The area labeled B is 9 times the area labeled A. Express b in terms of a.
b=_____?
Answers
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
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!
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
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)
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.
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:
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)
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!
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
could someone explain to me how to multiple/divide equations in scientific notation im super confused :(
Answers
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:
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
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
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
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
210 cartons is __% of 60 cartons
Answers
Answer:
should definitely be 28.56
Rewrite the expression x -3/11
in radical form.
Answers
Answer:
11x-3
11
Step-by-step explanation:
and that's the answer
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
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)
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:
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
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
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
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.
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%
Find the area. 9 cm 3 cm 12 cm 15_cm 3 cm
Answers
Answer:
What shape is the object in question?
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.
help please .and thank u :)
Answers
Answer:
5/8
Step-by-step explanation:
because 1 minus 3/8 is 5/8
Find the LCM of 20, 35 & 50.
Answers
Answer:
Answer: LCM of 20,35 and 50 is 1400
Step-by-step explanation:
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.