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Vaselesa [24]
4 years ago
14

How many kilometers in a marathon​

Mathematics
1 answer:
irina [24]4 years ago
5 0

Answer:

42.194988

Step-by-step explanation:

There are 42.194988 km in 1 marathon

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Answer:

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Step-by-step explanation:

You have the following curves:

y_1=\frac{4}{9}x^2=f(x)\\\\y_2=\frac{13}{9}-x^2=g(x)

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To determine the limits of the integral you equal both curves f=g and solve for x:

f(x)=g(x)\\\\\frac{4}{9}x^2=\frac{13}{9}-x^2\\\\\frac{4}{9}x^2+x^2=\frac{13}{9}\\\\\frac{13}{9}x^2=\frac{13}{9}\\\\x=\pm 1

Then, the limits are a = -1 and b = 1

You replace f(x), g(x), a and b in the equation (1):

V=\pi \int_{-1}^{1}[(\frac{13}{9}-x^2)^2-(\frac{4}{9}x^2)^2]dx\\\\V=\pi \int_{-1}^1[\frac{169}{81}-\frac{26}{9}x^2+x^4-\frac{16}{81}x^4]dx\\\\V=\pi \int_{-1}^1 [\frac{169}{81}-\frac{26}{9}x^2+\frac{65}{81}x^4]dx\\\\V=\pi [\frac{169}{81}x-\frac{26}{27}x^3+\frac{65}{405}x^5]_{-1}^1\\\\V\approx8.06\ cubed\ units

The volume of the solid of revolution is approximately 8.06 cubed units

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3 years ago
Miss Baker paid $2.50 for 5 lb of bananas write and write an equation relating to the cost of seeds or number of pounds P of ban
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for 8 pounds of bananas.

Step-by-step explanation:

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