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Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by
y
=
x
2
,
y
=
0
, and
x
=
9
,
about the
y
-axis.
V
=
Answers
Answer:
[tex]\displaystyle V = \frac{6561 \pi}{2}[/tex]
General Formulas and Concepts:
Algebra I
FunctionsFunction NotationGraphingCalculus
Integrals
Integration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Integration Property [Addition/Subtraction]: [tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]
Shell Method: [tex]\displaystyle V = 2\pi \int\limits^b_a {xf(x)} \, dx[/tex]
[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is volumeStep-by-step explanation:
Step 1: Define
y = x²
y = 0
x = 9
Step 2: Identify
Find other information from graph.
See attachment.
Bounds of Integration: [0, 9]
Step 3: Find Volume
Substitute in variables [Shell Method]: [tex]\displaystyle V = 2\pi \int\limits^9_0 {x(x^2)} \, dx[/tex][Integrand] Multiply: [tex]\displaystyle V = 2\pi \int\limits^9_0 {x^3} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle V = 2\pi \bigg( \frac{x^4}{4} \bigg) \bigg| \limits^9_0[/tex]Evaluate [Integration Rule - FTC 1]: [tex]\displaystyle V = 2\pi \bigg( \frac{6561}{4} \bigg)[/tex]Multiply: [tex]\displaystyle V = \frac{6561 \pi}{2}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Applications of Integration
Book: College Calculus 10e
Related Questions
i gave someone a Brainliest pls
Answers
Answer:
i think the mistake was in step 1
Step-by-step explanation:
8. When someone buys a ticket for an airline flight, there is a 0.0995 probability that the person will not show up for the flight. An agent for Air America wants to book 24 people on an airplane that can seat only 22. If 24 people are booked, find the probability that not enough seats will be available. You must show your work using a calculator function to receive credit.
Answers
Answer:
0.2952
Step-by-step explanation:
Not enough seats will be available if 23 or 24 people show up.
Required probability = 24C24(0.9005)24 + 24C23(0.9005)23*0.0995 = 0.2952
If JKL - PNM. then M = L and the sides NP and
KJ are proportional.
True
Or
False???
Answers
Answer:
True
Step-by-step explanation:
In similarity triangles, corresponding angles are congruent and corresponding sides are in proportion.
Can you help me figure out this question I’ve been stuck on this for 20 minutes
Answers
Step-by-step explanation:
[tex]\dfrac{2x^2+x-6}{x+x-6} = \dfrac{(2x-3)(x+2)}{2(x-3)}[/tex]
IF A=[2,4] and B=[0,3] then BUA=?
Answers
Answer:
it equal:
answer is : [0234]
If you apply for a job with Globo Corp, there is a 75% chance that you will get an interview.
If you get an interview, there is a 48% chance that you will get the job.
If you apply for a job with Globo Corp, what is the probability that you will get the job?
Express your answer as a decimal, rounded to the nearest hundredth.
Answers
Answer:
The probability that you will get the job If you apply for a job with Globo Corp=0.36
Step-by-step explanation:
We are given that
If you apply for a job with Globo Corp, then the probability of getting interview P(A)=75%=0.75
If you get an interview, then the probability of getting job=P(B)=48%=0.48
We have to find the probability that you will get the job If you apply for a job with Globo Corp.
If you apply for a job with Globo Corp, the probability of getting job=[tex]P(A)\times P(B)[/tex]
If you apply for a job with Globo Corp, the probability of getting job=[tex]0.75\times 0.48[/tex]
If you apply for a job with Globo Corp, the probability of getting job=0.36
Hence, the probability that you will get the job If you apply for a job with Globo Corp=0.36
Complete the following statement.
Answers
Answer:
Hello dude
[tex] - 1 \frac{21}{24} + 1 \frac{22}{24} = + \frac{1}{24} [/tex]
so it's positive
HAVE A NİCE DAY
Step-by-step explanation:
GREETİNGS FROM TURKEY ツ
A modified roulette wheel has 36 slots. One slot is 0, another is 00, and the others are numbered 1 through 34, respectively. You are placing a bet that the outcome is an even number. (In roulette, 0 and 00 are neither odd nor even.) a. What is your probability of winning?
Answers
Answer:
[tex]P(win) = 0.4722[/tex]
Step-by-step explanation:
Given
[tex]n = 36[/tex] --- slots
[tex]Even = 17[/tex] i.e. even numbers between 1 and 34 (inclusive)
Required
[tex]P(win)[/tex]
The probabiity of winning is the number of even numbers divided by the total slot;
i.e.
[tex]P(win) = \frac{Even}{n}[/tex]
So, we have:
[tex]P(win) = \frac{17}{36}[/tex]
[tex]P(win) = 0.4722[/tex]
A file that is 266 megabytes is being downloaded . 14.4 % is completed , how many megabytes have been downloaded round to the tenth
Answers
Answer:
38.3 megabytes
Step-by-step explanation:
Find how many megabytes have been downloaded by multiplying 266 by 0.144:
266(0.144)
= 38.304
Round this to the nearest tenth:
= 38.3
So, 38.3 megabytes have been downloaded
Someone please help me ASAP!
Answers
Answer:
The 3rd
Step-by-step explanation:
If x goes to infinity, f(x) goes to infinity too:
[tex]lim \: \frac{2 {x}^{2} }{3x - 1} = lim \frac{2x}{3 - \frac{1}{x} } = \frac{ 2 \times \infty }{3 - 0} = \infty [/tex]
What is the length of my
?
M
3x
X + 8
7639
630
N
¿
O
A. 8
B. 4
C. 16
a
D. 12
Answers
Answer:
The length of MN is 4
Choose B
How to solve it and explain it
Answers
Answer:
28.27 in²
Step-by-step explanation:
The equation for the area of a circle is A = π[tex]r^{2}[/tex]. However, we got the diameter.
diameter = 2(radius), so:
A = [tex]\frac{1}{4}[/tex]πd².
A = 1/4 * π * 6² ≈ 28.27433
(sec theta - tan theta)²
Answers
Answer:
(sec θ - tan θ)²
= sec² θ –2 sec θ tan θ + tan² θ
The sum of 5 consecutive integers is 505. What is the second number in this sequence?
Answers
Answer:
The second number is 100.
Step-by-step explanation:
Let the first integer be x.
Then since the five integers are consecutive, the second integer will be (x + 1), the third (x + 2), fourth (x + 3), and the fifth (x + 4).
They total 505. Hence:
[tex]\displaystyle x+(x+1)+(x+2)+(x+3)+(x+4)=505[/tex]
Solve for x. Combine like terms:
[tex]5x+10=505[/tex]
Subtract 10 from both sides:
[tex]5x=495[/tex]
And divide both sides by five. Hence:
[tex]x=99[/tex]
Thus, our sequence is 99, 100, 101, 102, and 103.
The second number is 100.
In a test of a heat-seeking rocket, a first rocket is launched at 2000 fts and the heat-seeking rocket is launched along the same flight path 20 s later at a speed of 3000 fts. Find
the timest, and t, of flight of the rockets until the heat-seeking rocket destroys the first rocket
What are the times of the flight?
Answers
Answer:
Time of flight of first rocket = 60 seconds
Time of flight of second rocket = 40 seconds
Step-by-step explanation:
Let the time of flight of first rocket be t1.
Since the second rocket is launched 20 seconds later, then it means that;
t1 = t2 + 20
Where t2 is the time of flight of the second rocket.
When destruction has occurred, it means that both of the rockets would have covered the same distance.
We know that;
Distance = speed × time
Thus;
2000t1 = 3000t2
We know that t1 = t2 + 20
Thus;
2000(t2 + 20) = 3000t2
2000t2 + 40000 = 3000t2
3000t2 - 2000t2 = 40000
1000t2 = 40000
t2 = 40000/1000
t2 = 40 seconds
Thus;
t1 = 40 + 20
t1 = 60 seconds
There are 4 contestants in a beauty pageant. How many results are possible for the first, second, and third place?
Answers
Explanation:
There are 4 choices for first place, 3 choices for second place, and 2 choices for third place. Overall, there are 4*3*2 = 24 permutations.
Identify the quantities that are equivalent to 250 meters.
Ratio Conversion Table
kilometer (km) : meter (m) 1 : 1,000
meter (m) : centimeter (cm) 1 : 100
centimeter (cm) : millimeter (mm) 1 : 10
Answers
Answer:
1. Convert all measurements to meters:
2.5km * 1,000 = 2,500m;.250km * 1,000 = 250m; 2,500cm / 100 = 25m
25,000cm / 100 = 250m; 250mm / 1,000 =.25m
2.) Compare the converted measurements. Therefore, the quantities that are equivalent to 250m are:
.250km; 25,000cm
Step-by-step explanation:
On Monday, Ray had $153.75 in his bank account. On Tuesday, he withdrew $71.00 from his account. After depositing #292.50 on Wednesday, how much money did Ray have in his account
Answers
Answer:
$375.25
Step-by-step explanation:
[tex]===========================================[/tex]
Withdrew- taking out money (-)
Deposit- putting in money (+)
[tex]===========================================[/tex]
Ray started off with 153.75. He withdraws (-) 71.
[tex]153.75-71=82.75[/tex]
Then he deposits (+) 292.5.
[tex]82.75+292.5=375.25[/tex]
That's your answer!
I hope this helps ❤
A student selecting 3 classes for Winter quarter there are 4 drawing and design courses 3 general education courses and 3 other majors that can fit in their schedule it said student is only taking one course from each category determine the number of possible class schedules
Answers
Answer:
36 possible class schedules
Step-by-step explanation:
1st - 4 ways
2nd - 3 ways
3rd - 3 ways
4 x 3 x 3 = 36 possible class schedules
The number of possible class schedules is 36.
What is a permutation?The number of possible arrangements for a given set is calculated mathematically, and this process is known as permutation. Simply said, a permutation is a term that refers to the variety of possible arrangements or orders. The arrangement's order is important when using permutations.
Given:
A student selecting 3 classes for Winter quarter.
There are 4 drawing and design courses, 3 general education courses and 3 other majors that can fit in their schedule,
it said student is only taking one course from each category.
The possible class schedules,
= 4 x 3 x 3
= 36 possible ways.
Therefore, there are 36 possible ways.
To learn more about the permutation;
https://brainly.com/question/1216161
#SPJ2
find the measures of m and n.
Answers
Answer:
m = 4
n = 5
Step-by-step explanation:
[tex]m + 8 = 3m\\\\m - 3m = - 8\\\\-2m = - 8\\\\m = 4[/tex]
[tex]2n - 1 = 9 \\\\2n = 9 + 1\\\\2n = 10\\\\n = 5[/tex]
What is the measure of angle WZY? 54.5° 71° 125.5° 180°
Answers
Answer:
71
Step-by-step explanation:
The measure of angle WXY will be thee ame as the measure of the intercepted arc, 109°.
W and Y are both tangent to the circle; this means angle XWZ and angle XYZ are both 90°.
Every quadrilateral has a total measure of 360°; to find the measure of WZY, we subtract:
360-90-90-109 = 71°
The measure of angle WZY (∠WZY) is; 71°
What is the measure of the angle?From the attached image, we can say that the measure of ∠WXY will be the same as the measure of the intercepted arc, 109°.
Now, W and Y are both tangent to the circle and this means that ∠XWZ and ∠XYZ are both equal to 90°.
Now, every quadrilateral has a total internal sum of angles as 360°.
Thus, ∠WZY is gotten from;
∠WZY = 360 - (90 + 90 + 109)
∠WZY = 71°
Read more about angles in cyclic quadrilaterals at; https://brainly.com/question/24368895
Which of the following consists of discrete data?
A. Number of suitcases on a plane.
B. Amount of rainfall.
C. Hair color.
D. Tree height.
Answers
Answer:
A
Step-by-step explanation:
Number of suitcases on a plane is discrete because you can only have an integer amount. You can't have a fraction of a suitcase on a plane.
Sameer bought 8kg 500g mango and 5kg 250g apples and Anil bought 7kg 800g Guava and 4kg 625g Banana. Who bought more fruits? And by how much?.
Answers
Answer:
Below.
Step-by-step explanation:
Sameer:-
Number of mango's = total weight / weight of 1 mango
= 5 kg / 500g
= 5000/500
= 10.
Number of apples: = 5000/250 = 20.
Total number of fruit = 30.
Anil :-
Number of guava = total weight / weight of 1 guava
= 7 kg / 800g
= 7000/800
= 9.
Number of banana: = 4000/625 = 6.
Total number of fruit = 15.
Sameer bought the most fruit, 15 more than Anil.
Note: in Anil's case I rounded the values to the nearest whole number.
Cole biked at 5 mph for 1 hours. Which of the following choices show how far he biked?
A=5.5 miles
B=6.5 miles
C=7.5 miles
D=10 miles
Answers
Answer:
Most Likely A, 5.5 Miles
Step-by-step explanation:
However the question doesn't make sense as the logical answer is simply 5 miles, but the safest choice is 5.5
f(X) = 10x^3 find inverse
Answers
Or
10x10x10
Or
10/3
Answer: [tex]y=\sqrt[3]{\frac{x}{10} }[/tex]
Step-by-step explanation:
[tex]f(x)=10x^{3}\\y=10x^{3}[/tex]
switch the x and y:
[tex]x=10y^{3}[/tex]
Now solve for y:
[tex]x=10y^{3} \\\frac{x}{10} =y^{3} \\\sqrt[3]{\frac{x}{10} } =y\\[/tex]
Therefore, the inverse of that function is: [tex]y=\sqrt[3]{\frac{x}{10} }[/tex]
The length of a rectangle is 12 m and its diagonal is 15 m. find
the breadth and area of the rectangle.
Answers
Answer:
108 square metres
Step-by-step explanation:
A=√d square - l square
here
A = area
d= diagonal
l= length
When Claire chooses a piece of fruit from a fruit bowl, there is a 22% chance that it will be a plum, an 18%
chance that it will be an orange, and a 60% chance that it will be an apple. Which type of fruit is she least likely
to choose?
Answers
Answer:
Orange
Step-by-step explanation:
As the chance of choosing orange is 18% which is the least.
which exponential equation is equivalent to this logarithmic equation log x5 + log x12 =7
Answers
Answer:
x⁷ = 60
Step-by-step explanation:
Given :-
log x⁵ + log x ¹² = 7 .To Find :-
The expotential equation .Solution :-
Given logarithmic equation is ,
⇒ log x⁵ + log x ¹² = 7
⇒ log x ⁵ * ¹² = 7 [ log aⁿ + log aⁿ' = log aⁿ * ⁿ' ]
⇒log x ⁶⁰ = 7
In expotential form we can write it as ,
⇒ x⁷ = 60
From two points on the same level as the base of a tree, the angles of elevation to the top of the tree are found to be 24° and 46°. If the two points are 42 feet apart and on the same side of the tree, how tall is the tree? (Give your answer to the nearest tenth of an inch.)
Answers
Answer:
the answer is 32.8in.
Step-by-step explanation:
(sin 22)/42 = (sin 24)/x
x = 45.60
sin 46 = x/45.60
x = 32.80
32.8in.
hope it helped :)
mark me brainliest!
round 6.8 to nearest hundredth
Answers
Answer:
6.8
Step-by-step explanation:
The number is already rounded to the nearest tenth and hundredth.