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sveta [45]
4 years ago
9

Determine whether the improper integral converges or diverges, and find the value of each that converges.

Mathematics
1 answer:
Whitepunk [10]4 years ago
4 0

Answer:

\int^{-1}_{-\infty} \frac{2}{x^{3}}dx=-1

Step-by-step explanation:

We have:

\int^{-1}_{-\infty} \frac{2}{x^{3}}dx  

Now if integrate this using the power rule, we will have:

\int^{-1}_{-\infty} \frac{2}{x^{3}}dx=-\frac{1}{x^{2}}|^{-1}_{-\infty}  

Evaluating this integral we have:

\int^{-1}_{-\infty} \frac{2}{x^{3}}dx=-(\frac{1}{(-1)^{2}}-\frac{1}{(-\infty)^{2}})=-1

Let's recall that 1/∞ is 0.

Therefore this integral converge at -1.

I hope it helps you!

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Each interior angle of a regular polygon measures 140 degrees how many sides does the polygon have
anygoal [31]
The sum of the measures of the interior angles of a polygon of n sides is
180(n - 2)

If the polygon is regular, all angles are congruent, and each angle measures
[180(n - 2)]/n

Set the measure of one angle equal to 140, and solve for n, the number of sides.

[180(n - 2)]/n = 140

180(n - 2) = 140n

180n - 360 = 140n

40n = 360

n = 9

The number of sides is 9.

6 0
3 years ago
Read 2 more answers
Is it possible to draw a triangle whose sides are as follows? 6 cm, 7 cm, 17 cm. Give reasons to support your answer.
RUDIKE [14]

Answer:

No

Step-by-step explanation:

The sum of two random sides of a triangle must be bigger than the third side and their differences must be smaller than the third side

For example

3 - 4 - 5 can be made into a triangle because 3 + 4 > 5 and 4 - 3 < 5

6 0
4 years ago
Use the tables to complete the statements,
Blababa [14]

Answer:

Short term Capital gain and $1200

Step-by-step explanation:

Any investment held under a year falls under short term capital gain

5,000 X 0.24 = 1,200

6 0
3 years ago
The perimeter of a rectangular pool is 314 m.
ycow [4]

Answer:

The length is 91 meters

Step-by-step explanation:

The perimeter formula is 2W · 2L = 314

We know the width is 66 m, so we can then say:

132 · 2L = 314

-132          -132

2L = 182

L = 91

Hope this helped!

7 0
3 years ago
The sum of 4 times a number and 15 is 47. Find the number.
Bezzdna [24]

Answer:

The number is 8.

Step-by-step explanation:

Write an equation then solve by isolating the variable.

let x be the number

4x + 15 = 47  Subtract 15 from both sides

4x = 47 - 15

4x = 32     Divide both sides by 4

x = 32/4

x = 8

Therefore the number is 8.

7 0
3 years ago
Read 2 more answers
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