Answer:
C 36
Step-by-step explanation:
1/2(base)(height)
1/2(8)(9)
1/2(72)
=36
The answer is C because the radius is half of the cylinder which is 2 so the Diameter will be 4 meaning the whole cylinder and 8 times 4 is 32.
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Answer:
x=8 y=24
Step-by-step explanation:
y=3x x=y-16
x=3x-16
-3x -3x
<u>-2x=-16</u>
2 2
x=8
y=3(8)
y=24
Answer:
-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C
Step-by-step explanation:
∫ 15 sin(√(at)) dt
Use substitution:
If x = √(at), then:
dx = ½ (at)^-½ (a dt)
dx = a / (2√(at)) dt
dx = a/(2x) dt
dt = (2/a) x dx
Plugging in:
∫ 15 sin x (2/a) x dx
30/a ∫ x sin x dx
Integrate by parts:
If u = x, then du = dx.
If dv = sin x dx, then v = -cos x.
∫ u dv = uv − ∫ v du
= 30/a (-x cos x − ∫ -cos x dx)
= 30/a (-x cos x + ∫ cos x dx)
= 30/a (-x cos x + sin x + C)
Substitute back:
30/a (-√(at) cos(√(at)) + sin(√(at)) + C)
-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C
