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Semmy [17]
3 years ago
10

3-(x-1)=-1-(5-x) pls help

Mathematics
1 answer:
Alika [10]3 years ago
3 0

Answer:

- 3(x - 1) =  - 1(5 - x) \\  \\ 3 - x + 1 =  - 5 + x \\  \\  - x - x =  - 5 - 3 - 1 \\  \\  - 2x =  - 5 - 3 - 1 \\  \\  - 2x =   - 9 \\  \\ x =  \frac{ - 9}{ - 2}  \\  \\ x = 4.5

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Step-by-step Explanation:

We are going to solve this problem using integration by parts. We can write the integrand as

\dfrac{4x}{x^2+4x+3} = \dfrac{4x}{(x+3)(x+1)}

\:\:\:\:\:\:\:\:\:\:\:\:\:= \dfrac{A}{x+3} + \dfrac{B}{x+1}

\:\:\:\:\:\:\:\:\:\:\:\:\:= \dfrac{Ax + A + Bx + 3B}{x^2+4x+3}

\:\:\:\:\:\:\:\:\:\:\:\:\:=\dfrac{(A+B)x + (A+3B)}{x^2+4x+3}

Comparing the above term to the left hand side, we can see that

(A + B)x = 4x

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Solving for A and B, we find that A = 6 and B = -2 so our integrand becomes

\dfrac{4x}{x^2+4x+3} = \dfrac{6}{x+3} - \dfrac{2}{x+1}

We can now easily integrate this expression as follows:

\displaystyle \int{\dfrac{4x}{x^2+4x+3}}dx = 6\int{\dfrac{dx}{x+3}} - 2\int{\dfrac{dx}{x+1}}

\:\:\:\:\:\:\:\:\:\:\:\:\:= 6\ln|x+3| - 2\ln|x+1| + C

7 0
3 years ago
If a bus driver leaves her first stop by 7:00 a.m., her route will take less than 37 minutes. If she leaves after 7:00 a.m., she
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Step-by-step explanation:

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Answer:

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 ---

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