Help me fast please!! Ill give 5 stars!

Mathematics

2 answers:

Allisa [31]3 years ago

7 0

Answer:

1/3 of an hour faster

Step-by-step explanation:

3/4 = 9/12

9/12 - 5/12 = 4/12 = 1/3

Answer: 1/3 of an hour faster

lesya692 [45]3 years ago

3 0

Answer:

1/3 faster

.3333333

Step-by-step explanation:

We need to find a common denominator, so multiply the numerator and denominator of 3/4 by 3 to get a common denominator. The result is 9/12. He was 4/12 or 1/3 faster today.

Hope this helps! Brainliest please!

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rosijanka [135]

$\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx$

Notice that $x^3+x^2-4x-4=x^2(x+1)-4(x+1)=(x-2)(x+2)(x+1)$ . Decompose the integrand into partial fractions:

$\dfrac{x^2+x-3}{(x-2)^2(x+2)^2(x+1)^2}$
$=\dfrac1{3(x+1)}-\dfrac{11}{32(x+2)}-\dfrac1{3(x+1)^2}-\dfrac1{16(x+2)^2}+\dfrac1{96(x-2)}+\dfrac1{48(x-2)^2}$

Integrating term-by-term, you get

$\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx$
$=-\dfrac1{48(x-2)}+\dfrac1{3(x+1)}+\dfrac1{16(x+2)}+\dfrac1{96}\ln|x-2|+\dfrac13\ln|x+1|-\dfrac{11}{32}\ln|x+2|+C$