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algol13
2 years ago
6

HELP FAST!Which triangle has an angle measure greater than 50 degrees. explain why you chose your answer

Mathematics
1 answer:
igomit [66]2 years ago
8 0

Answer:

Step-by-step explanation:

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Integral of x"2+4/x"2+4x+3
dolphi86 [110]

I'm guessing you mean

\displaystyle \int\frac{x^2+4}{x^2+4x+3}\,\mathrm dx

First, compute the quotient:

\displaystyle \frac{x^2+4}{x^2+4x+3} = 1 + \frac{4x-1}{x^2+4x+3}

Split up the remainder term into partial fractions. Notice that

<em>x</em> ² + 4<em>x</em> + 3 = (<em>x</em> + 3) (<em>x</em> + 1)

Then

\displaystyle \frac{4x-1}{x^2+4x+3} = \frac a{x+3} + \frac b{x+1} \\\\ \implies 4x - 1 = a(x+1) + b(x+3) = (a+b)x + a+3b \\\\ \implies a+b=4 \text{ and }a+3b = -1 \\\\ \implies a=\frac{13}2\text{ and }b=-\frac52

So the integral becomes

\displaystyle \int \left(1 + \frac{13}{2(x+3)} - \frac{5}{2(x+1)}\right) \,\mathrm dx = \boxed{x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C}

We can simplify the result somewhat:

\displaystyle x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C \\\\ = x + \frac12 \left(13\ln|x+3| - 5\ln|x+1|\right) + C \\\\ = x + \frac12 \left(\ln\left|(x+3)^{13}\right| - \ln\left|(x+1)^5\right|\right) + C \\\\ = x + \frac12 \ln\left|\frac{(x+3)^{13}}{(x+1)^5}\right| + C \\\\ = \boxed{x + \ln\sqrt{\left|\frac{(x+3)^{13}}{(x+1)^5}\right|} + C}

3 0
2 years ago
Find the distance traveled in 35 seconds by an object traveling at a velocity of v(t) = 20 + 5cos(t) feet per second
rosijanka [135]
s(t)= \int\limits^{35}_0 {v(t)} \, dt \\ =\int\limits^{35}_0 {(20+5cos(t))} \, dt \\ =[20t+5sin(t)]^{35}_0 \\ =(20(35)+5sin(35))-(20(0)+5sin(0)) \\ =700+2.868=702.868 \, feet
8 0
3 years ago
Can someone help me please!!!!!!!!!!!!!!!!!!HELPPPPPO
lord [1]

Step-by-step explanation:

Well, each marker is 1/2, and the number line goes from 0-5/2, and A is on the first marker, A=1/2

8 0
3 years ago
Write the phrase as a numerical expression; the product of 5 and 7
steposvetlana [31]

Answer: 12 = 7 + 5

Step-by-step explanation:

12 = 7 + 5

8 0
2 years ago
F(x)=2(x)^2+5 sqrt (x+2)<br><br> f(0)
krek1111 [17]
F(0) = replace every x with 0

2 ({0})^{2}  + 5 \sqrt{0 + 2}  \\  = 2 + 5 \sqrt{2}
=9.0710678119
=9.07
7 0
2 years ago
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