Let S denote the plane region bounded by the following curves:
x=0, y=e^(x/6), y=e^(35/6)
Find the volume generated by rotating S about the y-axis:
Answers
The volume of the solid of revolution is approximately 37439.394 cubic units.
How to find the solid of revolution enclosed by two functions
Let be [tex]f(x) = e^{\frac{x}{6} }[/tex] and [tex]g(x) = e^{\frac{35}{6} }[/tex], whose points of intersection are [tex](x_{1},y_{1}) =(0,1)[/tex], [tex](x_{2}, y_{2}) = (35, e^{35/6})[/tex], respectively. The formula for the solid of revolution generated about the y-axis is:
[tex]V = \pi \int\limits^{e^{35/6}}_{1} {f(y)} \, dy[/tex] (1)
Now we proceed to solve the integral: [tex]f(y) = 6\cdot \ln y[/tex]
[tex]V = \pi \int\limits^{e^{35/6}}_{1} {6\cdot \ln y} \, dy[/tex] (2)
[tex]V = 6\pi \int\limits^{e^{35/6}}_{1} {\ln y} \, dy[/tex]
[tex]V = 6\pi \left[(y-1)\cdot \ln y\right]\right|_{1}^{e^{35/6}}[/tex]
[tex]V = 6\pi \cdot \left[(e^{35/6}-1)\cdot \left(\frac{35}{6} \right)-(1-1)\cdot 0\right][/tex]
[tex]V = 35\pi\cdot (e^{35/6}-1)[/tex]
[tex]V \approx 37439.392[/tex]
The volume of the solid of revolution is approximately 37439.394 cubic units. [tex]\blacksquare[/tex]
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Related Questions
to calculate 587 ÷ 1,000, how many decimal points to the left should the decimal in 587 move?
Answers
Answer:
3 decimal points
Step-by-step explanation:
The trick here is to count the zeros.
Verify that each equation is an identity.
Show Work plzz!!
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Answer:
Step-by-step explanation:
sin²x + cos²x = 1 ⇒ cos²x = 1 - sin²x
[tex]\frac{cos^2x}{cos^2x}[/tex] = 1
The probability of winning the 2010 Megamillions lottery was about 0.0000000057. Write the number in scientific notation.
Answers
Answer:
5.7 × 10^-9
Step-by-step explanation:
decimal point is 9 spots to the left that's why it's 10^-9
Marley had $495.66 in her bank account after she paid her monthly bills. She took her sister out to lunch, and paid $38.90. How much money does she have now?
Answers
Answer: the answer is $456.76
Step-by-step explanation: All you have to do is subtract 38.90 from 495.66 and get your answer
The width of a rectangle is six meters less than the length. The perimeter is 56 meters. Find the length and width (in meters)
Answers
18-6 is 12 you take away 6 because the width is 6 less then the length
12 times 2 is 24
36 + 24=56
therefore the length is 18 and the width is 12
joe has a handful of dimes and quarters that values to $5.30. He has one fewer than twice as many dimes than quarters. How many of each coin does he have?
Answers
Answer:
12 quarters 23 dimes
Step-by-step explanation:
x(0.25)+(2x-1)(0.10)=5.30
0.25x+0.2x-0.10=5.30
0.45x=5.40
x=12
12 quarters
12(2)=24-1=23 dimes
Joe has 12 quarters coins and 23 dimes coins .
What is equation ?Equation is a combination of mathematical variables, in which two mathematical expressions are equal.
Let the number of quarters be n,
Therefore the number of dimes will be 2n-1.
Given that,
The total value of dimes and quarters is $5.30.
Write above text in equation form.
(0.25)n+(0.10)(2n-1)=5.30
0.25n+0.20n-0.10=5.30
.45n=5.40
n=12
And 2n-1=23
Means Joe has 12 quarters coin and 23 dimes coins .
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What is the sum of the roots of the polynomial shown below?
f(x) = 3r?+ 12x² + 3x - 18
Answers
Answer:
24x+3
Step-by-step explanation:
This probability distribution shows the
typical grade distribution for a Geometry
course with 35 students.
Grade
А
B
C D
F
Frequency 5
10
15
3
2
Find the probability that a student earns a
grade of A, B, or C.
p = [?]
Enter a decimal rounded to the nearest hundredth.
Answers
Answer:
0.714
Step-by-step explanation:
P(A or B or C) = P(A) + P(B) + P(C)
=(5/35)+(10/35)+(15/35)
=25/35
=0.714
Probability that a student earns a grade of A, B, or C is equals to 0.86.
What is probability?
" Probability is defined as the ratio of number of favourable outcomes to the total number of outcomes."
Formula used
Probability = [tex]\frac{Number of favourable outcomes}{Total number of outcomes}[/tex]
According to the question,
Given,
Total number of students = 35
Number of students getting grade A = 5
Number of students getting grade B = 10
Number of students getting grade C = 15
Substitute the value in the formula of probability we get,
P(A or B or C) = P(A) + P(B) + P(C)
= [tex]\frac{5}{35} +\frac{10}{35} +\frac{15}{35}[/tex]
= [tex]\frac{30}{35}[/tex]
= 0.8571
= 0.86 (decimal rounded to the nearest hundredth)
Hence, probability that a student earns a grade of A, B, or C is equals to 0.86.
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The total current of a parallel circuit is 9+j2 amps and the current of one component of the circuit is 3−j5 amps. What is the current of the other component of the circuit?
Answers
Apply law of total resistance in parallel circuit
[tex]\\ \tt\hookrightarrow \dfrac{1}{R}=\dfrac{1}{R_1}+\dfrac{1}{R_2}[/tex]
[tex]\\ \tt\hookrightarrow \dfrac{1}{9+2J}=\dfrac{1}{3-5j}+\dfrac{1}{R_2}[/tex]
[tex]\\ \tt\hookrightarrow \dfrac{1}{R_2}=\dfrac{1}{9+2J}-\dfrac{1}{3-5J}[/tex]
[tex]\\ \tt\hookrightarrow \dfrac{1}{R_2}=\dfrac{3-5J-9-2J}{(9+2J)(3-5J)}[/tex]
[tex]\\ \tt\hookrightarrow R_2=\dfrac{(9+2J)(3-5J)}{-6-7J}[/tex]
Age If you add Natalie's age and Fred's age, the result is 40. If you add Fred's age to 4 times
Natalie's age, the result is 76. Write and solve a system of equations to find how old Fred and
Natalie are.
Answers
Answer:
Fred is 28 yrs old. Nathalie is 12yrs old
Step-by-step explanation:
Let Nathalie's age be x
Let Fred's age be a
x+a=40 yrs•••••1
4x+a=76yrs•••••2
a=40-x
Substitute a for 40-x in equation (2)
4x+40-x=76
3x=76-40
3x=36
x=12
a=40-12
a=28
What is the value of X in the equation
Answers
Answer:
X = 5 1/6 + 3/4 = 71/12
PLEASEE HELP WILL GIVE BRAINLIEST
Answers
Allen, Bill, and Carl split $2000 among them to be invested in different ways. Each begins with a different amount. At the end of one year, they have a total of $3000 dollars. Bill and Carl have both doubled their money, whereas Allen has managed to lose $200 dollars. What was Allen's original portion?
Answers
What is the length of the missing side if given the area of 11 square meters?
Answers
Answer:
the answer is use a app called m4thw4y its a great way to get all of your math right
HELP ASAP!!!!!!!!!!!!!
The sale price of a pair of pants is $20. This sale price is 80% of the original price.
What was the original price?
Enter your answer in the box.
Answers
Answer:
25
Step-by-step explanation:
I took the 2.04 Quiz: Percent Tables quiz on k12
the answer is 25
2.04 Quiz: Percent Tables
Please help and i will give 200 points next time NEED A ANSWER FAST
Answers
Answer:
I gotchu the answer is 47
described below.
raise v to the 5th power, then find the difference of the result and 2
Do not simplify any part of the expression.
Answers
Answer:
2x2x2x2x2, 32
Step-by-step explanation:
Basically just multiplying 2 by itself 5 times.
2x2=4
2x2x2=8
2x2x2x2=16
2x2x2x2x2=32
Please help me I really need this
Answers
Answer:
Step-by-step explanation:
Draw a horizontal line at the end of the 8 meter horizontal line.
Find the area of the horizontal rectangle
L = 8 + 3
W = 2
Area = L*w
Area = 11*2
area = 22 m^2
Now do the vertical rectangle
L = 8
w = 3
Area = L*w
Area = 8 * 3
Area = 24 m^2
Total Area = 24 + 22 = 46 m^2
ABC and edc are straight lines ea is a parallel to dB ec=11.5 dc=4.6 dB =3.8
Answers
Answer:
the answer is 9.5 cm
Step-by-step explanation:
so CD=CE=BD=AE\
CD=4.6cm
CE=11.5cm
BD=8.3cm so AE=BD times ce=3.8 times 11.5=4.6=9.5cm YOUR WELCOME
The measure of AE is 9.5 cm and the length of AB is 6.3 cm.
Given that, ABC and EDC are straight lines EA is a parallel to DB. EC= 11.5 cm, DC =4.6 cm DB =3.8 cm.
What are similar triangles?Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.
From the figure,
∠CAE=∠CEA (Corresponding angles of parallel lines are congruent)
∠CBD=∠CDB (Corresponding angles of parallel lines are congruent)
From AA similarity ΔCAE≈CDB
Now, EC/DC = AE/DB
⇒11.5/4.6 =AE/3.8
⇒ AE = (11.5 × 3.8)/4.6
⇒ AE = 9.5 cm
⇒11.5/4.6 =10.5/BC
⇒ BC = (4.6 × 10.5)/11.5
⇒ BC = 4.2 cm
Then, AB=10.5-4.2 = 6.3 cm
Therefore, the measure of AE is 9.5 cm and the length of AB is 6.3 cm.
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Find the value of t for which WXYZ is a parallelogram. A. 5 B. 15 C. 25 D. 30
Answers
Answer:
can u show a diagram
Step-by-step explanation:
Answer:
( C ) 25
Step-by-step explanation:
Inference: All _______ postulates and theorems prove ______.
Answers
Answer:
All conjecture postulates and theorems prove a logical argument.
This is my opinion
Step-by-step explanation:
Theorems are the basics of mathematics.
They are verified multiple times in past.
They are certified by all famous mathematicians of world.
Some famous theorems are
Pythagorean theoremThales theoremI need help with this please
Answers
Answer:
This alot but ill help you with 2 of them to learn em
Step-by-step explanation:
1) 2x^2 +5 =167
Subtract the 5 from both sides to get the equation 2x² = 162
Then divide the 2 from both sides to get x² = 81, Then square root from both sides to get x= 9
6) 2(2y +4)²=72
Divide 2 from both sides to get (2y+4)²=36
Then square root that to get 2y+4 = 6
subtract 4 from both sides to get 2y =2
Then divide both sides from 2. Y=2
Part 22. NO LINKS!!!! What is the area of this figure?
Answers
Answer:
479 yd²Step-by-step explanation:
To solve this question, I have divided the shape into squares and rectangles. Then, I found out the area of each square and rectangle. Lastly, I added up all the areas and found the area of the shape. Please consider looking at the picture uploaded to understand better.
When looking at the picture, we can say that the area is 55 + 120 + 304.
=> 55 + 120 + 304=> 175 + 304=> 479 yd²Hence, the area of the shape is 479 yd².
What percent of 300 is 2 1/2
Enter your percent as a fraction in simplest form by filling in the boxes
Answers
Answer:
the answer is 5/6
Step-by-step explanation:
I just used the formula I'll find the link for and a video to help me answer my question when I was taking the test. Sorry my explanation couldn't be of greater help! I 2 looked up the question but couldn't find the correct answer so I did my research that I'll post the links for.
HELP!!!!!!!!!!!! PLZZZZZZZZ!!!!!!!!!!!!!!!!!
Answers
Answer:
5x4=20 so, 2x10 also equals 20
Step-by-step explanation:
Last year, students planted 8 tomato plants and 16 pepper plants in a school
garden. This year, the students planted 15 tomato plants. They want to have the
same ratio of tomato plants to pepper plants as last year. Pepper plants cost
$4.33 each. What is the cost, in dollars, of the pepper plants for this year's garden
Answers
From the ratio gotten, the total cost of the pepper will be $129.90.
How to solve a ratioSince the students planted 8 tomato plants and 16 pepper plants in a school garden. The ratio will be:
= 8/16 = 1:2
This year, the students planted 15 tomato plants, the number of pepper will be:
= 15 × 2 = 30
Since pepper plants cost $4.33 each, the total cost will be:
= 30 × $4.33
= $129.90
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How do I solve the equation:
-3x + 2 (x + 3) = 6
Answers
Answer:
x = 0
Step-by-step explanation:
-3x + 2 (x + 3) = 6
-3x + 2x + 6 = 6
-x = 6 - 6
x = 0
Hope this helps!
Answer:
x=0
Step-by-step explanation:
step 1. -3x+2(x) +2(3)=6
-3x+2x+6=6
step 2. -x+6=6
step 3. -x+6-6= 6-6
step 4. x=0
what is 5 less than the product of 10 and c?
Answers
Hi, the equation you typed is 10c-5
less than is subtraction and the product of two numbers is multiplying them together.
Jennifer's school is selling tickets to a chorus concert. On the first day of ticket
sales, the school sold 3 senior citizen tickets and 1 child ticket for a total of $38.
On the second day of ticket sales, the school sold another 3 senior citizen tickets
and 2 child tickets for $52.
Answers
Answer:
senior: $8child: $14Step-by-step explanation:
The given price relations allow us to write two equations involving the prices of the tickets. Those can be solved to find ticket prices.
Let s and c represent the prices of senior and child tickets respectively. Then the described sales can be written as ...
3s +c = 38 . . . . first day's sales
3s +2c = 52 . . . second day's sales
__
Subtracting the first equation from the second eliminates the s variable and gives the price of a child ticket:
(3s +2c) -(3s +c) = (52) -(38)
c = 14 . . . . . simplify
Then the price of a senior citizen ticket can be found using the first equation:
3s +14 = 38 . . . . . substitute for c
3s = 24 . . . . . . . subtract 14
s = 8 . . . . . . . divide by 3
The price of a senior citizen ticket is $8; the price of a child ticket is $14.
does anyone know where y=x-8 is on a graph lol
