Find the volume between the cone
X= sqrt(y^2 + z^2) and the sphere
x^2 + y^2 + z^2 = 16.
Answers
The volume between the cone and the sphere is approximately 23.55 cubic units.
We are given that;
[tex]X= sqrt(y^2 + z^2)[/tex]
[tex]x^2 + y^2 + z^2 = 16.[/tex]
Now,
To find the volume between the cone and the sphere, we can use a triple integral in spherical coordinates.
The cone corresponds to the equation [tex]$\rho = 2\cos(\phi)$[/tex], where [tex]$\rho$[/tex] is the radial distance, [tex]$\phi$[/tex]is the polar angle, and [tex]$\theta$[/tex] is the azimuthal angle. The sphere corresponds to the equation [tex]$\rho = 4$[/tex]. The limits of integration are:
[tex]$0 \leq \theta \leq 2\pi$$0 \leq \phi \leq \frac{\pi}{4}$$2\cos(\phi) \leq \rho \leq 4$[/tex]
The volume element in spherical coordinates is [tex]$\rho^2\sin(\phi)d\rho d\phi d\theta$[/tex]
Therefore, the volume is:
[tex]$V = \int_{0}^{2\pi}\int_{0}^{\frac{\pi}{4}}\int_{2\cos(\phi)}^{4}\rho^2\sin(\phi)d\rho d\phi d\theta$[/tex]
Evaluating this integral, we get:
[tex]$V = \frac{32}{3}\pi - 8\sqrt{2}\pi + 16\pi$[/tex]
Therefore, by volume of cone the answer will be 23.55 cubic units.
Learn more about volume of cone here:
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Mrs adam walk between 4\10 and 6\10 mile every day. which is the best estimate of the number of miles she walks in 30 day
Answers
5/10 is between 4/10 and 6/10, so you could say they average 5/10 miles per day.
5/10 = 1/2
1/2 mile per day x 30 days = 15 miles
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Answer:
True
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Step-by-step explanation:
10x -4x = 6x
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If you combine like terms you subtract-4x from -6x which your get you 6x+3.
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Step-by-step explanation:
There are 6 numbers on a standard number cube. If the rolling is random, there should be a 1/6 chance of rolling a certain number. Basically, someone would theoretically roll each number 100 times out of 600. Because there are two numbers on the dice greater than 4, multiply 100 by 2 to find the answer.
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Answer:
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Step-by-step explanation:
For real numbers a and b, a number written in form a+bi is called a acomplex number. The value a is called the real part and b is called the imaginary part of complex number.
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8x + 2y = 46
Answers
Answer:
y=-17 x=10
Step-by-step explanation:
4x-3y=11
8x+2y=46
8x-6y-22 8x+2(-17)=46
8x+2y=46 8x-34=46
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Lacy graduated from college with $37,500 in student loans and is looking to refinance. The current interest rate is 4% for a 10 year loan or 6% for a 20 year loan.
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Loan B (20 years) results in monthly payments of $268.66.
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Answer:
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Loan A
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Answer:
d 40 times 23=920
Step-by-step explanation:
if you did 60 times 15= 900
the highest is 920
Why do people ask on here if there's some body that would go out with them? I don't get can some someone please tell why.
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The load that can be supported by a rectangular beam varies jointly as the width of the beam and the square of itsâ height, and inversely as the length of the beam. A beam feetâ long, with a width of inches and a height of inches can support a maximum load of pounds. If a similar board has a width of inches and a height of âinches, how long must it be to support âpounds?
Answers
The question is incomplete.Here is the complete question.
The load that can be supported by a rectangular beam varies jointly as the width of the beam and the square of its length, and inversely as the length of the beam. A beam 13 feet long, with a width of 6 inches and a height of 4 inches can support a maximum load of 800 pounds. If a similar board has a width of 8 inches and a height of 7 inches, how long must it be to support 1300 pounds?
Answer: It must be 392 inches or approximately 33 feet.
Step-by-step explanation: According to the question, the measures (width, length and height) of a beam and the weight it supports are in a relation of proportionality, i.e., if divided, the result is a constant.
For the first load:
width = 6in
height = 4in
length = 13ft or 156in
weight = 800lbs
Then, constant will be:
[tex]\frac{6.4^{2}}{156} k = 800[/tex]
[tex]k=\frac{800.156}{96}[/tex]
k = 1300
For the similar beam:
[tex]\frac{8.7^{2}}{L}1300=1300[/tex]
L = 49.8
L = 392in or 32.8ft
A similar board will support 1300lbs if it has 392 inches or 32.8 feet long.
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Answers
Answer:
0.02683<x<0.133173
Step-by-step explanation:
The confidence interval formula is expressed as;
CI = p ± z√p(1-p)/n
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CI = 0.08 ± 1.96√0.08(0.92)/100
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Answer:
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Answers
Answer:
I believe the answers are= 2, 3, 6, 8
Step-by-step explanation:
For #2, you would subtract 2 from both sides. 10-2=8. x=8.
For #3, you would add 4 to both sides of the equation, making the final answer: x=8
For #6, you would divide both sides by 3. 24 divided by three is 8.
For #8, I multiplied the whole equation by 8, which is the denominator of x/8. 1 times 8=8. The final answer would be x=8.
Hope this helps!
The equations whose solution is 8 will be x + 2 = 10, x - 4 = 4, 3x = 24, and x/8 = 1. Then the correct options are B, C, F, and H.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Let's check all the options. Then we have
A. x + 6 = 2, simplify the equation, then we have
x + 6 = 2
x = - 4
B. x + 2 = 10, simplify the equation, then we have
x + 2 = 10
x = 8
C. x - 4 = 4, simplify the equation, then we have
x - 4 = 4
x = 8
D. x - 2 = 10, simplify the equation, then we have
x - 2 = 10
x = 12
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x = 2
F. 3x = 24, simplify the equation, then we have
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x = 8
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x / 2 = 16
x = 32
H. x/8 = 1, simplify the equation, then we have
x/8 = 1
x = 8
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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x will equal 5.57!
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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