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ddd [48]
3 years ago
5

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

4(θ) dθ
Mathematics
1 answer:
ozzi3 years ago
7 0

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

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How many numbers of possible live card hands (hands in five-card poker) drawn without replacement from a standard deck of 52 pla
makkiz [27]

The combination shows that the numbers of possible live card hands drawn without replacement from a standard deck of 52 playing cards is 2,598,960.

<h3>How to explain the information?</h3>

A permutation is the act of arranging the objects or numbers in order while combinations are the way of selecting the objects from a group of objects or collection such that the order of the objects does not matter.

Since the order does not matter, it means that each hand is a combination of five cards from a total of 52.

We use the formula for combinations and see that there are a total number of C( 52, 5 ) = 2,598,960 possible hands.

Learn more about permutations and combination on:

brainly.com/question/4658834

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3 0
2 years ago
A student has a savings account earning 3% simple interest. She must pay $1200 for first-semester tuition by September 1 and $12
Bingel [31]

Using simple interest, it is found that she needs to earn $2,391.07 during the summer.

<h3>Simple Interest</h3>

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

A(t) = A(0)(1 + rt)

In which:

  • A(0) is the initial amount.
  • r is the interest rate, as a decimal.

For this problem, the objective is to have <u>$1200 in 3 months = 0.25 years</u>, hence the parameters are given as follows:

A(0.25) = 1200, t = 0.25, r = 0.03.

Hence we have to solve for A(0):

A(0)(1 + 0.03 x 0.25) = 1200

A(0) = 1200/(1 + 0.03 x 0.25)

A(0) = $1,191.07.

She also needs to earn $1,200 to pay the first-semester bill on time, hence:

1200 + 1191.07 = $2,391.07.

She needs to earn $2,391.07 during the summer.

More can be learned about simple interest at brainly.com/question/16646150

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3 0
1 year ago
What is the answer to this question?
harina [27]

Answer:

f(g(0) )= -1

Step-by-step explanation:

Find g(0) = -1

Then find f(-1) = 1

f(g(0) )= -1

4 0
3 years ago
Quadrilateral $abcd$ is a trapezoid with $ab$ parallel to $cd$. we know $ab = 20$ and $cd = 12$. what is the ratio of the area o
alekssr [168]
Draw a diagram to illustrate the problem as shown below.

The area of triangle acb is
A₁ = (1/2)*20*h = 10h

The area of trapezoid abcd is
A₂ = (1/2)*(20+12)*h = 16h

The ratio A₁/A₂ is
A₁/A₂ = (10h)/(16) = 5/8

Answer:
The ratio of triangle acb to the area of trapezoid abcd is 5/8.

4 0
3 years ago
Write the linear equation in slope intercept form from passing through the point with the given slope (-5,-3);slope =-3/5
forsale [732]

Answer:

The answer is y=-3/5x-6

Step-by-step explanation:

y-y=m(x-x1)

y-(-3)=-3/5(x-(-5))

y+3=-3/5x-3

-3 -3

y=-3/5x-6

8 0
3 years ago
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