The area labeled B is 9 times the area labeled A. Express b in terms of a.
b=_____?

Answers

Answer 1

Hi there!

For the graph on the left, we know that the area A is equal to:
[tex]A = \int\limits^a_0 {e^x} \, dx[/tex]

Area 'B' is 9 times this area, so:
[tex]B = 9 \cdot \int\limits^a_0 {e^x} \, dx[/tex]

We can evaluate the integral:
[tex]B = 9 \cdot \int\limits^a_0 {e^x} \, dx \\\\B = 9 \cdot e^x \left \| a}} \atop {0}} \right. \\\\B = 9 (e^a - 1)[/tex]

We also know that:
[tex]B = \int\limits^b_0 {e^x} \, dx[/tex]

Evaluate:

[tex]B = e^x \left \| b}} \atop {0}} \right. = e^b - 1[/tex]

Set the two equations for 'B' equal:
[tex]e^b - 1 = 9(e^a - 1)\\\\e^b - 1 = 9e^a - 9 \\\\e^b = 9e^a - 8[/tex]

Take the natural log of both sides:
[tex]ln(e^b) = ln(9e^a - 8)\\\\\boxed{b = ln(9e^a - 8)}[/tex]

Related Questions

Stacy performed an experiment in which she rolled a six-sided die multiple times. The results are shown below

Based on the results above, predict the number of times a 3 would be rolled if Stacy performs the experiment a total of 480 times

Answers

Answer:

5/9

Step-by-step explanation:

Let the probability of getting a multiple of 3 is "A"

Let the probability of getting an even number is "B"

Total number of outcomes=36

Total number of favourable outcomes of either a multiple of 3 or an even number are

(1,1) ,(1,2) ,(2,1) ,(1,3) ,(3,1) ,(2,2) ,(1,5) (5,1) ,(3,3) ,(2,4) ,(4,2) ,(2,6) ,(6,2) ,(3,5) ,(5,3) ,(4,4) ,(6,4) ,(4,6) ,(5,5) ,(6,6)

That is we have 20 favourable outcomes

Hence, Probability=\frac{\text{favourable outcomes}}{\text{total number of outcomes}}Probability=

total number of outcomes

favourable outcomes

Therefore, after substituting the values we get

probability=\frac{20}{36}probability=

After simplification we will get

probability=\frac{5}{9}probability=

Latoya just bought a refrigerator for $931. She paid $139.80 in a down payment and will pay the rest in 4 equal installments. How much does she need to pay for each installment?

Answers

Answer:

$197.80

Step-by-step explanation:

$931.00 - $139.80 = $791.20

$791.20 / 4 equal installments = $197.80

If 10 mm = 1 cm, how many millimeters are in 22 centimeters?

Group of answer choices

Answers

Answer:

220 millimeters

Step-by-step explanation:

If you take 22 cm * 10mm/1cm you get 220 mm

Please rate!

The Adventure Zone amusement park asked all of their employees who attend college how many hours of
homework they had per week and determined that they had an average of 24 hours of homework per
week.
Based on this data, which of the following conclusions are valid?
Choose 1 answer:
24% of all of the amusement park employees who attend school have homework each week.
24% of all of the amusement park employees who attend college have homework each week.
The amusement park employees who attend college have an average of 24 hours of
homework per week, but we cannot conclude anything about the percent of the population
who have homework.

Answers

The amusement park employees who attend college have an average of 24 hours of homework per week, but we cannot conclude anything about the percent of the population who have homework.

What is the valid conclusion?

The survey was to determine the average number of hours per week for employees that attended college. The result was that college students had an average of 24 hours of homework per week.

To learn more about surveys, please check: https://brainly.com/question/18521835

Answer:

the last

answer

Step-by-step explanation:

Kevin uses 36 ounces of dried apples and 18 ounces of
dried cranberries to make a fruit snack. He plans to sell the snack in 1\2
containers. How may containers will he fill? Will any fruit snack be left over?

Answers

Answer:

6 containers

6 ounces of fruit snack will be left over

Step-by-step explanation:

1 pound = 16 ounces

⇒ ¹/₂ pound = 8 ounces

Total weight = weight of dried apples + weight of dried cranberries

= 36 + 18

= 54 ounces

Containers needed = total weight ÷ weight of snacks in one container

= 54 ÷ 8

= 6.75

Therefore, he will fill 6 containers

Snack left over = total weight - (number of containers × weight of snacks one container will hold)

= 54 - (6 × 8)

= 54 - 48

= 6 ounces

the table shows the letter grades in science class for a random sample of 300 sixth grade students. Find the relative frequency for each letter grade to complete the table. Use pencil and paper. What additional information does the relative frequency give that the frequency doesn't? Explain.

Answers

Answer:

0.12,0.16,0.37,0.2,0.15

Step-by-step explanation:

A. 36 divided by 300 = 0.12

B. 49 divided by 300 = 0.16

C. 111 divided by 300 = 0.37

D. 60 divided by 300 = 0.2

F. 44 divided by 300 = 0.15

An investor just purchased a rectangular 1-acre retail lot for $250 a frontage foot. If she paid $100,000 total, what was the depth of the lot?

Answers

The answer is 218’. A foot front is measured by property. So for this question, you need to find the frontage feet.

what is the angle measure of an arc bounding sector with an area of 5pie square miles?

Answers

if the diameter is 20, the its radius must be half that or 10.

[tex]\textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ A=5\pi \\ r=10 \end{cases}\implies \begin{array}{llll} 5\pi =\cfrac{\theta \pi (10)^2}{360}\implies 5\pi =\cfrac{5\pi \theta }{18} \\\\\\ \cfrac{5\pi }{5\pi }=\cfrac{\theta }{18}\implies 1=\cfrac{\theta }{18}\implies 18=\theta \end{array}[/tex]

Frank ate 2/8 of the apple pie and
Jose at 3/8 of the cherry pie. How
much pie did Frank and Jose eat
altogether?

Answers

The answer is 5/8 because 2+3 is 5

Answer:

answer 5/8 because 2/8 + 3/8= 5/8

Find the area of the 2.5 m circle using 3.14 or 2/7 four pi

Answers

Answer:

Formula for area of circle;

A = π[tex]r^{2}[/tex]

Where 'π' represents pi (22/7 or 3.14), and 'r' is the radius which is being squared.

Plug in your values:-

A = π[tex]r^{2}[/tex]

A = 3.14(2.5^2)

A = 3.14(6.25)

A = 19.625 meters is your answer.

.325 equals what fraction

Answers

Answer:

according to desmos scientific calculator, the answer is 13/40

13/40 is the correct answer

The largest possible sum, less than 10, of two consecutive prime number is

Answers

Answer:

Step-by-step explanation:

Primes below 10 are 1,2,3,5,7

the two consecutive primes that would add up less than 10 would be 3 and 5. 3+5 = 8

Triangle ABC is isosceles.

Triangle A B C is shown. The lengths of sides A C and A B are congruent. Angle C A B is (x + 5) degrees. Angle A B C is (3 x) degrees.

What is the measure of angle C?

25°
30°
60°
75°

Answers

Answer: 75⁰°

Answer: 75⁰°Step-by-step explanation:

Answer: 75⁰°Step-by-step explanation:Using the Base Angles Theorem, we can conclude that <ABC and <ACB are congruent. The angles of a triangle add up to 180 degrees so we can write this equation to solve for x:x + 5+ 3x + 3x = 180simplify7x + 5 = 180subtract 5 from both sides

40 Points !!!!

Find the slope of line e.

a. -1/2

b. 1/2

c. -2

d. 2

Answers

maybe d i actually don’t know i’m just copying the first person who said that

Write the percent as a decimal.

78% =

Answers

0.78 or .78 and Brainly says I need twenty characters so here

Answer:

.78

Step-by-step explanation:

i belive its .78 as you can multiply any given number by both and get the same answer

There is a bag filled with 5 blue and 6 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting at least 1 blue?

Answers

The probability of getting at least 1 blue is 6/11

Let me know if you want an explanation :)

Subtract 55 from the sum of 234 and 8

Answers

234+ 8= 242
242-55=187
187 is the answer :)

Sketch a graph of − 3 x − y = − 4

Answers

Answer:

Step-by-step explanation:

Your backyard is 60 feet long and 50 feet wide. You install a circular pool with a 10-foot radius. What is the area of the backyard, in square feet, that can be planted with grass? Round your answer to the nearest whole number (Area of a rectangle = base x height) (Area of a circle = 3.14 x (radius) ^2)

Answers

Answer:

2686

Step-by-step explanation:

First let's find the area of the garden.

[tex]60 \times 50 = 3000ft {}^{2} [/tex]

Now let's find the area of the pool.

[tex]3.14 \times 10 {}^{2} [/tex]

[tex]3.14 \times 100 = 314ft {}^{2} [/tex]

Lastly subtract both products.

[tex]3000 - 314 = 2686[/tex]

What are the solutions to the system of equations graphed below?
A. (-2, 0) and (6,0)
B. (-3, -3) and (0,6 )
C. (-3,3) and (6,0)
D. (-2,0) and (2,0)

Answers

Answer:

looking at the straight line, it touches the axis at (-2,0) and (6,0)

Step-by-step explanation:

You spent $24 more than Pam. If you spent $82, how much money did Pam spend?Write and solve an equation.

Answers

Answer:

Step-by-step explanation:

its basically saying that pam spent 24 dollars less than you. soo 82 - 24 = 58

SOLVE THE INEQUALITY FOR X - 27 < 12

Answers

Answer:

x < 39

Step-by-step explanation:

x - 27 < 12

Add 27 to both sides.

x - 27 + 27 < 12 + 27

x < 39

[tex]\qquad\qquad\huge\underline{{\sf Answer☂}}[/tex]

Let's solve the inequality ~

[tex]\qquad \sf \dashrightarrow \: x - 27 < 12[/tex]

[tex]\qquad \sf \dashrightarrow \: x < 12 + 27[/tex]

[tex]\qquad \sf \dashrightarrow \: x < 39[/tex]

what is the area of the triangle

Answers

Answer:

Use this to answer your question :)

Step-by-step explanation:

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.

Answer:

54 units²

Step-by-step explanation:

Formula we use,

→ Area = ½ × b × h

Now the area of the triangle is,

→ ½ × b × h

→ ½ × 18 × 6

→ 9 × 6

→ 54 units²

Hence, the area is 54 units².

A theater is selling tickets for a musical. One attendee purchased 2 adult tickets and 5 student tickets, and the total cost was $64. Another attendee purchased 3 adult tickets and 4 student tickets, and the total cost was $68. Write a system of equations to find the price of an adult ticket and a student ticket. Let x be the price of an adult ticket and y be the price of a student ticket.

Answers

Answer:

Price of an adult ticket: 12$

Price of a student ticket: 8$

Step-by-step explanation:

Let x be the price of an adult ticket, and y be the price of a student ticket.

We have the equation:

2x + 5y = 64

3x + 4y = 68

=> x - y = 4

2x + 5y = 64

=> x = 4+y

2*(4+y) + 5y = 64

=> x = 4+y

8 + 2y + 5y = 64

=> x = 4 + y

7y = 56

=> x = 4 + y

y = 8

=> x = 12

y = 8

What's the value of X in the figure

145 (degrees) X (2x + 15)

Answers

Answer:

x=65°

Step-by-step explanation:

2x + 15= 145

2x+15-15=145-15 (Subtract)

2x=130 (Simplify)

2x/2=130/2 (Divide)

x=65 ← (Answer)

｡☆✼★━━━━━ ( ~ ) ━━━━━━━★✼☆｡

Kushbu decides to order a combination platter at her favorite restaurant. The platter comes with a choice of 2 entrees and 3 sides.

If there are 8 entrees and 6 sides available, how many different meal combinations could she order?

Enter your answer as an integer, like this: 42

Answers

Answer:

560

Step-by-step explanation:

To find the total combination you have to multiply the combination of entrees with combination of sides. U have to use the nCr equation to find these separate equations. n is number of items in total of the set and r is the number of items you want to choose from the set.

See the pic below for work

A card is drawn at random from a standard deck of playing cards (no jokers). If the card is a spade, the player wins $7; if it is not a spade, the player loses $1.

What is the expected value of this game? $________________

Answers

The expected value of the game is the mean value of the game

The expected value of the game is $1

How to determine the expected value?

There are 13 spades in a deck of card of 52

So, the probability of selecting a spade is:

P(Spade) = 13/52

Simplify

P(Spade) = 1/4

Winning = $7

The probability of not selecting a spade is:

P(Not spade) = 1 - 1/4

Simplify

P(Not spade) = 3/4

Lose = $1

The expected value of the game is:

[tex]E(x) = \sum x * P(x)[/tex]

This gives

[tex]E(x) = \frac 14 * 7 - 1 * \frac34[/tex]

Simplify

[tex]E(x) = \frac 74 - \frac34[/tex]

Evaluate

[tex]E(x) = 1[/tex]

Hence, the expected value of the game is $1

Answers

Answer:

Step-by-step explanation:

Which of the following expressions are equivalent to 6 + (-4) - 56+(−4)−56, plus, left parenthesis, minus, 4, right parenthesis, minus, 5?
Choose 2 answers:
Choose 2 answers:

(Choice A)
A
-(-6+4)-5−(−6+4)−5minus left parenthesis, minus, 6, plus, 4, right parenthesis, minus, 5

(Choice B)
B
6-4-(-5)6−4−(−5)6, minus, 4, minus, left parenthesis, minus, 5, right parenthesis

(Choice C)
C
6-(4+5)6−(4+5)6, minus, left parenthesis, 4, plus, 5, right parenthesis

(Choice D)
D
6+4-56+4−56, plus, 4, minus, 5

(Choice E)
E
-(-6)+(-4)-(-5)−(−6)+(−4)−(−5)

Answers

Choice a (-6+4)-5(-6+4)-5

Answer:

Step-by-step explanation:

−5+6−4

and

−4+(−5)+6

Solve and will mark brainliest

Answers

Answer:

24 degrees

Step-by-step explanation:

24 degrees because

angle a is 24 degrees

and since its the middles and main angle

24 degrees is the answer

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The area labeled B is 9 times the area labeled A. Express b in terms of a. b=_____?

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The area labeled B is 9 times the area labeled A. Express b in terms of a.
b=_____?