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Alex17521 [72]
3 years ago
7

What's the pattern and what's the next term?

Mathematics
1 answer:
mojhsa [17]3 years ago
8 0
The pattern of the first one is multiplying x 1 x 10  x 100 x 1000 x 10000 if you want the next term multiply and one zero every time the next term is 30000

the pattern of the next one is start from january and skip one month the next term is july
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Find the particular solution that satifies the differential equation and the initial condition. f"(x) = x2 f'(0) = 8, f(0) = 4
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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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