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Mathematics

1 answer:

hoa [83]3 years ago

5 0

Answer:

Step-by-step explanation:

Triangle FEG is a right angle triangle.

From the given right angle triangle

GE represents the hypotenuse of the right angle triangle.

With ∠E as the reference angle,

EF represents the adjacent side of the right angle triangle.

GF represents the opposite side of the right angle triangle.

To determine FG, we would apply Pythagoras theorem. It is expressed as

Hypotenuse² = opposite side ² + adjacent side²

Therefore,

13² = 5² + FG² = 25 + 169

169 = 25 + FG²

FG² = 169 - 25 = 144

FG = √144 = 12

To determine tan E, we would apply trigonometric ratio

Tan θ = opposite side/adjacent side. Therefore,

Tan E = 12/5

Tan E = 2.4

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A sphere has a volume of V=900 in cubed. What is the surface area?

ycow [4]

First, we must solve for the radius of the sphere:
V= $\frac{4}{3}$ $\pi$ $r^{3}$
r=(3 $\frac{V}{4 \pi }$ ) $^{ \frac{1}{3} }$
r=(3* $\frac{900}{4 \pi }$ ) $^{ \frac{1}{3} }$
r≈5.99

Second, we must solve for surface area:
A=4 $\pi$ $r^{2}$
A=4* $\pi$ * $5.99^{2}$
A≈450.88 $in^{2}$