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Ilya [14]
3 years ago
8

Find the particular solution that satifies the differential equation and the initial condition. f"(x) = x2 f'(0) = 8, f(0) = 4

Mathematics
1 answer:
viva [34]3 years ago
5 0

Answer:

f(x) = x^4/12 + 8x + 4

Step-by-step explanation:

f"(x) = x^2

Integrate both sides with respect to x

f'(x) = ∫ x^2 dx

= (x^2+1)/2+1

= (x^3)/3 + C

f(0) = 8

Put X = 0

f'(0) = 0+ C

8 = 0 + C

C= 8

f'(x) = x^3/3 + 8

Integrate f(x) again with respect to x

f(x) = ∫ (x^3 / 3 ) +8 dx

= ∫ x^3 / 3 dx + ∫8dx

= x^(3+1) / 3(3+1) + 8x + D

= x^4/12 + 8x + D

f(0) = 4

Put X = 0

f(0) = 0 + 0 + D

4 = D

Therefore

f(x) = x^4 /12 + 8x + 4

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7 0
2 years ago
If money in a bank doubles every 7 years, then what factor is the money multiplied by over a 28 year period?
Vesnalui [34]

The money would be multiplied by a factor of 16 after 28 years

<h3>How to determine the factor?</h3>

The rate is given as:

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There are 4 7 years in 28 years.

So, the factor would be:

Factor = Rate^4

This gives

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Factor = 16

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6 0
2 years ago
Brett paid $229 for 8 tickets to a baseball game, which includes the $13 service fee applied to every order. How much will Brett
nataly862011 [7]

Answer:

$418

Step-by-step explanation:

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Subtract the service fee to get how much it cost for 8 tickets.

229-13=216

Then divide that number by 8 to find how much a single ticket costs.

216÷8=27

1 ticket costs $27.

Multiply that by 15 to get how much 15 tickets cost.

27×15=405

Then add back the service fee.

405+13=418

5 0
2 years ago
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What is the measure of ehg?
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4 0
2 years ago
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The question is on the picture
Vadim26 [7]

<em>Answer,</em>

100,000,000 > 334,605,925

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7 0
3 years ago
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