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3 years ago

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

Mathematics

1 answer:

Vanyuwa [196]3 years ago

8 0

Answer:

The integral diverges

Step-by-step explanation:

Consider the integral from 0 to infinity of

$xe^{4x}$

We can do this in parts

$\int {xe^{4x} } \, dx =\int {x} \, d(e^{4x})/4\\ = x/4 e^{4x}-e^{4x}/16$

When we substitute limits infinity we find that the values become infinity

Hence the integral diverges

The given improper integral diverges

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In the solution of the equation 5 + 3x = -2x + 9, 2 x is added to the equation first. which of the following should be done next

wariber [46]

Hi!

<h3>Let's do the first step (add 2x). </h3>

5 + 3x + 2x = -2x + 2x + 9

<h3>Our goal is to isolate x on one side, so the next step would be to subtract 5 (or add -5).</h3>

5 + -5 + 5x = 9 + -5

<h2>The answer is B. add -5</h2><h3><em>And if you want to finish solving, you would divide by 5 on both sides.</em></h3>

5x/5 = 4/5

x = 0.8

Hope this helps! :)

-Peredhel

4 0

3 years ago

Please explain this to me!

Charra [1.4K]

One meaning of a 'linear' equation is that if you draw the graph
of the equation, the graph will be a straight line.

That's an easy way to test the equation . . . find 3 points on the
graph, and see whether they're all in a straight line.

This equation is y = 4 / x .

To find a point on the graph, just pick any number for 'x',
and figure out the value of 'y' that goes with it.
Do that 3 times, and you've got 3 points on the graph.

Here ... I'll do 3 quick points:

Point-A: x = 1 y = 4 / 1 = 4
Point-B: x = 2 y = 4 / 2 = 2
Point-C: x = 4 y = 4 / 4 = 1

Look at this:

Slope of the line from point-A to point-B
= (change in 'y') / (change in 'x') = -2 .

Slope of the line from point-B to point-C
= (change in 'y') / (change in 'x') = -1/2 .

The two pieces of line from A-B and from B-C don't even have
the same slope, so they're not pieces of the same straight line !
So my points A, B, and C are NOT in a straight line.

So the equation is NOT linear.

Try it again with three points of your own.

5 0

3 years ago

A man has mislaid his wallet. He thinks there is a 0.4 chance that the wallet is somewhere in his bedroom, a 0.1 chance it is in

lana [24]

Answer:

a. Probability = 0.15

b. Probability = 0.3

Step-by-step explanation:

Given

$P(Bedroom) = 0.4$

$P(Kitchen) = 0.1$

$P(Bathroom) = 0.2$

$P(Living\ room) = 0.15$

Solving (a): Probability of being somewhere else

This is calculated by subtracting the sum of given probabilities from 1.

$Probability = 1 - (0.4 + 0.1 + 0.2 + 0.15)$

$Probability = 1 - 0.85$

$Probability = 0.15$

Solving (b): Probability of being in bedroom or kitchen

This is calculated as:

$Probability = P(Bedroom) + P(Kitchen)$

$Probability = 0.2 + 0.1$

$Probability = 0.3$

6 0

3 years ago

What is 4 3/8 - 2 2/3

docker41 [41]

6/3 + 2/3 = (6 + 2)/3:
4 + 3/8 - (6 + 2)/3

6 + 2 = 8:
4 + 3/8 - 8/3

Put 4 + 3/8 - 8/3 over the common denominator 24. 4 + 3/8 - 8/3 = (24×4)/24 + (3×3)/24 + (8 (-8))/24:
(24×4)/24 + (3×3)/24 + (8 (-8))/24

24×4 = 96:
96/24 + (3×3)/24 + (8 (-8))/24

3×3 = 9:
96/24 + 9/24 + (8 (-8))/24

8 (-8) = -64:
96/24 + 9/24 + (-64)/24

96/24 + 9/24 - 64/24 = (96 + 9 - 64)/24:
(96 + 9 - 64)/24

| 1 |
| 9 | 6
+ | | 9
1 | 0 | 5:
(105 - 64)/24

| 0 | 10 |
| 1 | 0 | 5
- | | 6 | 4

| 0 | 4 | 1:
Answer: 41/24 or decimal 1.70833333.....

7 0

3 years ago

A bakery uses 300 pounds of flour to make 120 wedding cakes of the same size. At this rate how many pounds of flour are needed t

slega [8]

Answer:

A: 2.5 pounds

Step-by-step explanation:

300 divided by 120 is 2.5

2.5 pounds per cake

3 0

3 years ago