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2 years ago

9

Lucas cut a board that is 3 1/5 ft. long and 3 1/3 ft. wide. What is the area of the board? Express your answer in simplest form

.

2 answers:

aliya0001 [1]2 years ago

8 0

First let have these mixed number to improper fractions.
3 1/5 = 16/5
3 1/3 = 10/3
A=l×w
16/5 × 10/3 = 160/15

tankabanditka [31]2 years ago

8 0

3 1/5 x 3 1/3
= 16/5 x 10/3
= 32/3
= 10 2/3

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<u><em>Here is why:</em></u>

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2 years ago

1. Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants.

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Answer:

Step-by-step explanation:

1.

To write the form of the partial fraction decomposition of the rational expression:

We have:

$\mathbf{\dfrac{8x-4}{x(x^2+1)^2}= \dfrac{A}{x}+\dfrac{Bx+C}{x^2+1}+\dfrac{Dx+E}{(x^2+1)^2}}$

2.

Using partial fraction decomposition to find the definite integral of:

$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}dx$

By using the long division method; we have:

$x^2-8x-20 | \dfrac{2x}{2x^3-16x^2-39x+20 }$

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$x+ 20$

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$\dfrac{2x^3-16x^2-39x+20}{x^2-8x-20}= 2x+\dfrac{x+20}{x^2-8x-20}$

By using partial fraction decomposition:

$\dfrac{x+20}{(x-10)(x+2)}= \dfrac{A}{x-10}+\dfrac{B}{x+2}$

$= \dfrac{A(x+2)+B(x-10)}{(x-10)(x+2)}$

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x + 20 = (A + B)x + (2A - 10B)

Now; we have to relate like terms on both sides; we have:

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$A = \dfrac{5}{2}$ $B = \dfrac{3}{2}$

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Thus;

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Now; the integral is:

$\int \dfrac{2x^3-16x^2-39x+20}{x^2-8x-20} \ dx = \int \begin {bmatrix} 2x + \dfrac{5}{2(x-10)}+ \dfrac{3}{2(x+2)} \end {bmatrix} \ dx$

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2 years ago

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