This question is incomplete, the complete question is;
Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places.
x² + 9y² = 9
(a) About
y = 3
(b) About
x = 3
Answer:
a) the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288
b) the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288
Step-by-step explanation:
a) the volume of solid of revolution
about y=3
Using SHELL METHOD;
Volume V = 2π . [tex]\int\limits^1_{y=-1} \,[/tex] (3-y) (2.3√(1-y²)) dy
= 12π . [tex]\int\limits^1_{y=-1} \,[/tex] (3-y) √(1-y²) dy
= 12π . [tex]\int\limits^1_{y=-1} \,[/tex] (( 3√(1-y²) - y(√(1-y²)) dy
= 12π[ [tex]\frac{3}{2}[/tex]π - 0 ]
= 18π² = 177.652879 ≈ 177.65288
Therefore, the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288
b)
the volume of solid of revolution
about x=3
Using SHELL METHOD;
Volume V = [tex]\frac{4}{3}[/tex]π . [tex]\int\limits^3_{y=-3} \,[/tex] (3-x) ([tex]2.\frac{1}{3}[/tex]√(9-x²)) dx
= [tex]\frac{4}{3}[/tex]π . [tex]\int\limits^3_{y=-3} \,[/tex] (3-x) √(9-x²) dx
= [tex]\frac{4}{3}[/tex]π . [tex]\int\limits^3_{y=-3} \,[/tex] (3√9-x² -x√(9-x²) dx
= [tex]\frac{4}{3}[/tex]π [ [tex]\frac{27}{2} \pi[/tex] - 0 ]
= 18π² = 177.652879 ≈ 177.65288
Therefore, the volume of solid revolution is 18π² = 177.652879 ≈ 177.65288
8k - 6 = 10k + 6
No idea how to figure this out
8k - 6 = 10k + 6
K= -6
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
8*k-6-(10*k+6)=0
Step by step solution :
STEP
1
:
Pulling out like terms
1.1 Pull out like factors :
-2k - 12 = -2 • (k + 6)
Equation at the end of step
1
:
STEP
2
:
Equations which are never true:
2.1 Solve : -2 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Solving a Single Variable Equation:
2.2 Solve : k+6 = 0
Subtract 6 from both sides of the equation :
Which gives k = -6
Answer: K = -6
Step-by-step explanation:
When you add or subtract on one side, you have to do the same to the other side. You also have to get all the numbers with vairables on one side, and the ones without on the other side.
When you have a positive number, if you want to bring it to the other side, you have to subtract it. For example, if you want to bring 8k from the left side onto the right side, you have to subtract 8k from a number on the right side.
For this equation, lets bring all the numbers with vairables onto one side, and the ones without vairables on the other side. The ones with vairables will be on the left, and the numbers without will be on the right.
To bring 10k from the right side to the left, we have to subtract 10k from 8k. 8k - 10k = -2k.
Now we have to bring the -6 from the left side onto the right side. Since -6 is a negative number, we have to make it into a positive number to swap it to the other side. So it because 6. We add 6 to -6, and 6 to 6. The leaves the left side to be -2k, and the right side to be 12.
Now we have to divide. 12 ÷ -2 = -6. Therefore, k = -6. I hope this helps, and good luck on whatever you're doing :D
A round pizza was cut into 8 equal pieces. 7 pieces were eaten. What is the angle measure of the piece not eaten?
Answer:
sorry didnt mean to answer
edit: it should be around 45
Help ASAP!!!! Will mark you brainliest
Answer:
OK so... I know the answer to x(4)+4x(3)+5x(2)-4x-4 = -4
The part i don't understand is the f(x)=k=1 part.
Step-by-step explanation:
So overall the only answer I know is -4 Sry i couldn't help more.
Brainliest?
what function equation is represented by the graph
f(x) = 4^x+5
f(x) = 3^x+4
f(x) = 3^x+5
f(x) = 4^x+4
Answer:
B
Step-by-step explanation:
We know that when x=0 y=5
B and D are the only ones that meet this criteria
we know that when x=2 y= 13 or so
D no longer works
it has to be B
6/q= k/27
what is q?
what is k?
The average cost for vacation is $1050 if a family borrows money for the vacation at an interest rate of 11.9% for six months what is the total cost of the vacation including the interest on the loan
How to write log6(35) in exponential form?
Answer:
10^35=6
Step-by-step explanation:
All you need to remember is the picture above and you could do it.
Please help me solve |m| = -10.
Answer:
m=10
Step-by-step explanation:
-10 is 10 away from zero which is what the lines are asking for
David keeps records of his monthly earnings. Last month he worked 140 hours and earned $3700. This month he worked 120 hours and earned $3200. Part A: what is David's rate of pay?
please help on this one.
Answer:
it's A
Step-by-step explanation:
look at the bolded line, it's after 4.4 which would mean z> 4.4
Answer:
A
Step-by-step explanation:
so we have a less than sign, which immediately tells us this going to be going left as 4.4 is greater. and obviously since the number is 4.4, the graph will have targeted that number. Hope this helps!
3(2k-5)=6(k-4)+9
Determine whether the equation has one solution, no solution, or infinitely many solutions
Answer:
many solutions
Step-by-step explanation:
3×2k=????
3×5=??
6×k=??
6×4=??
then put all those together in a 2 step equation and then add 9 to the answer
The equation 3(2k-5)=6(k-4)+9 has infinitely many solutions.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
3(2k-5)=6(k-4)+9
In the given equation k is the variable
Now apply distributive property to the RHS and LHS wherever it is required
6k-15=6k-24+9
6k-15=6k-15
Shift all terms to one side
6k-15-6k+15=0
0=0
Hence the equation 3(2k-5)=6(k-4)+9 has infinitely many solutions.
To learn more on Equation:
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Which of the following statements is true? A square is ALWAYS a rectangle. A rectangle is ALWAYS a square. A rectangle is NEVER a square. A square is NEVER a rectangle.
Answer:
A square is always a rectangle
Step-by-step explanation:
Every hour, a research assistant removes half the mass of a bacteria culture originally weighing 4,800 micrograms to observe under a microscope. The research assistant will stop this process once the mass is equal to 300 micrograms.
Which equation represents this situation, and after how many hours will the research assistant stop removing half the mass of the bacteria culture?
Answer:
Step-by-step explanation:
4,800 mcg × 0.5^t = 300 mcg
0.5^t = 1/16 = (1/2)⁴
t = 4
Answer:
[tex]4,800\left(\frac{1}{2}\right)^{t} \, = \, 300; \ 3 \ \text{hours}[/tex]
Step-by-step explanation:
Every hour, the research assistant is removing half the mass from the original 4,800 micrograms of the bacteria culture. So, the mass remaining after t hours can be represented by an exponential expression, a(b)t, where a is the initial mass of the bacteria culture and b is the base of the exponent that represents the decay factor. Since half of the mass of bacteria is being removed every hour, half of the mass remains. So, b = [tex]\frac{1}{2}[/tex]. The exponential expression for this situation is [tex]4,800\left(\frac{1}{2}\right)^{t}[/tex].
The research assistant will stop removing half the mass from the original bacteria culture after the original bacteria culture has a mass of 300 micrograms. Hence, set the expression for the mass remaining after t hours equal to 300.
[tex]4,800\left(\frac{1}{2}\right)^{t} \, = \, 300[/tex]
In order to solve this equation for t, the base needs to be isolated. Divide both sides of the inequality by 4,800.
[tex]\begin{array}{rclC40C40} 4,800\left(\frac{1}{2}\right)^{t} &=& 300\\ \left(\frac{1}{2}\right)^{t} &=& \frac{1}{16} \end{array}[/tex]
Next, rewrite the base of [tex]\frac{1}{16}[/tex] as a power of [tex]\frac{1}{2}[/tex]. Then, set the exponents equal to each other to solve for t.
[tex]\begin{array}{rclC40C40C30} \left(\frac{1}{2}\right)^{t} &=& \frac{1}{16} \\ \left(\frac{1}{2}\right)^{t} &=& \left(\frac{1}{2}\right)^{4} \\ t &=& 4 \end{array}[/tex]
So, after 4 hours the research assistant will stop removing half the mass of the bacteria culture.
Please help ASAP really need this
Answer:
[tex]21.79 + c \leq 25[/tex]
Joshua can spend up to 3.21 on a card.
Step-by-step explanation:
[tex]21.79 + c \leq 25[/tex] is the correct equation because Joshua is spending 21.79 on flowers, a certain amount on the card, and the maximum he can spend is 25. That is why you use the less than or equal to sign.
To solve, first subtract 21.79 from both sides to get: [tex]c \leq 3.21[/tex]. This means that Joshua can spend up to 3.21 on a card.
Hope it helps!
Suppose you buy 2 marbles for $0.16 each. You pay for it with 4 quarters. How much change should you get back? Enter your answer.
Answer: You should get 0.68 back
Step-by-step explanation: I just did a test and got 100%
Answer:
3 $0.16 = $0.48
or
4 $0.25 = $1.00 hope this helps
Step-by-step explanation:
Your cousin borrows $1125 to repair her car. The simple annual interest rate is 10%. She makes equal monthly payments of $25. How many years will it take to pay off the loan?PLEASE EXPLAIN. I know interest =. principal times rate times time
Answer:
neat
Step-by-step explanation:
Which expression is equivalent to 3x + 3 x + 3x
3x3
9x
9x3
27x
Pls help I have today to finish this
Answer:
50
Step-by-step explanation:
because 50 pints
Answer:
50
Step-by-step explanation:
Barbara has a part-time lawn-mowing job. The table below shows the amount of money Barbara earned for different numbers of hours of work:
Barbara's Earnings from Lawn Mowing
Number of Hours Worked Money Earned (dollars)
5 40
6 48
8
56
Part A: What are the missing numbers in the table? Show your work.
Part B: Barbara also works part time at a theme park. The ratio of the number of hours Barbara works at the park to the money she earns in dollars is 1:9. Create a table to show the money earned by Barbara for 5, 6, and 8 hours of work at the theme park.
Part C: How many more dollars does Barbara earn working at the theme park for 5 hours than mowing lawns for 5 hours? Show your work.
Answer:
Part A: 5-40
6-48
8-64
7-56
Part b:
1-9
5-45
6-54
8-72
Part c:
Theme park
5-45
Mowing lawns
5-40
$5
Step-by-step explanation:
Part A: 5x8=40
6x8=48
8x8=64
56/7=8
Part C: Every 5 hours working at the theme park she earns 45 dollars, when mowing lawns she earns 40 dollars 45-40 equal $5 extra dollars at the theme park.
Each student wrote a two-step equation. Peter wrote the equation 6x − 3 = 12, and Andres wrote the equation 24x − 12 = 48. The teacher looked at their equations and asked them to compare them. Complete the description of one way in which the equations are similar.
To get Andres' equation, you can multiply every number in Peter's equation by
__.
Answer:
Step-by-step explanation:They are essentially the same equation. Andre's equation is the same as Peter's, just all the numbers are multiplied by 4. Both equations have the same answer, which is 13/6, or 2.167
What is the value of (1)³ ?
Step-by-step explanation:
the value of 1³ is 1* 1*1 = 1
Hope it will help :)
Which one goes in the box ? Pls help I’ll mark you brainly
Answer:
5 is co efficient
8x is term
9 is constant
Step-by-step explanation:
On a coordinate grid, point A is at (−2.0, −3.4) and point B is at (2.0, −3.4). Point B is a reflection of point A across the
–axis. Input either a lowercase x or y.
Answer:
Y axis is correct :))
Step-by-step explanation:
I need help with this please
the correct answer is A) 10x + 30
Answer:
The answer is "10x+30"
Step-by-step explanation:
(-5y^2-9y-4)-(-2y^2-y+8)
Answer:
−3y2−8y−12
Step-by-step explanation:
Let's simplify step-by-step.
−5y2−9y−4−(−2y2−y+8)
Distribute the Negative Sign:
=−5y2−9y−4+−1(−2y2−y+8)
=−5y2+−9y+−4+−1(−2y2)+−1(−y)+(−1)(8)
=−5y2+−9y+−4+2y2+y+−8
Combine Like Terms:
=−5y2+−9y+−4+2y2+y+−8
=(−5y2+2y2)+(−9y+y)+(−4+−8)
=−3y2+−8y+−12
Answer:
[tex]-3y^2-8y-12[/tex]
Step-by-step explanation:
Simplify each term.
[tex]-5y^2-9y-4+2y^2+y-8[/tex]
Simplify by adding terms.
[tex]-3y^2-8y-12[/tex]
hope this helps :)
In a student council election, Kyle receives 54 votes for president. If Kyle receives 60% of the votes, how many students vote in the election?
Answer:
90
Step-by-step explanation:
60%-> 54
100%-> 90
There are 90 students vote in the election.
What is mean by Percentage?A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.
To Calculate the percent of a number , divide the number by whole number and multiply by 100
Given that
In a student council election, Kyle receives 54 votes for president.
Now,
Let total student votes in election = x
Hence we can formulate
60% of x = 54
60/100 × x = 54
60x = 5400
x = 90
Therefore, There are 90 student votes in the election.
Learn more about the percent visit:
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Help me plzzz I will give the Brainliest!!!
Answer:
24 Blocks
Step-by-step explanation:
Michelle is purchasing a new picture frame to hang in her bedroom. The picture frame is square shaped. What is the area of the interior of the picture frame in terms of c and d?
can yoy please help solve yhis problem.2/5b+1=11
Answer:
(2/5)*b+1 = -11 // + 11
(2/5)*b+1+11 = 0
2/5*b+12 = 0 // - 12
2/5*b = -12 // : 2/5
b = -12/2/5
b = -30
b = -30
Step-by-step explanation:
hope this helped :)
Step-by-step explanation: First: Multiply 2/5 by 2. 5x2=10. 10 then turns into o a whole number +1=11.
10+1=11
Pls help me I’ll make brainliest
Answer:
60 cents for 1 pound
Step-by-step explanation:
2 pounds = $1.20
1 pound = 60 cents