Math

Problem 56801

Find the total sugar in tons from $2 \frac{3}{8}$ containers, each holding $3 \frac{1}{5}$ tons. Express as a mixed number.

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Problem 56802

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 56803

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

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Problem 56804

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

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Problem 56805

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

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Problem 56806

Find $f(g(x))$ for $f(x)=\frac{5}{2 x+1}$ and $g(x)=x^{2}-3$ . Identify Olivia's mistake and correct her work.

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Problem 56807

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 56808

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

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Problem 56809

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

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Problem 56810

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

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Problem 56811

Bella bought 1 container each of 12 ounces of blackberries, raspberries, and strawberries. How many ounces are left after baking?

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Problem 56812

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 56813

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

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Problem 56814

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

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Problem 56815

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

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Problem 56816

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 56817

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

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Problem 56818

Rita has 8.64 pounds of seed. If 7.2 pounds plants 1 acre, how many acres can she plant?

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Problem 56819

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

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Problem 56820

Rita has 8.64 pounds of seed. If 7.2 pounds plants 1 acre, how many acres can she plant? Calculate: $\frac{8.64}{7.2}$ .

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Problem 56821

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

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Problem 56822

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

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Problem 56823

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

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Problem 56824

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

See Solution

Problem 56825

Graph the line with slope $\frac{4}{3}$ and a $y$ -intercept of 1.

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Problem 56826

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

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Problem 56827

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

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Problem 56828

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 56829

Graph the line with a y-intercept of 4 and a slope of 2.

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Problem 56830

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

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Problem 56831

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 56832

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 56833

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 56834

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

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Problem 56835

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.

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Problem 56836

Write the slope-intercept equation for a line with slope 5 and $y$ -intercept -3.

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Problem 56837

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

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Problem 56838

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

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Problem 56839

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 56840

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

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Problem 56841

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

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Problem 56842

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 56843

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 56844

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

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Problem 56845

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

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Problem 56846

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 56847

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 56848

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

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Problem 56849

Identify the sequence with constant second differences from these options: $\{-0.5,5,13.5,23\}$ , $\{5,11.5,18.5,24.5\}$ , $\{0.5,5,12.5,23\}$ , $\{5,13.5,23,34.5\}$ .

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Problem 56850

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 56851

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

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Problem 56852

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 56853

Use long division to find which polynomial divides evenly by $x+3$ :
1. $x^{3}-5 x^{2}+10 x-15$
2. $x^{3}-3 x^{2}-13 x+15$
3. $3 x^{2}-6 x+9$
4. $5 x^{2}+7 x-12$

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Problem 56854

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

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Problem 56855

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

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Problem 56856

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

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Problem 56857

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

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Problem 56858

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

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Problem 56859

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

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Problem 56860

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

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Problem 56861

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. $V=$

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Problem 56862

Use long division to find which polynomial divides evenly by $x+3$ :
1. $x^{3}-5 x^{2}+10 x-15$
2. $x^{3}-3 x^{2}-13 x+15$
3. $3 x^{2}-6 x+9$
4. $5 x^{2}+7 x-12$

See Solution

Problem 56863

Rewrite $x^{2}-196$ using the identity $x^{2}-a^{2}=(x+a)(x-a)$ . Which polynomial is established?

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Problem 56864

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

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Problem 56865

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 56866

Which polynomial approximates $\frac{(4 x^{3}+5)(3 x^{6}-8 x^{2})}{2 x^{2}+8 x-4}+4 x^{3}-2 x+13$ ? Options: $12 x^{7}-27$ , $6 x^{7}+15$ , $6 x^{7}+13$ , $6 x^{7}-7$ .

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Problem 56867

Bianca's towel is 16 ft by 28 ft. Use the difference of two squares to find its area. Which expression is correct? $28^{2}-16^{2}$

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Problem 56868

Identify the expression showing that 127 is a Mersenne prime: $2^{7}+1$ , $2(63)+1$ , $2^{7}-1$ , or $2(64)-1$ .

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Problem 56869

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 56870

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

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Problem 56871

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

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Problem 56872

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

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Problem 56873

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.

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Problem 56874

Select numbers that round to 76.73 to the nearest hundredth: {76.732, 76.731, 76.736, 76.737, 76.739}.

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Problem 56875

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

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Problem 56876

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

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Problem 56877

Given $f(x)=5 x^{2}-x+2$ , find $f(-a)$ , $f(a+1)$ , $2 f(a)$ , $f(2 a)$ , $f(a^{2})$ , $[f(a)]^{2}$ , and $f(a+h)$ .

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Problem 56878

Select numbers that round to 76.73 to the nearest hundredth: a) 76.732 b) 76.731 c) 76.736 d) 76.737 e) 76.739

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Problem 56879

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

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Problem 56880

Find a term in the expansion of $(a+b)^{7}$ using the Binomial Theorem. Options include $21 a^{6} b$ , $21 a^{2} b^{4}$ , $21 a^{2} b^{5}$ , $a^{4} b^{3}$ .

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Problem 56881

Which number rounds to 25.34 when rounded to the nearest hundredths? a) 25.321 b) 25.344 c) 25.348 d) 25.356

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Problem 56882

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 56883

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 56884

Which number rounds to 25.34 when rounded to the nearest hundredths? a) 25.321 b) 25.344 c) 25.348 d) 25.356

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Problem 56885

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

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Problem 56886

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

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Problem 56887

Construct a polynomial for a sequence with constant 4th differences of 48. (4 points)

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Problem 56888

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 56889

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 56890

Exercice 0 : 1- Montrer que $(G=\mathbb{R}^{} \times \mathbb{R}, )$ est un groupe non commutatif. 2- Montrer que $(\mathbb{Z}^{2}, \oplus, \odot)$ est un anneau commutatif.

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Problem 56891

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

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Problem 56892

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

See Solution

Problem 56893

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 56894

Find the slope-intercept form of the line through $(9,-2)$ with slope $-\frac{4}{3}$ .

See Solution

Problem 56895

Find the slope-intercept form equation of a line through $(2,5)$ with a slope of 3.

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Problem 56896

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

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Problem 56897

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 56898

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

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Problem 56899

Find the formula for the bottom half of the parabola defined by $x + (y - 9)^{2} = 0$ . What is $y=$ ?

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Problem 56900

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

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1 ...566 567 568 569 570 571 572 ...662

Math

Problem 56801

Find the total sugar in tons from 2382 \frac{3}{8}283​ containers, each holding 3153 \frac{1}{5}351​ tons. Express as a mixed number.

Problem 56802

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

Problem 56803

Evaluate the integral using substitution: ∫x6x7−4dx=C\int \frac{x^{6}}{\sqrt{x^{7}-4}} d x = C∫x7−4​x6​dx=C.

Problem 56804

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

Problem 56805

Evaluate the integral using substitution: ∫7x3cos⁡(4x4) dx=C\int 7 x^{3} \cos(4 x^{4}) \, dx = C∫7x3cos(4x4)dx=C.

Problem 56806

Find f(g(x))f(g(x))f(g(x)) for f(x)=52x+1f(x)=\frac{5}{2 x+1}f(x)=2x+15​ and g(x)=x2−3g(x)=x^{2}-3g(x)=x2−3. Identify Olivia's mistake and correct her work.

Problem 56807

Find ∂f∂x\frac{\partial f}{\partial x}∂x∂f​, ∂f∂y\frac{\partial f}{\partial y}∂y∂f​, and evaluate at (1,-1) for f(x,y)=6xe5xyf(x, y)=6 x e^{5 x y}f(x,y)=6xe5xy.

Problem 56808

Solve for t in the equation: 1=prt1 = p r t1=prt

Problem 56809

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

Problem 56810

Evaluate the integral: ∫x6(x7+5)7 dx=\int \frac{x^{6}}{(x^{7}+5)^{7}} \, dx = ∫(x7+5)7x6​dx=

Problem 56811

Bella bought 1 container each of 12 ounces of blackberries, raspberries, and strawberries. How many ounces are left after baking?

Problem 56812

Evaluate the integral from 0 to 1: ∫016x4(1−x5)3dx=\int_{0}^{1} 6 x^{4}\left(1-x^{5}\right)^{3} d x=∫01​6x4(1−x5)3dx=

Problem 56813

Evaluate the integral: ∫−3sin⁡(x)cos⁡(x) dx=\int -3 \sin(x) \sqrt{\cos(x)} \, dx = ∫−3sin(x)cos(x)​dx=

Problem 56814

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

Problem 56815

Solve for xxx in the equation x−22=m+n\frac{x-2}{2}=m+n2x−2​=m+n.

Problem 56816

Find the second partial derivatives fxx(x,y),fyy(x,y),fxy(x,y),fyx(x,y)f_{xx}(x, y), f_{yy}(x, y), f_{xy}(x, y), f_{yx}(x, y)fxx​(x,y),fyy​(x,y),fxy​(x,y),fyx​(x,y) for f(x,y)=7x2yf(x, y)=7x^2yf(x,y)=7x2y and evaluate at (1,−1)(1,-1)(1,−1).

Problem 56817

Find the xxx and yyy intercepts of the line given by the equation 2x−4y=82x - 4y = 82x−4y=8.

Problem 56818

Rita has 8.64 pounds of seed. If 7.2 pounds plants 1 acre, how many acres can she plant?

Problem 56819

Evaluate the integral: ∫−π/2π/2sin⁡6(x)cos⁡(x)dx.\int_{-\pi / 2}^{\pi / 2} \sin ^{6}(x) \cos (x) d x.∫−π/2π/2​sin6(x)cos(x)dx.

Problem 56820

Rita has 8.64 pounds of seed. If 7.2 pounds plants 1 acre, how many acres can she plant? Calculate: 8.647.2 \frac{8.64}{7.2} 7.28.64​.

Problem 56821

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

Problem 56822

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 56823

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 56824

Find the yyy-intercept and xxx-intercept of the line given by 6x−5y=−306x - 5y = -306x−5y=−30.

Problem 56825

Graph the line with slope 43\frac{4}{3}34​ and a yyy-intercept of 1.

Problem 56826

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 56827

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

Problem 56828

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 56829

Graph the line with a y-intercept of 4 and a slope of 2.

Problem 56830

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

Problem 56831

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 56832

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 56833

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 56834

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

Problem 56835

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 56836

Write the slope-intercept equation for a line with slope 5 and yyy-intercept -3.

Problem 56837

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

Problem 56838

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 56839

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 56840

Find the total sugar in tons from $2 \frac{3}{8}$ containers, each holding $3 \frac{1}{5}$ tons. Express as a mixed number.

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 $f(g(x))$ for $f(x)=\frac{5}{2 x+1}$ and $g(x)=x^{2}-3$ . Identify Olivia's mistake and correct her work.

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

Rita has 8.64 pounds of seed. If 7.2 pounds plants 1 acre, how many acres can she plant? Calculate: $\frac{8.64}{7.2}$ .

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 $6x - 5y = -30$ .

Graph the line with slope $\frac{4}{3}$ and a $y$ -intercept of 1.

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

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

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.

Write the slope-intercept equation for a line with slope 5 and $y$ -intercept -3.

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 $x \geq 1$ .

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

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 $m = \frac{y_2 - y_1}{x_2 - x_1}$ .

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

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?

Identify the sequence with constant second differences from these options: $\{-0.5,5,13.5,23\}$ , $\{5,11.5,18.5,24.5\}$ , $\{0.5,5,12.5,23\}$ , $\{5,13.5,23,34.5\}$ .

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

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 $\frac{y_2 - y_1}{x_2 - x_1}$ .

Use long division to find which polynomial divides evenly by $x+3$ :
1. $x^{3}-5 x^{2}+10 x-15$
2. $x^{3}-3 x^{2}-13 x+15$
3. $3 x^{2}-6 x+9$
4. $5 x^{2}+7 x-12$

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. $V=$

Use long division to find which polynomial divides evenly by $x+3$ :
1. $x^{3}-5 x^{2}+10 x-15$
2. $x^{3}-3 x^{2}-13 x+15$
3. $3 x^{2}-6 x+9$
4. $5 x^{2}+7 x-12$

Rewrite $x^{2}-196$ using the identity $x^{2}-a^{2}=(x+a)(x-a)$ . Which polynomial is established?

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.

Which polynomial approximates $\frac{(4 x^{3}+5)(3 x^{6}-8 x^{2})}{2 x^{2}+8 x-4}+4 x^{3}-2 x+13$ ? Options: $12 x^{7}-27$ , $6 x^{7}+15$ , $6 x^{7}+13$ , $6 x^{7}-7$ .

Bianca's towel is 16 ft by 28 ft. Use the difference of two squares to find its area. Which expression is correct? $28^{2}-16^{2}$

Identify the expression showing that 127 is a Mersenne prime: $2^{7}+1$ , $2(63)+1$ , $2^{7}-1$ , or $2(64)-1$ .

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.