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Helga [31]
3 years ago
13

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

erivative.) f(x) = x2 − 7x + 5
Mathematics
1 answer:
Alex3 years ago
8 0

Answer:

F(x) = \frac{x^3}{3} - \frac{7x^2}{2} + 5x + c

Step-by-step explanation:

The antiderivative of a function (also called the integration of a function) is the reverse of the differentiation of that function. Given a function f(x), its integration, F(x), can be calculated as follows;

F(x) = \int\limits{f(x)} \, dx

From the question, f(x) = x² - 7x + 5

Therefore,

F(x) = \int\limits {(x^2 - 7x + 5)} \, dx

F(x) = \frac{x^3}{3} - \frac{7x^2}{2} + 5x + c

Where c is the constant of the integration (antiderivative).

PS: The constant of integration is used for indefinite integrals and allows to express integration of a function in its most general form.

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Lisa collects rainwater in a barrel that weighs 25 pounds. When there are 10 gallons of water in the barrel, the total weight of
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Answer:

The equation that matches this situation is y = 8.34x + 25 ⇒ B

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

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The rule of the slope is m = Δy/Δx, where

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∵ Lisa collects rainwater in a barrel that weighs 25 pounds

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∵ When there are 10 gallons of water in the barrel, the total weight

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∵ When there are 20 gallons of water, the total weight is 191.8 pounds

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→ Find Δx and Δy

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→ Substitute them in the rule of the slope above

∴ m = \frac{83.4}{10}

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→ Substitute the values of m and b in the form of the equation above

∵ y = 8.34x + 25

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1. 6/7÷2/7 = 3

2. 4/5÷2/5 = 2

3. 4/7÷2 = 2/7

4. 12/13÷3 = 4/13


HOPE THIS HELPS!!!!!!!!!!!

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In a standard deck of 52 cards, there are 2 red aces, 2 red Queens, and 13 spades.  That leaves 35 cards for everything else.

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