I'm in algebra 1 please help i'm lost

Determine whether each integral is convergent or divergent. If it is convergent evaluate it. (a) integral from 1^(infinity) e^(-

AVprozaik [17]

Answer:

a) So, this integral is convergent.

b) So, this integral is divergent.

c) So, this integral is divergent.

Step-by-step explanation:

We calculate the next integrals:

a)

$\int_1^{\infty} e^{-2x} dx=\left[-\frac{e^{-2x}}{2}\right]_1^{\infty}\\\\\int_1^{\infty} e^{-2x} dx=-\frac{e^{-\infty}}{2}+\frac{e^{-2}}{2}\\\\\int_1^{\infty} e^{-2x} dx=\frac{e^{-2}}{2}\\$

So, this integral is convergent.

b)

$\int_1^{2}\frac{dz}{(z-1)^2}=\left[-\frac{1}{z-1}\right]_1^2\\\\\int_1^{2}\frac{dz}{(z-1)^2}=-\frac{1}{1-1}+\frac{1}{2-1}\\\\\int_1^{2}\frac{dz}{(z-1)^2}=-\infty\\$

So, this integral is divergent.

c)

$\int_1^{\infty} \frac{dx}{\sqrt{x}}=\left[2\sqrt{x}\right]_1^{\infty}\\\\\int_1^{\infty} \frac{dx}{\sqrt{x}}=2\sqrt{\infty}-2\sqrt{1}\\\\\int_1^{\infty} \frac{dx}{\sqrt{x}}=\infty\\$

So, this integral is divergent.

4 0

2 years ago

The length of a rectangle is seven times its width. The area of the rectangle is 175 square centimeters. Find the dimensions of

dimulka [17.4K]

Answer:

<h3>The length is 35cm</h3><h3>The width is 5cm</h3><h3 />

Step-by-step explanation:

Area of a rectangle = l × w

where

l is the length

w is the width

The length is seven times the width is written as

l = 7w

Area of the rectangle = 175 cm²

7w × w = 175

7w² = 175

Divide both sides by 7

w² = 25

Find the square root of both sides

w = √25

w = 5cm

But l = 7w

l = 7(5)

l = 35cm

The length is 35cm

The width is 5cm

Hope this helps you.

7 0

2 years ago

It is believed that 44% of all Americans eat breakfast every day. For a class project, you randomly select Clemson students and

GaryK [48]

Answer:

For this case we want to conduct a test in order to see if the proportion of Clemson students who eat breakfast is different from 0.44 (alternative hypothesis). And the complement would represent the null hypothesis, and the system of hypothesis for this case are:

Null Hypothesis: $p =0.44$

Alternative hypothesis: $p \neq 0.44$

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Solution to the problem

For this case we want to conduct a test in order to see if the proportion of Clemson students who eat breakfast is different from 0.44 (alternative hypothesis). And the complement would represent the null hypothesis, and the system of hypothesis for this case are:

Null Hypothesis: $p =0.44$

Alternative hypothesis: $p \neq 0.44$

8 0

2 years ago

In ΔRST, r = 40 cm, s = 88 cm and t=70 cm. Find the measure of ∠S to the nearest degree.

sdas [7]

Answer:

102.835≈103

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Juan bought 4 pounds of chocolate

Andru [333]

Answer:

Step-by-step explanation:

This is a system of equations. The 2 equations are:

4c + 2p = 16

2c + 3p = 12

Let's get rid of the p's first. Do this by multiplying the first equation by -3 and the second equation by 2 to get a new system that looks like this:

-12x - 6p = -48

4c + 6p = 24

Now add to get

-8c = -24 and

c = 3

That means that chocolate is $3 per pound. Now sub that back in to either one of the original equations to get the price for peanuts:

4(3) + 2p = 16 and

12 + 2p = 16 and

2p = 4 so

p = 2

The price for peanuts is $2 per pound.

6 0

2 years ago