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atroni [7]
3 years ago
7

Laura has $720 and saves $30 a week. Taylor has $1200 and spends $30 a week. in how many weeks will Taylor and Laura have the sa

me amount of money? how much money will that be?
Mathematics
1 answer:
Setler79 [48]3 years ago
4 0
Let w = number of weeks.

In week w,
Laura has: 720 + 30w
Taylor has: 1200 - 30w

Set the two amounts equal and solve for w, the number of weeks.

720 + 30w = 1200 - 30w

60w = 480

w = 8

They will have the same amount of money in 8 weeks.

Laura will have in 8 weeks:
720 + 30w = 720 + 30 * 8 = 720 + 240 = 960

Taylor will have in 8 weeks:
1200 - 30w = 1200 - 30 * 8 = 1200 - 240 = 960

They will both have $960 in 8 weeks.
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evablogger [386]
3x = 6y

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3x = 6y ... divide both sides by 6
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3 years ago
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The volume of a cylinder is 40 ft3. Which expression represents the volume of a cone with the same base and height as the
Ber [7]

Answer:

1/3(40)ft³

Step-by-step explanation:

volume of cone=1/3 volume of cylinder

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3 years ago
Find the area of the region that lies inside the first curve and outside the second curve.
marishachu [46]

Answer:

Step-by-step explanation:

From the given information:

r = 10 cos( θ)

r = 5

We are to find the  the area of the region that lies inside the first curve and outside the second curve.

The first thing we need to do is to determine the intersection of the points in these two curves.

To do that :

let equate the two parameters together

So;

10 cos( θ) = 5

cos( θ) = \dfrac{1}{2}

\theta = -\dfrac{\pi}{3}, \ \  \dfrac{\pi}{3}

Now, the area of the  region that lies inside the first curve and outside the second curve can be determined by finding the integral . i.e

A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} (10 \ cos \  \theta)^2 d \theta - \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \  5^2 d \theta

A = \dfrac{1}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} 100 \ cos^2 \  \theta  d \theta - \dfrac{25}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \ \   d \theta

A = 50 \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix}  \dfrac{cos \ 2 \theta +1}{2}  \end {pmatrix} \ \ d \theta - \dfrac{25}{2}  \begin {bmatrix} \theta   \end {bmatrix}^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}}

A =\dfrac{ 50}{2} \int \limits^{\dfrac{\pi}{3}}_{-\dfrac{\pi}{3}} \begin {pmatrix}  {cos \ 2 \theta +1}  \end {pmatrix} \ \    d \theta - \dfrac{25}{2}  \begin {bmatrix}  \dfrac{\pi}{3} - (- \dfrac{\pi}{3} )\end {bmatrix}

A =25  \begin {bmatrix}  \dfrac{sin2 \theta }{2} + \theta \end {bmatrix}^{\dfrac{\pi}{3}}_{\dfrac{\pi}{3}}    \ \ - \dfrac{25}{2}  \begin {bmatrix}  \dfrac{2 \pi}{3} \end {bmatrix}

A =25  \begin {bmatrix}  \dfrac{sin (\dfrac{2 \pi}{3} )}{2}+\dfrac{\pi}{3} - \dfrac{ sin (\dfrac{-2\pi}{3}) }{2}-(-\dfrac{\pi}{3})  \end {bmatrix} - \dfrac{25 \pi}{3}

A = 25 \begin{bmatrix}   \dfrac{\dfrac{\sqrt{3}}{2} }{2} +\dfrac{\pi}{3} + \dfrac{\dfrac{\sqrt{3}}{2} }{2} +   \dfrac{\pi}{3}  \end {bmatrix}- \dfrac{ 25 \pi}{3}

A = 25 \begin{bmatrix}   \dfrac{\sqrt{3}}{2 } +\dfrac{2 \pi}{3}   \end {bmatrix}- \dfrac{ 25 \pi}{3}

A =    \dfrac{25 \sqrt{3}}{2 } +\dfrac{25 \pi}{3}

The diagrammatic expression showing the area of the region that lies inside the first curve and outside the second curve can be seen in the attached file below.

Download docx
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How to know what number is a rational number?
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Answer:

A rational number is a number that can be made by dividing two integers (an integer is a number with no fractional part).  The word rational includes the word "ratio." Rational numbers are basically numbers, either positive or negative that you get by dividing 2 numbers. Any number is a rational number, even fractions and decimals, except pi due to the fact that it's a irrational number.

Step-by-step explanation:

Examples of rational numbers include, 1, which you get by dividing 1 by 1, 2 which you get by dividing 2 by 1 and 2.12, which you get by dividing 212 by 100.

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serg [7]

Answer:

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Step-by-step explanation:

take 20 degree as reference angle .the,

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perpendicular(opposite) = PQ 3 (opposite of reference angle is perpendicular or also called as opposite)

base(adjacent) = OP (side which lies on the same line where 90 degree and reference angle)

using sin rule

sin 20 = opposite / hypotenuse

0.34 = 3 / x

x = 3/0.34

x = 8.82

x = 8.8

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