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3 years ago

PLEASE HELP AND HURRY!

Mathematics

1 answer:

Kamila [148]3 years ago

8 0

Answer:

ANSWER BELOW

Step-by-step explanation:

If the door is 9 x 2 ft (18 sq ft):

12 x 18 = 216 sq ft. (Front face including the door)

216 sq ft - 18 sq ft = 198 (Front face not including the roof or door)

For the roof, the formula is h b/2:

So if the height is 4 and the base is 18, the area of the roof is 36.

To find the total area, you must add the area of the front face and the roof (without the door).

198 + 36 = 234 sq ft

Have a wonderful day my friend!

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Step-by-step explanation:

From the given information:

r = 10 cos( θ)

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

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

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

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

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

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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