Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis.
y = 3 − x
Answers
The volume of the solid generated by revolving the plane region y=3−x about the y-axis is 9π cubic units.
What is integration?It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
We have a function:
y = 3 - x
From the graph:
Shell radius = y
Height = 3 - y
From the shell method, we can write the integral as follows:
[tex]\rm Volume =2\pi\int\limits^0_{-3} {y(3-y)} \, dy[/tex]
[tex]\rm Volume =2\pi\int\limits^0_{-3} {(3y-y^2)} \, dy[/tex]
After solving the above definite integral, we will get volume:
Volume = 9π cubic units
Thus, the volume of the solid generated by revolving the plane region y=3−x about the y-axis is 9π cubic units.
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Related Questions
what is the simplest form of 2/3 - 1/4 =
Answers
Answer:
I got 5/12
Step-by-step explanation:
Hope this helped
ANSWER
The answer will be
Step-by-step explanation:
5/2=0•416666667
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Answers
Answer:
use sine or cosine rule
Step-by-step explanation:
that's the answer by using the sine rule
Answer:
Step-by-step explanation:
Question 13
You deposit $8,400 in an account earning 3.6% interest compounded monthly.
a. How much will you have in the account in 20 years?
b. How much interest will you earn?
Answers
Answer:
A = $17,238.65
I (interest) = $8,838.65
Step-by-step explanation:
Using the formula A = P(1 + r/n)^nt
A = $17,238.65
A = P + I where
P (principal) = $8,400.00
I (interest) = $8,838.65
First, convert R as a percent to r as a decimal
r = R/100
r = 3.6/100
r = 0.036 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 8,400.00(1 + 0.036/12)^(12)(20)
A = 8,400.00(1 + 0.003)^(240)
A = $17,238.65
Summary:
The total amount accrued, principal plus interest, with compound interest on a principal of $8,400.00 at a rate of 3.6% per year compounded 12 times per year over 20 years is $17,238.65
What is the volume of this object?
__u3
Answers
Answer:
15u³
Step-by-step explanation:
To find volume ↓
Volume
= length × width × height
= 2u × 2½u × 3u
= 15u³
Hope this helps =)
Find the volume of this shape. Show work and round to the nearest hundredth pls.
Answers
Answer:
V = 150.80 cu.ft.
Step-by-step explanation:
shape is a cone
[tex]V=\frac{1}{3} \pi r^{2} h[/tex]
[tex]r=8/2=4ft[/tex]
[tex]h=9ft[/tex]
Then:
[tex]V=\frac{1}{3} \pi (4)^{2} (9)=48\pi =150.80cu.ft[/tex]
Hope this helps
The diameter of a circle is 20 m. Find the circumference to the nearest tenth.
Answers
explanation- c=2 pie
d=2r
c=pie d=pie • 20 = 62.83185 m
Answer:
about 62.8 meters
Step-by-step explanation:
[tex]c = 20\pi = 62.8[/tex]
use this dataset for the next three questions: 5, 10, 12, 4, 6, 11, 13, 5 1. Calculate the mean. 2 Ultimate Medical Academy.
calculate the mean
Answers
Answer:
11.8
Step-by-step explanation:
5 + 10 + 12 + 4 + 6 + 11 + 13 + 51= 118
The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.
Count = 10
Sum = 118
Average = Sum / Count
118/10= 11.8
NEED THIS ASAP
Which statement describes (²) ?
n=1
The series diverges because it has a sum of 1.
O The series converges because it has a sum of 1.
O The series converges because it has a sum of 4.
The series diverges because it does not have a sum.
Answers
Answer:
option b
please mark me as brainliest
Answer: the series converges because it has a sum of 1 (b)
Step-by-step explanation:
bec i said so
please help this is urgent!!
Answers
Answer:
x=37 and scalene or right triangle
Step-by-step explanation:
Answer:
37°
Step-by-step explanation:
Any Triangle his total angles = 180
then: 53 + 90 + X = 180
then: X= 180 - (90+53)
= 37
Can you crack the code?
One number is
correct and placed
well
2
6
5
Nothing is right
3
8
7
One number is correct but wrongly placed
2
3
4
Two numbers are correct but wrongly placed
4
7
1
The numeric logic has a digit of
?
?
?
Answers
Answer:
1,2,4 is the correct answer
hope it'll help you out
Let Vector f = LeftAngleBracket 4, 3, 7 RightAngleBracket. and Vector g = LeftAngleBracket negative 1, 0, 2 RightAngleBracket. . Which graph shows Vector f + vector g. ?
Answers
Vectors simply means a quantity that has both magnitude and direction but not position e.g acceleration.
What is a vector?Your information is incomplete as the graphs aren't given. Therefore, an overview of vectors will be given.
In this case, vectors simply means a quantity that has both magnitude and direction but not position e.g acceleration, velocity, etc.
A vector can also be an element of the vector space. The direction is typically equal to the angle formed with the x-axis.
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If the radius of the circle below is 12 feet, find the area of the shaded region.
Answers
If the radius of the circle below is 12 feet is given then the area of the circle would be 452.16 ft square.
What is the area of the circle?The area of the circle is defined as the product of the pie and the square of the radius.
The area of the circle = [tex]\pi r^{2}[/tex]
If the radius of the circle below is 12 feet is given then
The area of the circle = [tex]\pi r^{2}[/tex]
[tex]\pi 12^{2} \\\\3.14 \times 144\\\\452.16[/tex]
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The fox population in a certain region has an annual growth rate of 5 percent per year. It is estimated that
the population in the year 2000 was 28400.
(a) Find a function that models the population t years after 2000 (t = 0 for 2000).
Your answer is P(t)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer should be an integer)
Answers
Answer:
See below
Step-by-step explanation:
population = 28400* ( 1+.05)^t t = years past 2000
8 years from 2000 pop = 28400(1.05)^8= 41 960 foxes
28 out of 35 students in ms. baileys class have older siblings. what percent of the class has older siblings
Answers
Answer:
80%
Step-by-step explanation:
We can get the percent value of the amount of students who have older siblings by diving 28 by 35.
28 / 35 = 0.8
We can convert this decimal into a percentage, giving us 80%.
Therefore, we know that 80% of the students in Ms. Bailey's class have siblings.
Write the algebraic expression that matches each graph.
(WILL GIVE BRAINLIEST!)
Answers
Answer:
y=11
Step-by-step explanation:
A circular flower garden surrounds a sculpture on a square base as shown. What is an expression for the area of the flower garden?
The number from the center of the square is 6x and the flower garden area is 4x
Answers
The given object is made up of circle and squares. The expression for the area of the flower garden is 4π²(9π - 4)square units
Area of composite objectThe given object is made up of circle and squares. To find the area of the garden, we wil use the expression
Area of the garden = area of circle - area of square
Find the area of circle
Area = πr²
Area = π(6π)²
Area pf circle = 36π³ square units
For the square
A = length * length
A = 4²π²
A = 16π²square units
Take the difference
D = 36π³ - 16π²
D =4π²(9π - 4)square units
Hence the expression for the area of the flower garden is 4π²(9π - 4)square units
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Answer: (pi * r^2) - (6x*4x)
Step-by-step explanation:
Since the formula of the area of a circle is pi * r^2 and the area of a square is base* height or in this case 6x*4x the answer is: (pi * r^2) - (6x*4x). The reason we subtract is because your trying to find the area of the square inside the circle.
A pizza dough recipe has a ratio of 5 cups of flour to 2 cups of water. There are ?
cups of flour per cup of water
Answers
Answer:
2.5 cups of flour per cup of water.
Step-by-step explanation:
We can divide the entire recipe by two, to get the amount of flour to 1 cup of water.
5/2 = 2.5
2/2 = 1
Therefore, 2.5 cups of flour needs 1 cup of water.
Answer:
There are 2.5 cups of flour per cup of water
Step-by-step explanation:
Step 1: Find the ration
Cups of Flour : Cups of Water
5 : 2
2.5 : 1
Answer: There are 2.5 cups of flour per cup of water
help me pwesssssssssss
Answers
Answer:
858 Remainder 4
Step-by-step explanation:
A whole number is squared. The result is between 200 and 260. The number is between:
A) 10 and 11
B) 15 and 16
C) 13 and 14
Answers
Answer:
B
Step-by-step explanation:
b is correct
The sum of two fractions is 2/3.
One fraction is 1/2.
What is the other fraction?
Answers
Answer:
0.5/3
Step-by-step explanation:
1/2 can be turned into 2/4, which means that to be 1/3, it has to be 1.5/3. 1.5/3 + 0.5/3 equals 2/3.
3 Select the correct answer. How can you write the expression 7(b – 2) in words? A. two subtracted from the quotient of seven divided by b B. seven added to difference of b minus two C. the quotient of seven divided by b minus two D. two subtracted from seven times b E. the product of seven and the difference of b minus two
Answers
Answer:
option E is correct.
Step-by-step explanation:
from the options, the correct answer is:
the product of seven and the difference of b minus two.
HOPE THIS HELPSPLEASE RATE AND MARK BRIANLIEST!!!The cost of gas increases monthly at a rate of 3.2%. If gas cost $1.75 today. How much will it cost in 3 years? ( round to the nearest cent (2 decimal places) )
Answers
Answer:
$1.92
Step-by-step explanation:
present cost = $1.75
time = 3 years
rate = 3.2%
cost after three years = present cost (1 +[tex]\frac{R}{100}[/tex] )^3
=$1.75 ([tex]\frac{103.2}{100}[/tex])^3
=$1.75*1.099
=$1.92
Threrefore , after 3 years cost of gas will be $1.92.
I don't know the answer ccuh
Answers
Answer:
minor arc
Step-by-step explanation:
This is a vocabulary question:
major arc: has a measure more than 180°minor arc: has a measure less than 180°semicircle: has a measure of exactly 180° (connects the ends of a diameter)__
Arc EA is a minor arc.
_____
Additional comment
In general, unless the two named points are the ends of a diameter, the arc is a minor arc. A major arc will generally be defined by designating a third point on the long arc connecting the same points on the circumference. For example, EDA, ECA, and EBA all designate the major arc connecting points E and A. (We can also use the descriptor, "major arc EA.") Without any of these extras designating the major arc, EA is considered to be the minor arc.
NOTES
Lucia and Jack are training for a marathon. Lucia started the first day by running 2 miles and adds 0.25 mile to her distance every day, Jack
started the first day by running 0.5 mile and adds 0.5 mile to his distance every day. If both continue this plan, on what day will Lucia and
Jack run the same distance?
Answers
Answer:
Day 3
Step-by-step explanation:
2+0.25+0.25=2+0.50=2.50
0.5+0.5+0.5=2+0.5=2.5=2.50
they both run 2.50 miles on day three
6x -3y -15 = 0 please solve for me
Answers
Step-by-step explanation:
Add 3y to both sides
6x-3y- 15 + 3y =0+3y
Simplify
6x- 15 =3y
Add 15 to both sides
6x-15 + 15 =3y + 15
Simplify
6x =3y+ 15
Divide both sides by6
6x/6= 3y/6+ 15/6
x=y+5/2
PLEASE HELP!!!!!
Abigail is studying for the school spelling bee. She already knows 204 words from the vocabulary list. Each day, she learns
24 additional words from the vocabulary list.
Which equation can be used to determine the total
number of words Abigail knows from the vocabulary list, y, over x days?
• A. y=24-204
•b y=24+204
• y=24(x+204)
Answers
Answer:
I think that it is y=24(x+204)
okay so x is the number of days and you would multiply that by 24 because that’s how many words she learns each day and you would add 204 because that’s how many words she already knows. hope this helps
Estimate the amount of the tip by rounding the bill to the nearest dollar before calculating.
15% tip on a bill of $41.58 The amount of the tip is approximately $
Answers
Answer:
Approximately $6.24
Step-by-step explanation:
You have to multiply 41.58 by 0.15 (basically 15%) and you have your answer.
Question 7 of 10
How many different roots does the polynomial function, y = (x - 2)(+3)
have?
O A. 4
B. 3
O c. 2
O
D. 1
SUBMIT
Answers
c. 2
you should just get an app on ur phone its easier than asking here
Two different roots the given polynomial function have. Therefore, option C is the correct answer.
What is the solution of a quadratic equation?The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The given equation is y=(x-2)(x+3)
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.
Here, (x-2)(x+3)=0
(x-2)=0 and (x+3)=0
x=2 and x=-3
Therefore, option C is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
How many different roots does the polynomial function, y = (x - 2)(x+3)?
A. 4
B. 3
C. 2
D. 1
If x is 6 and y is -2 what’s the value of yx
Answers
Answer:
-12
Step-by-step explanation:
(6)(-2)= -12
6 multiply -2 equals 12.
Find the side length of a square with area 16/49 square inches
Answers
Answer: the correct answer is S= 4/7 inches.