The functions q and r are defined as follows.

Mathematics

1 answer:

Bad White [126]3 years ago

5 0

Answer:

9x = 1-1 is q r x= 2x2 + 2 is 4

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Evaluate the integral. (remember to use absolute values where appropriate. Use c for the constant of integration.) 5 cot5(θ) sin

ozzi

$I=5\int \frac{cos^{4}\theta }{sin\theta }\times cos\theta d\theta \\\\I=5\int \left ( 1-sin^{2}\theta \right )^{2}\times \frac{cos\theta }{sin\theta }d\theta \\put\ \sin\theta =t\\\\dt=cos\theta d\theta \\\\I=5\int\frac{t^{4}+1-2t^{2}}{t}dt\ \ \ \ \ \ \ \ \ \ \because (a-b)^2=a^2+b^2-2ab\\\\I=5\left ( \int t^{3}dt + \int \frac{1}{t} -2\int t \right )dt$

by using the integration formula

we get,

$\\I=5\left ( \frac{t^{4}}{4} +logt -t^{2}\right )\\\\I=\frac{5}{4}t^{4}+5\log t-5t^{2}+c$

now put the value of t=\sin\theta in the above equation

we get,

$\int 5\cot^5\theta \sin^4\theta d\theta=\frac{5}{4}sin^{4}\theta+5\log \sin\theta - 5sin^{2} \theta+c$

hence proved

7 0

3 years ago

Cooper earned $660 as a furniture salesman this month. His earns a

Grace [21]

Ya got to go $660 + 7% hours later on $450 hours later 00.578 to finish

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3 years ago

The denominator of a fraction is 10 more than its numerator.

Dennis_Churaev [7]

The right answer is Option C : 5

Step-by-step explanation:

Let,

The numerator of fraction = x

The denominator of a fraction is 10 more than its numerator.

$\frac{x}{x+10}$

When 1/3 is added to this fraction,

$\frac{x}{x+10}+\frac{1}{3}$

the resulting fraction’s denominator is three times the denominator of the original fraction its numerator is 15 less than its denominator

$\frac{3(x+10)-15}{3(x+10)}$

Therefore, it becomes

$\frac{x}{x+10}+\frac{1}{3} = \frac{3(x+10)-15}{3(x+10)}$

Taking LCM on left side

$\frac{3x+(x+10)}{3(x+10)}=\frac{(3x+30)-15}{3(x+10)}\\\\\frac{3x+x+10}{3(x+10)}=\frac{3x+30-15}{x(x+10)}\\\\\frac{4x+10}{3(x+10)}=\frac{3x+15}{3(x+10)}$