} + \begin{pmatrix}-2 & -9 \\ 8 & -2 \\ 5 & 6\end{pmatrix} - \begin{pmatrix}5 & 5 \\ 2 & -1 \\ -9 & 0\end{pmatrix}$ .
Simplify the resulting matrix.

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Problem 25163

Choose 6 letters from 15 distinct letters. (a) Without order, how many ways? (b) With order, how many ways?

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Problem 25164

Choose 4 objects from 18 distinct objects. How many ways can this be done if order doesn't matter? Use $C(18, 4)$ .

See Solution

Problem 25165

A basketball rolls off at $2 \mathrm{~m/s}$ and bounces after $2.5 \mathrm{~s}$ . Find the distance from the rack.

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Problem 25166

Choose 6 colors from 10 distinct colors with order relevant. How many ways? Use $P(10, 6)$ .

See Solution

Problem 25167

Choose 6 colors from 10 distinct colors. (a) How many ways if order matters? (b) How many ways if order doesn't matter?

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Problem 25168

Find the values of a, b, c, and d in the magic square where all rows, columns, and diagonals sum to 52.

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Problem 25169

A hunter shoots at a target $220 \mathrm{~m}$ away with a speed of $550 \mathrm{~m/s}$ . How long until the bullet hits?

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Problem 25170

Create a 3x3 magic square using the numbers 2, 5, 8, 12, 15, 18, 22, 25, and 28.

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Problem 25171

Find all $\theta$ in $[0^{\circ}, 360^{\circ})$ such that $\sin \theta = -\frac{\sqrt{3}}{2}$ .

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Problem 25172

Find all $\theta$ in $[0^{\circ}, 360^{\circ})$ such that $\csc \theta=\sqrt{2}$ . What are the values of $\theta$ ?

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Problem 25173

Choose 6 colors from 10 distinct colors. If order matters, how many ways can this be done?

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Problem 25174

Choose 6 colors from 10 distinct colors. (a) If order matters, how many ways? (b) If order doesn't matter, how many ways?

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Problem 25175

Use the Beverton-Holt model $R(N_{t})=\frac{R_{0}}{1+a N_{t}}$ with $a=0.03$ , $R_{0}=3$ . Find $N_{t}$ for $t=1,2,\ldots,5$ and $\lim_{t \to \infty} N_{t}$ for $N_{0}=2$ .

See Solution

Problem 25176

Choose 5 letters from 17 distinct letters: (a) How many ways without order? (b) How many ways with order?

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Problem 25177

Evaluate $\cos^{2} 60^{\circ} + \sec^{2} 150^{\circ} - \csc^{2} 210^{\circ}$ .

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Problem 25178

Calculate the integral $\int \ln \left(x^{2}\right) d x$ . Use "C" for the constant in your solution.

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Problem 25179

Calculate the indefinite integral $\int \ln \left(x^{2}\right) d x$ . Use "C" for the constant.

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Problem 25180

Find the roots of the equation $2x^{2}-13x+20=0$ .

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Problem 25181

Calculate the indefinite integral of $\ln \left(x^{2}\right)$ with respect to $x$ : $\int \ln \left(x^{2}\right) d x=$

See Solution

Problem 25182

If $x > 0$ and $x^{2} = 16$ , find $x^{3} + \sqrt{x}$ .

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Problem 25183

Choose 5 letters from 17 distinct letters.
(a) Without order, how many ways? (b) With order, how many ways?
Answers: (a) $\binom{17}{5} = 6188$ (b) $17P5$

See Solution

Problem 25184

Choose 7 from 10 distinct objects: (a) ways without order? (b) ways with order? Use $C(10,7)$ and $P(10,7)$ .

See Solution

Problem 25185

Choose 6 colors from 8 distinct colors. (a) How many ways if order matters? (b) How many ways if order doesn't matter?

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Problem 25186

Find the value of $a$ in the Beverton-Holt model $R(N_{t})=\frac{R_{0}}{1+a N_{t}}$ given $R_{0}=5$ and $N_{t} \rightarrow 400$ .

See Solution

Problem 25187

A zombie is pushed off a 45 m cliff with a horizontal speed of $19 \mathrm{~m/s}$ .
A) Find the fall time. B) Calculate the horizontal distance traveled before hitting the ground.

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Problem 25188

Convert the mixed number $8 \frac{4}{9}$ to a decimal.

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Problem 25189

Solve for $h$ in the cylinder surface area formula: $S=2 \pi r^{2}+2 \pi r h$ .

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Problem 25190

A water balloon is thrown from a 14m high school, traveling 25m horizontally.
A) How long to hit the ground? B) What is its horizontal velocity?
Use $d = vt + \frac{1}{2}at^2$ and $v = \frac{d}{t}$ .

See Solution

Problem 25191

You drop a penny from the Empire State Building (381 m). It travels 32 m.
A) How long does it fall? B) What was its initial speed?

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Problem 25192

A drug starts at $70 \mathrm{mg}$ and drops to $49 \mathrm{mg}$ in 1 hour. Find the hourly percentage removed.

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Problem 25193

Joe's income grew from \$15,200 to \$21,500 in 10 years. When will it reach \$25,000?

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Problem 25194

Find the six trigonometric functions for the angle $405^{\circ}$ .

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Problem 25195

Indy and Fort Wayne are 13 cm apart on a map, equating to 120 miles. If Kokomo is 6.5 cm from Indy, find the real distance between Indy and Kokomo, rounded to the nearest tenth of a mile.

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Problem 25196

Calculate the number of Tim Hortons stores per capita in Canada in 2015, given 3660 stores and a population of 35.75 million. Round to three decimal places in scientific notation.

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Problem 25197

Find the smallest number, $n$ , where the nth term of the geometric sequence (3, 9, 27, ...) exceeds the arithmetic sequence (400, 700, ...).

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Problem 25198

Find the mass of 60,000 hydrogen atoms, given one hydrogen atom's mass is $1.67 \times 10^{-24}$ grams. Express in scientific notation.

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Problem 25199

In 2006, the US had 285 million TVs and a population of 298.4 million. Find TVs per capita rounded to four decimal places. $\text { Answer }=0.9612$

See Solution

Problem 25200

Simplify the expression: $=\frac{7}{5} \cdot \frac{2}{7}$ . What is the result?

See Solution

1 ...249 250 251 252 253 254 255 ...307

Solve

Problem 25101

Evaluate the integral using substitution: ∫7sin⁡2(4x)cos⁡3(4x)dx.\int 7 \sin ^{2}(4 x) \cos ^{3}(4 x) d x.∫7sin2(4x)cos3(4x)dx.

Problem 25102

Solve for r2r_{2}r2​ in the equation R(r1+r2)=r1r2R(r_{1}+r_{2})=r_{1} r_{2}R(r1​+r2​)=r1​r2​.

Problem 25103

Evaluate the integral using substitution: ∫5tsin⁡(t2)cos⁡(t2) dt=\int 5 t \sin(t^{2}) \cos(t^{2}) \, dt =∫5tsin(t2)cos(t2)dt=

Problem 25104

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

Problem 25105

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

Problem 25106

Find the antiderivative for dxdt=2et−3\frac{d x}{d t}=2 e^{t}-3dtdx​=2et−3 with the condition x(0)=4x(0)=4x(0)=4. What is xxx?

Problem 25107

Find the antiderivatives of dxdt=2t−1+5\frac{d x}{d t}=2 t^{-1}+5dtdx​=2t−1+5. What is xxx? Include the constant CCC.

Problem 25108

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

Problem 25109

Find an antiderivative of f(x)=2x−10exf(x)=\frac{2}{x}-10 e^{x}f(x)=x2​−10ex.

Problem 25110

A crew built a 9 km road in 5145 \frac{1}{4}541​ days. How many km did they build daily? Answer as a mixed number.

Problem 25111

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

Problem 25112

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

Problem 25113

Evaluate the integral ∫−28f(x)dx\int_{-2}^{8} f(x) dx∫−28​f(x)dx where f(x)=xf(x)=xf(x)=x for x<1x<1x<1 and f(x)=1xf(x)=\frac{1}{x}f(x)=x1​ for x≥1x \geq 1x≥1.

Problem 25114

Calculate the slope of the line through points (2,2) and (-3,4) using the formula y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}x2​−x1​y2​−y1​​.

Problem 25115

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

Problem 25116

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

Problem 25117

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

Problem 25118

Find the slope of the line through (0,-2) and (1,1). Use the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}m=x2​−x1​y2​−y1​​.

Problem 25119

Find the product of the polynomials (2x3+3x2)(4x4−5x3−6x2)(2 x^{3}+3 x^{2})(4 x^{4}-5 x^{3}-6 x^{2})(2x3+3x2)(4x4−5x3−6x2).

Problem 25120

Calculate the product of (2q9+3q7)(−6q2+9)(2q^9 + 3q^7)(-6q^2 + 9)(2q9+3q7)(−6q2+9). What is the result?

Problem 25121

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

Problem 25122

Calculate the slope of the line through the points (-3, -2) and (1, 2) using the formula y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}x2​−x1​y2​−y1​​.

Problem 25123

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

Problem 25124

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

Problem 25125

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

Problem 25126

Calculate the slope of the line through the points (-1,-4) and (-4,3) using the formula y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}x2​−x1​y2​−y1​​.

Problem 25127

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

Problem 25128

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

Problem 25129

Calculate the slope of the line connecting the points (−4,−1)(-4, -1)(−4,−1) and (−4,3)(-4, 3)(−4,3).

Problem 25130

Calculate the volume VVV of the solid formed by rotating the area under y=4x2y=\frac{4}{x^{2}}y=x24​ from x=1x=1x=1 to x=∞x=\inftyx=∞ around the x\mathrm{x}x-axis. V= V= V=

Problem 25131

Calculate the slope between the points (3, -4) and (-4, -1) using the formula y2−y1x2−x1\frac{y_2 - y_1}{x_2 - x_1}x2​−x1​y2​−y1​​.

Problem 25132

Find the volume VVV of the solid formed by revolving the area under y=10e−xy=10 e^{-x}y=10e−x in the first quadrant around the yyy-axis.

Problem 25133

A diver runs at 3.60 m/s3.60 \mathrm{~m/s}3.60 m/s and dives from a cliff, hitting the water 2.00 s later. Find the horizontal distance traveled.

Problem 25134

Calculate the area under the curve y=7xe−xy=7 x e^{-x}y=7xe−x for xxx values starting from 2.

Problem 25135

Calculate the slope of the line through the points (−1,1)(-1,1)(−1,1) and (−4,−3)(-4,-3)(−4,−3).

Problem 25136

A swimmer jumps out at 2.30 m/s2.30 \mathrm{~m/s}2.30 m/s and lands in 1.50s. How far from the block does he land?

Problem 25137

Find a value of the Pythagorean triple using x=18x=18x=18 and y=9y=9y=9 with the identity (x2+y2)2=(x2−y2)2+(2xy)2(x^{2}+y^{2})^{2}=(x^{2}-y^{2})^{2}+(2xy)^{2}(x2+y2)2=(x2−y2)2+(2xy)2. Options: 162, 81, 324, 729.

Problem 25138

Find the third term in the expansion of (a+5)5(a+5)^{5}(a+5)5 using Pascal's Triangle.

Problem 25139

Find the slope between points (-5,8) and (-5,-5), then between (-9,-9) and (2,-9).

Problem 25140

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

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

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

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

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

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

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

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

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

A crew built a 9 km road in $5 \frac{1}{4}$ days. How many km did they build daily? Answer as a mixed number.

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

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

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

Calculate the slope of the line through points (2,2) and (-3,4) using the formula $\frac{y_2 - y_1}{x_2 - x_1}$ .

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

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

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

Find the slope of the line through (0,-2) and (1,1). Use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

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

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

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

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

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

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

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

Calculate the slope of the line through the points (-1,-4) and (-4,3) using the formula $\frac{y_2 - y_1}{x_2 - x_1}$ .

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

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

Calculate the slope of the line connecting the points $(-4, -1)$ and $(-4, 3)$ .

Calculate the volume $V$ of the solid formed by rotating the area under $y=\frac{4}{x^{2}}$ from $x=1$ to $x=\infty$ around the $\mathrm{x}$ -axis. $V=$

Calculate the slope between the points (3, -4) and (-4, -1) using the formula $\frac{y_2 - y_1}{x_2 - x_1}$ .

Find the volume $V$ of the solid formed by revolving the area under $y=10 e^{-x}$ in the first quadrant around the $y$ -axis.

A diver runs at $3.60 \mathrm{~m/s}$ and dives from a cliff, hitting the water 2.00 s later. Find the horizontal distance traveled.

Calculate the area under the curve $y=7 x e^{-x}$ for $x$ values starting from 2.

Calculate the slope of the line through the points $(-1,1)$ and $(-4,-3)$ .

A swimmer jumps out at $2.30 \mathrm{~m/s}$ and lands in 1.50s. How far from the block does he land?

Find a value of the Pythagorean triple using $x=18$ and $y=9$ with the identity $(x^{2}+y^{2})^{2}=(x^{2}-y^{2})^{2}+(2xy)^{2}$ . Options: 162, 81, 324, 729.

Find the third term in the expansion of $(a+5)^{5}$ using Pascal's Triangle.

Find the slope of the line through points $(-5,8)$ and $(-5,-5)$ . What is the slope?

Find a Pythagorean triple using $\left(11^{2}+4^{2}\right)^{2}=\left(11^{2}-4^{2}\right)^{2}+(2 \cdot 11 \cdot 4)^{2}$ . Which value is in the triple?

Find the second term in the expansion of $(2x - 3)^{6}$ using the Binomial Theorem.

Find the slope of the line through $(-5,1)$ and $(-5,7)$ , then through $(8,4)$ and $(8,-4)$ .

Find the slope of the line through $(4,-6)$ and $(-4,-6)$ . Then find the slope through $(-5,3)$ and $(9,3)$ .

Evaluate the integral from 4 to 3 of $\frac{\cos (\arctan (5 t))}{1+(5 t)^{2}} dt$ .

Find $f(x)$ given that $f'(x)=\frac{4}{\sqrt{1-x^{2}}}$ and $f\left(\frac{1}{2}\right)=8$ .

A cannon is fired horizontally from a height of $5.0 \mathrm{~m}$ . How long until it hits the ground?

Evaluate the integral for $x>0$ : $\int \frac{1}{x \sqrt{64 x^{2}-1}} d x=$

Evaluate the integral for $x>0$ : $\int \frac{1}{x \sqrt{64 x^{2}-1}} d x = C$ .

Find the exact values of these expressions in radians (or UNDEFINED if not defined): (a) $\sin^{-1}(-1)$ , (b) $\cos^{-1}(0)$ , (c) $\tan^{-1}\left(\frac{\sqrt{3}}{3}\right)$ .

A cannonball is shot horizontally at $50 \mathrm{~m/s}$ from an $80 \mathrm{~m}$ cliff. Find its horizontal distance before impact.

Find $f^{-1}(x)$ for $f(x)=x+2$ . What is $f^{-1}(-1)$ ?

Tad drops a cherry pit from $0.8 \mathrm{~m}$ at $18 \mathrm{~m/s}$ . How far does it land from the drop point?

Find $f^{-1}(x)$ for $f(x)=x+2$ . What is $f^{-1}(-1) ?-3$ and $f^{-1}(2) ?$

Factor and solve $4 x^{2}+12 x+5=-4$ . Find the values of $x$ .

Choose 4 objects from 18 distinct objects. How many ways can this be done if order doesn't matter? Use $C(18, 4)$ .

A basketball rolls off at $2 \mathrm{~m/s}$ and bounces after $2.5 \mathrm{~s}$ . Find the distance from the rack.

Choose 6 colors from 10 distinct colors with order relevant. How many ways? Use $P(10, 6)$ .

A hunter shoots at a target $220 \mathrm{~m}$ away with a speed of $550 \mathrm{~m/s}$ . How long until the bullet hits?

Find all $\theta$ in $[0^{\circ}, 360^{\circ})$ such that $\sin \theta = -\frac{\sqrt{3}}{2}$ .

Find all $\theta$ in $[0^{\circ}, 360^{\circ})$ such that $\csc \theta=\sqrt{2}$ . What are the values of $\theta$ ?