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TiliK225 [7]
3 years ago
5

The radius of a cylindrical gift box is ​(3x +4)) inches. The height of the gift box is twice the radius. What is the surface ar

ea of the​ cylinder? Write your answer as a polynomial in standard form.
Mathematics
1 answer:
musickatia [10]3 years ago
8 0
The answer is 54πx² + 144πx + 96π

The surface area of cylinder (SA) is:
SA = 2 π r h + 2 π r²

<span>The height of the gift box is twice the radius: h = 2r

r = 3x + 4
h = 2(3x + 4) = 6x + 8

SA = </span>2 π r h + 2 π r²
SA = 2π (r * h + r²)
SA = 2π ((3x + 4)(6x + 8) + (3x + 4)²)
SA = 2π(18x² + 24x + 24x + 32 + 9x² + 24x + 16)
SA = 2π(27x² + 72x + 48)
SA = 54πx² + 144πx + 96π
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The point P(6, –1) is translated according to the rule (x, y) → (x – 5, y – 2).
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The <em>resulting</em> point by considering that P(x, y) = (6, - 1) and P'(x, y) = P(x, y) + (- 5, - 2) is equal to the coordinates P'(x, y) = (1, - 3). (Right choice: C)

<h3>How to determined a resulting point by translation</h3>

In this question we need to determine the new location of a point by using a <em>translation</em> formula. Translations are rigid transformations in which a point is translated on a <em>Cartesian</em> plane. We have the following formula:

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Where:

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If we know that P(x, y) = (6, - 1), then the resulting point is:

P'(x, y) = (6, - 1) + (- 5, - 2)

P'(x, y) = (1, - 3)

The <em>resulting</em> point by considering that P(x, y) = (6, - 1) and P'(x, y) = P(x, y) + (- 5, - 2) is equal to the coordinates P'(x, y) = (1, - 3). (Right choice: C)

To learn more on translations: brainly.com/question/17152175

#SPJ1

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