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Butoxors [25]
3 years ago
12

A baker makes 84 loaves of bread, she burns 4. What fraction of the loaves does the burn? Simplify your answer.

Mathematics
1 answer:
svetoff [14.1K]3 years ago
3 0

Answer:

1/21

Step-by-step explanation:

The baker makes 84 loaves of bread,

Out of the 84 bread, 4 of them got burn.

Fraction that the loaves does the burn will be expressed in 4/84 = 1/21.

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Step-by-step explanation:

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The integral of (5x+8)/(x^2+3x+2) from 0 to 1
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Compute the definite integral:
 integral_0^1 (5 x + 8)/(x^2 + 3 x + 2) dx

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 = integral_0^1 ((5 (2 x + 3))/(2 (x^2 + 3 x + 2)) + 1/(2 (x^2 + 3 x + 2))) dx

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Evaluate the antiderivative at the limits and subtract.
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For the integrand 1/(x^2 + 3 x + 2), complete the square:
 = (5 log(3))/2 + 1/2 integral_0^1 1/((x + 3/2)^2 - 1/4) dx

For the integrand 1/((x + 3/2)^2 - 1/4), substitute s = x + 3/2 and ds = dx.
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Factor -1/4 from the denominator:
 = (5 log(3))/2 + 1/2 integral_(3/2)^(5/2) 4/(4 s^2 - 1) ds

Factor out constants:
 = (5 log(3))/2 + 2 integral_(3/2)^(5/2) 1/(4 s^2 - 1) ds

Factor -1 from the denominator:
 = (5 log(3))/2 - 2 integral_(3/2)^(5/2) 1/(1 - 4 s^2) ds

For the integrand 1/(1 - 4 s^2), substitute p = 2 s and dp = 2 ds.
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 = (5 log(3))/2 - integral_3^5 1/(1 - p^2) dp

Apply the fundamental theorem of calculus.
The antiderivative of 1/(1 - p^2) is tanh^(-1)(p):
 = (5 log(3))/2 + (-tanh^(-1)(p)) right bracketing bar _3^5


Evaluate the antiderivative at the limits and subtract. (-tanh^(-1)(p)) right bracketing bar _3^5 = (-tanh^(-1)(5)) - (-tanh^(-1)(3)) = tanh^(-1)(3) - tanh^(-1)(5):
 = (5 log(3))/2 + tanh^(-1)(3) - tanh^(-1)(5)

Which is equal to:

Answer:  = log(18)
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X/7+x-2/14=1/7<br> Please answer x as a fraction!
V125BC [204]

Answer:

x = \frac{1}{4}

Step-by-step explanation:

Given

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x = \frac{4}{16} = \frac{1}{4}

4 0
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