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Dmitry [639]
3 years ago
10

Two similar polygons have areas of 4 square inches and 64 square inches. The ratio of a pair of corresponding sides is 1/4. True

False
Mathematics
2 answers:
Zanzabum3 years ago
8 0

Answer:

<u><em>True</em></u>

step-by-step explanation:

Just in case you needed a second opinion.

konstantin123 [22]3 years ago
3 0

Answer:

That is true

Step-by-step explanation:

The ratio is a one-to-one measure, literally a ratio of the sides in reduced form.  The area is that one-to-one ratio squared.

Our numbers are already squared, so in order to find the one-to-one we have to take the square roots of both of them.  

\frac{\sqrt{4} }{\sqrt{64} } =\frac{2}{8} =\frac{1}{4}.

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Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2
HACTEHA [7]

This question is incomplete, the complete question is;

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2 = 2x, x = 2y; about the y-axis

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V = π (512/15)

Step-by-step explanation:

Given that;

region of rotation

y² = 2x, x = 2y

Region is rotated about y-axis as shown in the image

for the point of intersection,

y²/2 = 2y

y² - 4y = 0

y(y-4) = 0

∴ y = 0, y = 4

so the region lies in 0 ≤ y ≤ 4

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A(y) = π(outer radius)² = π(inner radius)²

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A(y) = π(4y²) - π(y⁴/4)

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now volume of the solid of revolution is

V = ⁴∫₀ A(y) dy

V = ⁴∫₀ π(4y² - (y⁴/4))dy

V =  π {4⁴∫₀ y² - 1/4⁴∫₀y⁴ dy }

V = π { 4/3 [y³]₀⁴ - 1/20 [y⁵]₀⁴ }

V = π { 4/3 [4]₀⁴ - 1/20 [4]₀⁴ }

V = π { 4/3 [64]₀⁴ - 1/20 [1024]₀⁴ }

V = π { 256/3 - 1024/20 }

V = π { (5120 - 3072) / 60 }

V = π (512/15)

8 0
3 years ago
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