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3 years ago

8

Jack is 20 miles due north of Edward. Sarah is due east of Edward. The angle between the direction of the shortest distance from

Sarah to Jack and due east is 25°. To the nearest mile, how far is Sarah from each man?

1 answer:

OLEGan [10]3 years ago

4 0

Answer:

The distance between Sarah and Jack is approximately 22 miles

The distance between Sarah and Jack is approximately 9 miles

Step-by-step explanation:

The explanation in the attached file

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How do you write this in standard notation<br><br>6x10 to the power of 3

Olin [163]

The way to write this would be 6000

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3 years ago

Drag the tiles to the correct boxes to complete the pairs. Match the systems of equations with their solutions.

Oksanka [162]

Answer:

See explanation for matching pairs

Step-by-step explanation:

Equations

(1)

$x - y = 25$

$2x + 3y = 180$

(2)

$2x - 3y = -5$

$11x + y = 550$

(3)

$x - y = 19$

$-12x + y = 168$

Solutions

$(-17,-36)$

$(47, 33)$

$(51, 26)$

Required

Match equations with solutions

(1) $x - y = 25$ and $2x + 3y = 180$

Make x the subject in: $x - y = 25$

$x = 25 + y$

Substitute $x = 25 + y$ in $2x + 3y = 180$

$2(25 + y) + 3y = 180$

$50 + 2y + 3y = 180$

$50 + 5y = 180$

Collect like terms

$5y = 180-50$

$5y = 130$

Solve for y

$y =26$

Recall that: $x = 25 + y$

$x = 25 + 26$

$x = 51$

So:

$(x,y) = (51,26)$

(2) $2x - 3y = -5$ and $11x + y = 550$

Make y the subject in $11x + y = 550$

$y = 550 - 11x$

Substitute $y = 550 - 11x$ in $2x - 3y = -5$

$2x - 3(550 - 11x) = -5$

$2x - 1650 + 33x = -5$

Collect like terms

$2x + 33x = -5+1650$

$35x = 1645$

Solve for x

$x = 47$

Solve for y in $y = 550 - 11x$

$y = 550 - 11 * 47$

$y = 550 - 517$

$y = 33$

So:

$(x,y) = (47,33)$

(3)

$x - y = 19$ and $-12x + y = 168$

Make y the subject in $-12x + y = 168$

$y = 168 + 12x$

Substitute $y = 168 + 12x$ in $x - y = 19$

$x - 168 - 12x = 19$

Collect like terms

$x -12x = 168 + 19$

$-11x = 187$

Solve for x

$x = -17$

Solve for y in $y = 168 + 12x$

$y =168-12 *17$

$y =-36$

So:

$(x,y) = (-17,-36)$

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Answer:

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Step-by-step explanation:

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77. the volume of a cube is increasing at a rate of <img src="https://tex.z-dn.net/?f=10%20%5Cmathrm%7B~cm%7D%5E%7B3%7D%20%2F%20

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Answer:

$\displaystyle \frac{4}{3}\text{cm}^2/\text{min}$

Step-by-step explanation:

<u>Given</u>

<u /> $\displaystyle \frac{dV}{dt}=10\:\text{cm}^3/\text{min}\\ \\V=s^3\\\\SA=6s^2\\\\\frac{d(SA)}{dt}=?}\:;s=30\text{cm}$

<u>Solution</u>

(1) Find the rate of the cube's edge length with respect to time at s=30:

$\displaystyle V=s^3\\\\\frac{dV}{dt}=3s^2\frac{ds}{dt}\\ \\10=3(30)^2\frac{ds}{dt}\\ \\10=3(900)\frac{ds}{dt}\\\\10=2700\frac{ds}{dt}\\\\\frac{10}{2700}=\frac{ds}{dt}\\\\\frac{ds}{dt}=\frac{1}{270}\text{cm}/\text{min}$

(2) Find the rate of the cube's surface area with respect to time at s=30:

$\displaystyle SA=6s^2\\\\\frac{d(SA)}{dt}=12s\frac{ds}{dt}\\ \\\frac{d(SA)}{dt}=12(30)\biggr(\frac{1}{270}\biggr)\\\\\frac{d(SA)}{dt}=\frac{360}{270}\biggr\\\\\frac{d(SA)}{dt}=\frac{4}{3}\text{cm}^2/\text{min}$

Therefore, the surface area increases when the length of an edge is 30 cm at a rate of $\displaystyle \frac{4}{3}\text{cm}^2/\text{min}$ .

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2 years ago