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schepotkina [342]
3 years ago
8

Find the value of the integral that converges. ∫^-5_-[infinity] x^-2 dx.

Mathematics
1 answer:
Bingel [31]3 years ago
8 0

Answer:

\int_{-\infty}^{-5} x^{-2}dx= \frac{1}{5} + \lim_{x\to -\infty} \frac{1}{x} =\frac{1}{5}

Because the \lim_{x\to -\infty} \frac{1}{x} =0

The integral converges to \frac{1}{5}

Step-by-step explanation:

For this case we want to find the following integral:

\int_{-\infty}^{-5} x^{-2}dx

And we can solve the integral on this way:

\int_{-\infty}^{-5} x^{-2}dx= \frac{x^{-2+1}}{-2+1} \Big|_{-\infty}^{-5}

\int_{-\infty}^{-5} x^{-2}dx= -\frac{1}{x} \Big|_{-\infty}^{-5}

And if we evaluate the integral using the fundamental theorem of calculus we got:

\int_{-\infty}^{-5} x^{-2}dx= \frac{1}{5} + \lim_{x\to -\infty} \frac{1}{x} =\frac{1}{5}

Because the \lim_{x\to -\infty} \frac{1}{x} =0

The integral converges to \frac{1}{5}

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The length of a room is 19 1/2 feet. When using 1 /4 inch = 1 foot scale, what would be the length of the wall on a floor plan?
erastovalidia [21]

Answer:

234 inches

Step-by-step explanation:

There are 12 inches per foot 12/4 =1/4 inch

1/4 x 4 x 12 x 19.5 = 234inches.

4 0
3 years ago
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Q8 Q17.) Find the numbers.
Katarina [22]
Let x = the first number
      y = the second number
-------------------------------------
First: set up the equations.

Four times a first number: 4x
Decreased by a second number: - y
Is 4: = 4

4x - y = 4.

The first number increased by: x + 
three times the second number: 3y
is -25: = -25

x + 3y = -25.
------------------------
You can make your system of equations now.

4x - y = 4
x + 3y = -25

I would use substitution to solve these.

To do substitution, isolate a variable first, in one of the equations. I would probably isolate x in the second equation.

x + 3y = -25
x = -25 - 3y

Now, you can substitute -25 - 3y into 4x - y = 4, as x.

4x - y = 4
4(-25 - 3y) - y = 4

Now just solve for y.

-100 - 12y - y = 4
-13y = 104
y = -8

Now, you can put -8 as y into one of the original equations, I'll just use 4x - y = 4.

4x -  y = 4
4x - (-8) = 4
4x + 8 = 4
4x = -4
x = -1

So the first number is -1, and the second -2.
7 0
3 years ago
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A cone has a slant height of 25 inches and a radius of 7 cm what is the volume of the cone.
Sergeeva-Olga [200]

Answer:

3238.5

Step-by-step explanation:

6 0
3 years ago
Bryan has a bag containing 12 red marbles, 8 blue marbles, 5 green marbles and 3 yellow marbles. He will randomly select one mar
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Answer:

3/28

Step-by-step explanation:

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3 years ago
A counter top is 18 feet long and 3 feet wide. What is the area of the counter top in square meters? Use the conversion 1 foot =
podryga [215]

Answer:

Area of the counter top is 5.02\ m^2.

Step-by-step explanation:

Given:

Length of the Counter top = 18 feet

Width of the counter top = 3 feet

We need to find the area of the counter top is square meter;

Solution:

Now we need to find the area of the counter top is square meter.

But given data is in feet so we will first convert feet into meters.

1 foot = 0.305 meter.

So 18 feet = Number of meters in 18 feet.

By Using Unitary method we get;

Number of meters in 18 feet = 18\times 0.305 = 5.49\ m

Length of the Counter top = 5.49 m

Also 3 feet = Number of meters in 3 feet.

Again Using Unitary method we get;

Number of meters in 3 feet = 3\times 0.305 = 0.915\ m

Width of the counter top = 0.915 m

Now we know that;

Area of the counter top can be calculated by multiplying Length of the counter top with width of the counter top.

framing in equation form we get;

Area of the counter top = 5.49\times 0.915 = 5.0233\ m^2

Rounding up to 2 decimals we get;

Area of the counter top =  5.02\ m^2

Hence Area of the counter top is 5.02\ m^2.

3 0
3 years ago
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