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3 years ago

A pipe is leaking at 1.5 cups per day. How many gallons per week is the pipe leaking?

1 answer:

4 0

1.5 cups per day...7 days per week....1.5 * 7 = 10.5 cups per week
16 cups = 1 gallon

16/1 = 10.5/x....16 cups to 1 gal = 10.5 cups to x gal
cross multiply
(16)(x) = (1)(10.5)
16x = 10.5
x = 10.5/16
x = 0.65625 rounds to 0.66 gallons per week

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3 years ago

\int (x+1)\sqrt(2x-1)dx

Nezavi [6.7K]

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Step-by-step explanation:

$\int (x+1)\sqrt {(2x-1)} dx\\Integrate \ using \ integration \ by\ parts \\\\u = x + 1, v'= \sqrt{2x - 1}\\\\v'= \sqrt{2x - 1}\\\\integrate \ both \ sides \\\\\int v'= \int \sqrt{2x- 1}dx\\\\v = \int ( 2x - 1)^{\frac{1}{2} } \ dx\\\\v = \frac{(2x - 1)^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}} \times \frac{1}{2}\\\\v= \frac{(2x - 1)^{\frac{3}{2}}}{\frac{3}{2}} \times \frac{1}{2}\\\\v = \frac{2 \times (2x - 1)^{\frac{3}{2}}}{3} \times \frac{1}{2}\\\\v = \frac{(2x - 1)^{\frac{3}{2}}}{3}$

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