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Sonbull [250]
3 years ago
10

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antid

erivative. Remember to use absolute values where appropriate.) f(x) = 2 5 − 3 x , x > 0
Mathematics
1 answer:
storchak [24]3 years ago
8 0

Answer:

C + ⅖|x| - (³/₂)x²

Step-by-step explanation:

ƒ(x) = ⅖ - 3x ; x > 0

The antiderivative of ƒ(x) is a function that you can differentiate to get ƒ(x). It is the indefinite integral of ƒ(x).

Thus, if ƒ(x) = ⅖ - 3x, we must find ∫(⅖ - 3x)dx .

∫(⅖ - 3x)dx = ∫⅖dx - ∫3xdx = ⅖∫dx - 3∫xdx

(a) Integrate the first term

⅖∫dx = ⅖x

(b) Integrate the second term

∫xdx =½x², so

3∫xdx = (³/₂)x²

(c) Add the constant of integration, C

Remember that dC/dx =0 when C is a constant.

We don't know if there's a constant term in the antiderivative (there may or may not be one), so we include the constant term C to make it general.

(d) Combine the three terms

∫(⅖ - 3x)dx = C + ⅖x - (³/₂)x²

We must have x  > 0, so

∫ƒ(x)dx = C + ⅖|x| - (³/₂)x²

Check:

(d/dx)( C + ⅖|x| - (³/₂)x²) = 0 + ⅖ - 3x  = ⅖ - 3x

Differentiating the integral returns the original function.

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ICE Princess25 [194]

Answer:

25 + 2x= 325 x=150

Step-by-step explanation:

-25 -25

2x 300

/2 /2

×= 150

8 0
2 years ago
Julio’s father is four times as old is Julio. The sum of their ages is no less than 55. Find the any quality that can be used to
rosijanka [135]

Answer:

Step-by-step explanation

dont really understand the question but you can see if it is the correct answer

represent julios age as x

represnt julios father age as 4x

so x+4x=5x

5x<55

not sure if this is correct bare that in mind

3 0
3 years ago
Hi!
goblinko [34]
You can always add or subtract same value to/from both sides of equation. The same is true about multiplication and division.

In your case you have to subtract x from both sides of equation in order to get rid of it on the left side:
x+2y-x=8-x
2y=8-x

But it's easier to remember that if you want to move some member of equation to other side, you just have to change it's sign. Let's practice a bit using your equation (I have added "plus" signs where they are usually omitted to better understend what's going on):
+x+2y=+8

Move 2y to the right side:
+x=+8-2y

Move 8 to the left side:
+x+2y-8=0

Move both x and 2y to the right side:
0=8-x-2y
8 0
3 years ago
Hi!! Please help, thank you lots !!!
11Alexandr11 [23.1K]
3k²+11k+6, or (k+3)(3k+2), which is the 3rd one. :)
7 0
3 years ago
A bike wheel as a radius of 13 inches. About how far does the bike wheel travel in:
kumpel [21]

Answer:

a. 81.6 inches

b. 408 inches

c. 2480 inches

Step-by-step explanation:

circumference  = 2 π r = 2 x 3.14 x 13 = 81.6 inchess

in feet = 81.6 /12

6.8 feet

7 0
3 years ago
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