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notsponge [240]
3 years ago
6

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Mathematics
1 answer:
uranmaximum [27]3 years ago
5 0

Answer: 10,000

Step-by-step explanation:

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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
viva [34]

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

5 0
3 years ago
What is the average speed of a cheetah that sprints 100 miles in 4 seconds? How about if it sprints 50 miles in 2 seconds?
hichkok12 [17]
The cheetah is traveling at 25m per second.
3 0
3 years ago
Write the equation of a line that is parallel to y=0.6x+3 and that passes through the point
a_sh-v [17]
A line parallel to y = 0.6x + 3 will be of the form:

y = 0.6x + k

where k is a constant.

It passes through (-3,-5)

Thus,

y = 0.6x + k \\ \\ -5 = 0.6 \times (-3) + k \\ \\ -5 = -1.8 + k \\ \\k = -5 + 1.8 \\ \\ k = -3.2

\textbf{The equation is \: \: y = 0.6x - 3.2}
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3 years ago
Ethan's grade on course I tests were 90
Svetlanka [38]

The mode of his grade is 90 because it is the number most frequented

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3 years ago
What's two thirds plus six seventh?
vfiekz [6]

Answer:

32/21

Step-by-step explanation:

multiply (2/3) by (7/7) and (6/7) by (3/3). (14/21) + (18/21) is (32/21)

7 0
3 years ago
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