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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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Answer:

8/5 < x < 12/5

Step-by-step explanation:

(2 - x)² < 4/25​

2 - x < ±2/5

2 - x < 2/5

-x < -8/5

x > 8/5

2 - x > -2/5

-x > -12/5

x < 12/5

Therefore, your answer is 8/5 < x < 12/5

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3 years ago
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Due soon!! <br>Find the measure of GE¯¯¯¯¯¯¯¯. A. 14 B. 20 C. 15 D. 16
Nataly_w [17]

Answer:

D. 16

Step-by-step explanation:

GH^2 = GF \times GE

12^2 = 9 \times (9+x - 2)

144= 9 \times (7+x)

\frac{144}{9}= (7+x)

16= 7+x

16-7=x

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GE = 9 + x - 2 = 9 + 9 - 2 = 18 - 2

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4 0
3 years ago
Read 2 more answers
Reposting because I didn’t get an answer and I need one asap. fake answers/links will be reported.
daser333 [38]

Answer:

B

Step-by-step explanation:

(x+5)^2

x^2+10x+25

(y+3)^2

y^2+6y+9

then it would be

x^2+10x+34+y^2+6y

subtract 34-36 since ur moving 36 to the left

where u get -2

so ur final equation would be x^2+y^2+10x+6y-2=0

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3 years ago
FREE BRAINLIST 2
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Answer:

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Step-by-step explanation:

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