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3 years ago

Help integrate: cot^3(x)

1 answer:

8 0

$\int {cot^{3} x} \, dx = \int { \frac{cos^{3} }{sin^{3} x} } \, dx = \\ = \int {(1-sin ^{2}) cosx}/sin^{3} x \, dx = \\ \int { \frac{cosx}{sin^{3} x} } \, dx - \int { \frac{cos x}{sin x} } \, dx$
We will use u-substitution:
u = sin x, du = cos x dx
= $\int { \frac{du}{u^{3} }} - \int { \frac{du}{u} }=- \frac{1}{2u^{2} } - ln (u) = \\ =- \frac{1}{2 sin^{2} x} +ln (sin x)+C$

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What is the value of z in the equation 2(4z − 9 − 7) = 166 − 46?

kari74 [83]

Answer:

z = 19

Step-by-step explanation:

Given

2(4z - 9 - 7) = 166 - 46 ← simplify both sides

2(4z - 16) = 120 ← distribute parenthesis on left side

8z - 32 = 120 ( add 32 to both sides )

8z = 152 ( divide both sides by 8 )

z = 19

4 0

3 years ago

Read 2 more answers

You are scheduled to receive $15,000 in two years. When you receive it, you will invest it for six more years at 7.1 percent per

olga_2 [115]

Answer:

$22,637

Step-by-step explanation:

When u recive $15,000 you invest it at 7.1 percent per year.

To solve this we have to do a sume of all dollars that we have at the first year with the intrest, and that wil be the total for the second years. And repeat for the follows years.

1º year= 15,000*1.071 (7.1%)=$16,065

2º year= 16,065*1.071 (7.1%)=$17,206

3º year= 17,206*1.071 (7.1%)=$18,427

4º year= 18,427*1.071 (7.1%)=$19,735

5º year= 19,735*1.071 (7.1%)=$21,137

6º year= 21,137 *1.071 (7.1%)=$22,637

The total is the money at the end of the years= $22,637

7 0

3 years ago

What is the percent of 60 is 15

frutty [35]

To find the percent of 15 out of 60, you have to divide fifteen by sixty.
Then, you multiply your answer by 100. (We do this because 100 percent is a exact amount. 100% of sixty is...well, sixty.)

15 / 60 = 0.25

Now, we can multiply 0.25 by 100:

0.25 * 100 = 25 (basically just moving the decimal two places to the right.)

Next, add a percent sign:

25%, is your answer.

15 is 25% of 60.

5 0

4 years ago

In ATUV, the measure of _V=90°, the measure of ZT=42°, and UV = 20 feet. Find

Svetradugi [14.3K]

Answer:

T=21

Step-by-step explanation:

Sorry if wrong

I hope this helps

6 0

3 years ago

Suppose that the members of a student governance committee will be selected from the 40 members of the student senate. There are

Len [333]

Answer:

The total number of ways to form a student governance committee is 1,211,760.

Step-by-step explanation:

The students senate consists of a total of 40 students.

The students are either Sophomores or Juniors or Seniors.

The number of students in each of these categories are as follows:

Sophomores = 18

Juniors = 12

Seniors = 10

A governance committee have to be selected from the students senate.

The committee have to made up of 2 sophomores, 2 juniors and 3 seniors.

Combinations can be used to select 2 sophomores from 18, 2 juniors from 12 and 3 seniors from 10.

Combinations is a mathematical technique used to determine the number of ways to select k items from n distinct items.

The formula is:

${n\choose k}=\frac{n!}{k!(n-k)!}$

(1)

Compute the number of ways to select 2 sophomores from 18 as follows:

${n\choose k}=\frac{n!}{k!(n-k)!}$

${18\choose 2}=\frac{18!}{2!(18-2)!}=\frac{18\times 17\times 16!}{2\times 16!}=153$

Thus, there are 153 ways to select 2 sophomores from 18.

(2)

Compute the number of ways to select 2 juniors from 12 as follows:

${n\choose k}=\frac{n!}{k!(n-k)!}$

${12\choose 2}=\frac{12!}{2!(12-2)!}=\frac{12\times 11\times 10!}{2\times 10!}=66$

Thus, there are 66 ways to select 2 juniors from 12.

(3)

Compute the number of ways to select 3 seniors from 10 as follows:

${n\choose k}=\frac{n!}{k!(n-k)!}$

${10\choose 3}=\frac{10!}{3!(10-3)!}=\frac{10\times 9\times 8\times 7!}{2\times 3\times 7!}=120$

Thus, there are 120 ways to select 3 seniors from 10.

The total number of ways to form a student governance committee that must have 2 sophomores, 2 juniors and 3 seniors is:

Total number of ways = ${18\choose 2}\times {12\choose 2}\times {10\choose 3}$

$=153\times 66\times 120\\=1211760$

Thus, the total number of ways to form a student governance committee is 1,211,760.

7 0

3 years ago