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2 years ago

Trayvon has a mug shaped like a hemisphere. Its diameter is 18 cm. To the nearest hundredth, what is the capacity of her mug?

Mathematics

1 answer:

bulgar [2K]2 years ago

6 0

Answer:

The capacity of the mug is 1,527.43 cm^3

Step-by-step explanation:

In this question, we are asked to calculate the capacity of the hemisphere. This is same as calculating the volume of the hemisphere.

A hemisphere is a sharpe which is half a sphere. Meaning to get a hemisphere, we shall be diving a sphere into 2.

Mathematically, the volume of a hemisphere V = 2/3 * π * r^3

Since D = 18cm , r = D/2 = 18cm/2 = 9 cm

The volume V is thus = 2/3 * 22/7 * 9^3

V = 1,527.428 cm^ 3

To the nearest hundredth,

V = 1,527.43 cm^3

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2 years ago

Find y as a function of x if y"' + 9y' = 0, y(0) = 6, y'(0) = 9, y"(0) = 18. y(x) =

Andreas93 [3]

Answer:

y(x) = 8 - 2cos 3x + 3sin 3x

Step-by-step explanation:

Given the equation:

y''' + 9y' = 0

The characteristic equation :

⇒r³ + 9r =0

Solving for r, we get r = 0 and r = ± 3i

The general equation for such equation is :

y = C₁ + C₂cos 3x + C₃sin 3x

Given:

y(0) = 6

Thus, Applying in the above equation, we get

6 = C₁ + C₂ .......................................................1

Differentiating y , we get:

y' = -3C₂sin 3x + 3C₃cos 3x

Given:

y'(0) = 9

Thus, Applying in the above equation, we get

9 = 3C₃

or,

C₃ = 3

Differentiating y' , we get:

y'' = -9C₂cos 3x - 9C₃sin 3x

Given:

y''(0) = 18

Thus, Applying in the above equation, we get

18 = -9C₂

or,

C₂ = -2

Applying in equation 1 , we get:

C₁ = 8

Thus,

y(x) = 8 - 2cos 3x + 3sin 3x

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Answer:

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3 years ago