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

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

solve ~
[tex]x {}^{2} - 5x + 6 = 0[/tex]

don't spam .-.
thankyou ~​

Answers

Δ = (-5)² - 4*1*6 = 25 - 24 = 1 = 1²

x' = (5 + 1) / (2*1) = 6/2 = 3

x" = (5-1) / (2*1) = 4/2 = 2

2 solutions : 2 and 3

x² - 5x + 6 = (x - 2) (x - 3)

1: The number of hours, h, spent studying and the score s, on a test (find the independent variable and the dependent variable.

Answers

Answer:

independent - number of hours (h)

dependent - the score (s)

Step-by-step explanation:

could someone explain to me how to multiple/divide equations in scientific notation im super confused :(

Answers

Hi you can change the scientific notation to standard notation. Then go from there

Find the LCM of 20, 35 & 50.

Answers

Answer:

Answer: LCM of 20,35 and 50 is 1400

Step-by-step explanation:


Rewrite the expression x -3/11
in radical form.

Answers

Hey i put the answer in the picture

Answer:

11x-3

11

Step-by-step explanation:

and that's the answer

JKL and RST are shown below. Which of the following statements is true? Look at picture.

Answers

Answer:

Triangle JLK congruent to Triangle RTS is the only true statement

Step-by-step explanation:

AngleJKL is not corresponding to AngleRTS because AngleRTS is a right angle and AngleJKL is not.

The triangles are congruent by HL because one leg and the hypotenuse are congruent.

Triangle congruence can be determined so the third statement is incorrect.

TR is not congruent to KJ. TR=3.7 and KJ=4.5

HELPPPPP PLEASE I DONT UNDERSTANDDDD

Answers

Answer:

Step-by-step explanation:

Solve for the equation equal to y

[tex]3x+4y=12\\4y=-3x+12\\y=\frac{-3}{4}+\frac{12}{4}[/tex]

The slope here is -3/4. The slope of a line perpendicular to the original has a negated and inverted slope. Therefore the slope is 4/3

help please .and thank u :)​

Answers

Answer:

5/8

Step-by-step explanation:

because 1 minus 3/8 is 5/8

I well give u brainliest
What are the x- and y-intercepts for the linear equation 2x – 4y = 8 ?

Question 6 options:

(4,0) and (0,-2)


(2,0) and (0,4)


(-2,0) and (4,0)


(-2,0) and (0,4)

Answers

The answer is a. (4,0) and (0,-2)

What is the solution to use the following equation 5(2x-6)+20=10

Answers

Answer:

first you distribute the five making it 10x-30+20=10

second you combine like terms making it 10x-10=10

third you isolate the variable making it 10x=20

Finally you divide both terms by ten giving you x=2 as your answer.

210 cartons is __% of 60 cartons

Answers

Answer:

should definitely be 28.56

An assembly line consists of 21 tasks grouped into 5 workstations. The sum of the 21 task times is 90 minutes. The largest assigned cycle time is 20 minutes. What is the efficiency of this line?

Answers

Answer:

ok

Step-by-step explanation:

10 cm equal to cm can you help me.

Answers

Answer:

1000cm

Step-by-step explanation:

there are 100cm in a meter. so we multiply 10 by 100 to get the amount of centimeters in 10 meters which is 1000cm

Answer: There Are 1000 Centimeters(Cm) In 10 Meters(M)

The height h(t) (in feet) of the seat of a child’s swing above ground level is given by the equation
below where t is the time in seconds after the swing is set in motion.
ℎ() = −1.1 cos ((2/3) ) + 3.1
a. Find the maximum and minimum height of the swing.
b. When is the first time after t = 0 that the swing is at a height of 3 feet?
c. When is the second time after t = 0 that the swing is at a height of 3 ft?

Answers

Answer: See below

Step-by-step explanation:

The function of the seat’s height from the ground level is given as,

[tex]h(t)=-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1[/tex]

Here, t denotes the time.

(a) The height will be maximum or minimum when the derivative of the function of height is equal to zero.

[tex]\begin{aligned}h^{\prime}(t) &=0 \\\frac{d}{d t}\left(-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1\right) &=0 \\-1.1 \times \frac{2 \pi}{3}\left(-\sin \left(\frac{2 \pi}{3} t\right)\right) &=0 \\t &=0,1.5\end{aligned}[/tex]

The height of the seat at time t = 0 s can be determined as,

[tex]\begin{aligned}h(0) &=-1.1 \cos \left(\frac{2 \pi}{3}(0)\right)+3.1 \\&=2 \mathrm{ft}\end{aligned}[/tex]

Therefore, the maximum height of the swing is 4.2 ft and the minimum height of the swing is 2 ft.

(b) The height of the swing is given as,

[tex]\begin{aligned}h &=3 \mathrm{ft} \\-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1 &=3 \\t &=0.7 \mathrm{~s}\end{aligned}[/tex]

Therefore, the first time after t = 0 s that the swing’s height of 3 ft is 0.7 s.

(c) The height of the swing is given as,

[tex]\begin{aligned}h &=3 \mathrm{ft} \\-1.1 \cos \left(\frac{2 \pi}{3} t\right)+3.1 &=3 \\\frac{2 \pi}{3} t &=1.47976+2 \pi \\t &=3.7 \mathrm{~s}\end{aligned}[/tex]

Therefore, the second time after t = 0 s that the swing’s height of 3 ft is 3.7 s.

Susan reads a book at a rate of 1 page every 3 minutes. If her reading rate remal
the same, which method could be used to determine the number of minutes for t
to read 18 pages?

Answers

18x3 = 54 1 page every 3 minutes 18 pages x3 = 54

Make an accurate drawing of two rectangles with the same perimeter, but different areas. Indicate the dimensions of the rectangles, as well as the perimeter and the area in each figure.​

Answers

I don’t know what the answer is

A team sells their jerseys for 40% more than it costs to have them made. What is the selling price of a jersey that cost the team $25.

Answers

Answer:

$35.

Step-by-step explanation:

SP = 25 + 0.40*25

= 25 + 10

= $35.

eometry Part 4 - Lesson 1 Assessment - EDCP.MA004.D
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What is the area of a sector of a circle with a central angle of measure 180° and whose radius is 5
cm? Leave your answer in terms of I.

o
ле?
o com
35
O 2 cm

Answers

Answer: it would be 34

Step-by-step explanation:

What would you do if fear was not a factor and you could not fail?`

i know it's not a maths question but let's try

Answers

Answer:

Well, i would just say you just had to do your best in everything that you do. No pressure , no stress don't overwork yourself and simply take action. Then you will have a chance to get what you want because you tried your best to get to it. Although sometimes we don't get what we want, atleast we'll be closer. As they say, 'Aim for the sun to reach the moon"

Step-by-step explanation:

You're welcome

A city that has an elevation of 15 meters is closer to sea level than a city that has an elevation of -10 meters.

Answers

Answer:

Step-by-step explanation: Your answer will be -10 because even though -10 is much lower than 15 it’s still closer to sea level.

Find the missing side length using the Pythagorean Theorem.
a²+6² = ²

Answers

The missing length is 18

Using Pythagorean rule

Hyp^2 = Opp^2 + adj^2

Opp^2 = hyp^2 - adj^2

Opp^2 = 30^2 - 24^2

Opp^2 = 900 - 576

Opp^2 = 324

Opp = sqrt ( 324 )

Opp = 18

A gas tank holds exactly 14 gallons of gas. If the tank is 2/3 empty, how many gallons remain in the tank?

Answers

2/3 empty would mean 1/3 of the total would remain:


14 gallons x 1/3 = 4 2/3 gallons are left in the tank

Joy's class voted on whether or not to do science fair projects in groups. Out of 24 votes, 18
were in favor of working in groups. What percentage of the votes were in favor of working in
groups
Write your answer using a percent sign (%).
Submit

Answers

Answer:

75%.

Step-by-step explanation:

That would be (18/24) * 100

= 3/4 * 100

= 75%

The correct answer would be 75 percent

A manager drew this box-and-whisker plot to represent the number of minutes each of the company's 360 employees took on their break.

How many employees took a break that lasted between 37 and 41 minutes?

Select from the drop-down menu to correctly complete the statement.

About (blank) employees took a break that lasted between 37 and 41 minutes.

36
90
120
180

Answers

Answer:

on k12 im pretty sure its 90

Step-by-step explanation:

there is 360 minutes and between the 37 and 41 (this took me a while ) then you should get 90!!!!! hope this helped

write an expression to m+m+m+m that is a product of a coefficient and a variable

Answers

[tex]m+m+m+m=(1+1+1+1)m=4m[/tex]

10+500000000 wats the answer

Answers

Answer:

500,000,010

Step-by-step explanation:

The 10 would be added to the last 2 digits (00) of the number. Therefore, the last 2 digits (00) plus 10 would be 10. The remainder of the number would remain the same, making the answer: 500,000,010

how many cubic inches of hot air would be needed to completely inflate a 12 in diameter beach ball

Answers

Answer:

904.78 cubic inches

Step-by-step explanation:

Since a beach ball is a sphere, use the formula for volume, V = 4/3 * pi * r^3 to find the volume of the beach ball, using 6 for radius since diameter is two times the radius and the diameter is 12 inches. 4/3 * pi * 6^3 = 904.78, so that many cubic inches of air would be needed to inflate the beach ball.

Hopefully this helps- let me know if you have any questions!

Ms. Gardner is thinking of a number
The number is even.
It is not divisible by 6
It is not divisible by 7
it is not greater than 81
It is not less than 64

Answers

Answer:

74

Step-by-step explanation: 74 is not divisible by 6 or 9not nor 7 and it's less than 81 and greater than 64

Find the area. 9 cm 3 cm 12 cm 15_cm 3 cm​

Answers

Answer:

What shape is the object in question?

Find the volume. Please help! Thanks!
hehe

Answers

Volume of a Square Pyramid: 1/3 x length x width x height

Length = 2

Width = 2

Height = 3

Volume = 1/3 x 2 x 2 x 3

Volume = 1/3 x 4 x 3

Volume = 1/3 x 12

Volume = 4

Volume = 4 cm^3

Hope this helps!

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