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Ksenya-84 [330]
2 years ago
7

The equation 9(u – 2) + 1.5u = 8.25 models the total miles Michael traveled one afternoon while sledding, where u equals the num

ber of hours walking up a hill and (u – 2) equals the number of hours sledding down the hill. Which is the value of u?
A. u = 0.25
B. u = 0.75
C.u = 1.1
D. u = 2.5
Mathematics
2 answers:
earnstyle [38]2 years ago
8 0

The <u>equation </u>9(u-2) + 1.5u = 8.25 <u>models</u> the total miles Michael traveled one afternoon while sledding. u equals to <u>number of hours</u> walking up a hill and (u – 2) equals to number of hours sledding down the hill.

Solve this equation:

9(u-2) + 1.5u = 8.25,\\ \\9u-18+1.5u=8.25,\\ \\9u+1.5u=8.25+18,\\ \\10.5u=26.25,\\ \\u=2.5\ hours

Answer: correct choice is D

Greeley [361]2 years ago
4 0

D is the correct answer

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Find the mass and center of mass of the lamina that occupies the region D and has the given density function rho. D = {(x, y) |
Bas_tet [7]

Answer:

M=168k

(\bar{x},\bar{y})=(5,\frac{85}{28})

Step-by-step explanation:

Let's begin with the mass definition in terms of density.

M=\int\int \rho dA

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M=k\int^{9}_{1}\frac{y^{3}}{3}|^{4}_{1}dx

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So the mass will be:

M=21k*8=168k

Now we need to find the x-coordinate of the center of mass.

\bar{x}=\frac{1}{M}\int\int x*\rho dydx

\bar{x}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}x*ky^{2} dydx

\bar{x}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}x*y^{2} dydx

\bar{x}=\frac{1}{168}\int^{9}_{1}x*\frac{y^{3}}{3}|^{4}_{1}dx

\bar{x}=\frac{1}{168}\int^{9}_{1}x*21 dx

\bar{x}=\frac{21}{168}\frac{x^{2}}{2}|^{9}_{1}

\bar{x}=\frac{21}{168}*40=5

Now we need to find the y-coordinate of the center of mass.

\bar{y}=\frac{1}{M}\int\int y*\rho dydx

\bar{y}=\frac{1}{M}\int^{9}_{1}\int^{4}_{1}y*ky^{2} dydx

\bar{y}=\frac{k}{168k}\int^{9}_{1}\int^{4}_{1}y^{3} dydx

\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{y^{4}}{4}|^{4}_{1}dx

\bar{y}=\frac{1}{168}\int^{9}_{1}\frac{255}{4}dx

\bar{y}=\frac{255}{672}\int^{9}_{1}dx

\bar{y}=\frac{255}{672}8=\frac{2040}{672}

\bar{y}=\frac{85}{28}

Therefore the center of mass is:

(\bar{x},\bar{y})=(5,\frac{85}{28})

I hope it helps you!

3 0
2 years ago
Jim is building a rectangular deck and wants the length to be 1 ft greater than the width. what will be the dimensions of the de
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Jan had $126. she spent 1/6 of her money on her makeup and 2/3 of her money on shoes. How Much does Jan have left?
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Read 2 more answers
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AysviL [449]

Answer:

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Step-by-step explanation:

To better understand the solution, see attachment for the diagram.

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BC parallel to DE

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Arc SC = 29°

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Arc CE = 180-100

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<CFE = 1/2(Arc CE )

<CFE = 1/2(80)

< CFE = 40°

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2 years ago
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