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Kobotan [32]
2 years ago
14

What is the exact area of the following circle?

Mathematics
2 answers:
Vsevolod [243]2 years ago
5 0

Answer:

2nd option

› 56.25π cm²

Step-by-step explanation:

<u>we know , </u>

area of circle is πr²

so,

<u>given,</u>

diameter,d = 15cm

radius,r = d/2 = 15/2 = 7.5 cm

so,

area = πr²

= (7.5×7.5)π

= 56.25π cm²

i hope you find it helpful !!!!

pychu [463]2 years ago
3 0

Answer:

56.25 pi  cm^2

Step-by-step explanation:

To find the area of the circle,

we use the formula

A = pi r^2, where r is the radius

We know the diameter is 15 so we can find the  radius from

r = d/2  where d is the diameter

r = 15/2

A = pi ( 15/2) ^2

A = pi ( 225/4)

A = 56.25 pi  cm^2

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Which of the following functions are solutions of the differential equation y'' + y = 3 sin x? (select all that apply)
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C

Step-by-step explanation:

We must compute the derivatives and check if the equation is satisfied.

A. y'=(3\sin x)'=3\cos x. Differentiate again to get y''=(3\cos x)'=-3\sin x, then y''+y=-3\sin x+3\sin x=0\neq 3\sin x so this choice of y doesn't solve the equation.

B. y'=3\sin x+3x\cos x-5\cosx +5x\sin x=(5x+3)\sin x+(3x-5)\cos x and y''=5\sin x+(5x+3)\cos x+3\cos x-(3x-5)\sin x=(10-3x)\sin x+(5x+6)\cos x, then y''+y=10\sin x+6\cos x\neq 3\sin x so y is not a solution

C. y'=\frac{-3}{2}\cos x+\frac{3}{2}x\sin x hence y''=\frac{3}{2}\sin x+\frac{3}{2}\sin x+\frac{3}{2}x\cos x=3\sin x+\frac{3}{2}x\cos x. Then y''+y=3\sin x+\frac{3}{2}x\cos x-\frac{3}{2}x\cos x=3\sin x so y is a solution.

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3 years ago
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