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bija089 [108]
2 years ago
5

How do you do this question?

Mathematics
1 answer:
Nikitich [7]2 years ago
3 0

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

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Solve u^2 = -4, where u is a real number. Simplify your answer as much as possible.
alexdok [17]

Answer:

2i and -2i

Step-by-step explanation:

I'll change u to x to be easier to understand.

x^2 = -4

sqrt(x^2) = sqrt(-4)

sqrt(-4) = 2i, or -2i

8 0
2 years ago
Three times a number n plus 16
HACTEHA [7]

Answer:

3n+16

Step-by-step explanation:

three times: (3) a number n +16

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3n+16

4 0
3 years ago
An investment of $5000 has an annual growth rate of 8% for 3 years
Fudgin [204]

Answer: The final balance is $6,341.21.

The total compound interest is $1,341.21.

Step-by-step explanation:

8 0
2 years ago
Lin’s road trip is 75 miles long. She has completed 20% of a trip so far. How many miles has Lin gone so far?
Lynna [10]

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7 0
3 years ago
Use the net to find the surface area of the rectangular prism. A) 48 cm2 B) 120 cm2 C) 384 cm2 D) 432 cm2
Marina86 [1]
Formula: length · width 

2 big rectangles:96 + 96 = 192
(12 × 8) · 2

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(6 × 12) · 2

2 small rectangles: 48 + 48 = 96
(6 × 8) · 2

Add all 3 numbers:

192 + 144 + 96 = 432

Your answer is D. 432 cm²

Hope this helps :)

6 0
3 years ago
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