If f(x) = 2x – 6 and g(x) = x – 2x2, find each value.<br><br><br> f(h + 9)

Determine whether the integral is convergent or divergent. ∫[infinity] 2 e^−1/x / x^2 dx : O Convergent O divergent If it is con

monitta

Let $f(x)=e^{-1/x}$ . Then $f'(x)=\frac1{x^2}e^{-1/x}>0$ for all $x\ge2$ , so $f$ is strictly increasing. As $x\to\infty$ , $e^{-1/x}\to e^0=1$ , so $f$ is bounded above by 1. This is to say,

$e^{-1/x}$

and the integral of $\frac1{x^2}$ converges over the same domain, so this integral must also converge by comparison.

We have, by setting $y=-\frac1x$ ,

$\displaystyle\int_2^\infty\frac{e^{-1/x}}{x^2}\,\mathrm dx=\int_{-1/2}^0e^y\,\mathrm dy=e^0-e^{-1/2}=1-\frac1{\sqrt e}$

8 0

3 years ago

7. Consider the purchase of two cereal boxes.

AveGali [126]

Answer:

a) 0.25

b) 0.25

c) 0.0625

Step-by-step explanation:

The complete question is:

Do you remember when breakfast cereal companies placed prizes in boxes of cereal? Possibly you recall that when a certain prize or toy was particularly special to children, it increased their interest in trying to get that toy. How many boxes of cereal would a customer have to buy to get that toy? Companies used this strategy to sell their cereal.

One of these companies put one of the following toys in its cereal boxes: a block (B), a toy watch (W), a toy ring (R), and a toy airplane (A). A machine that placed the toy in the box was programmed to select a toy by drawing a random number of 1 to 4. If a 1 was selected, the block (or B) was placed in the box; if a 2 was selected, a watch (or W) was placed in the box; if a 3 was selected, a ring (or R) was placed in the box; and if a 4 was selected, an airplane (or A) was placed in the box. When this promotion was launched, young children were especially interested in getting the toy airplane.

What is the probability of getting an airplane in the first cereal box?

Since the machine randomly selects toys, each toy has the same probability of being obtained in a cereal box.

Then, the total outcomes are 4 and the probability of getting an airplane in the first cereal box is 0.25 (25%).

What is the probability of getting an airplane in the second cereal box?

Two independent events do not change the probability of occurrence of one event or another.

The probability of getting an airplane in the second cereal box is 0.25 (25%).

What is the probability of getting airplanes in both cereal boxes?

P(1°∩2°)= P(1°) × P(2°) = $\frac{1}{4} \times \frac{1}{4} =\frac{1}{16}$

P(1°∩2°)= 0.0625 = 6.25%

4 0

3 years ago

Which of the following points represents the number 4-3i on the complex plane?

HACTEHA [7]

In the given point 4-3i, 4 is a real number and is positive and 3i is an imaginary number and is negative, so point T is on real number positive 4 and imaginary number -3i.

The answer would be D. T

8 0

3 years ago

If you earn $13/hour and you work 2 hours overtime at a rate of time and a half, how much will you earn for each hour of overtim

ser-zykov [4K]

Answer:

32.50

Step-by-step explanation:

It is simple. You need to know the basics of money, fractions, and well... Math! :)

if you take 13 and multiply it by 2 you get 26

Take the 26 and put it aside -------------> 26

divide 13 in half. that would be 6.50

6.50 + 6.50 = 13

Now get the 26 --------------------------> 26

and add 6.50 to 26.

That would be 32.50!

Please make sure to follow and like! :)

3 0

3 years ago

7 45° x y y= √ help needed ?

Effectus [21]

Whats the total length that has to be solved???

4 0

3 years ago

If f(x) = 2x – 6 and g(x) = x – 2x2, find each value. f(h + 9)