Answer:
250π
1000π
Step-by-step explanation:
(refer to attached)
volume of cylinder is given by:
V = π r²h,
where r = radius of base and h = height of cylinder
Given r = 5 and h = 10, hence
V = π r²h
V = π (5)²(10)
V = π (25) (10)
V = 250π (answer)
For the second case, r = 10 cm
V = π r²h
V = π (10)²(10)
V = π (100) (10)
V = 1000π (answer)
Part a)
Answer: 5*sqrt(2pi)/pi
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Work Shown:
r = sqrt(A/pi)
r = sqrt(50/pi)
r = sqrt(50)/sqrt(pi)
r = (sqrt(50)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(50pi)/pi
r = sqrt(25*2pi)/pi
r = sqrt(25)*sqrt(2pi)/pi
r = 5*sqrt(2pi)/pi
Note: the denominator is technically not able to be rationalized because of the pi there. There is no value we can multiply pi by so that we end up with a rational value. We could try 1/pi, but that will eventually lead back to having pi in the denominator. I think your teacher may have made a typo when s/he wrote "rationalize all denominators"
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Part b)
Answer: 3*sqrt(3pi)/pi
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Work Shown:
r = sqrt(A/pi)
r = sqrt(27/pi)
r = sqrt(27)/sqrt(pi)
r = (sqrt(27)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(27pi)/pi
r = sqrt(9*3pi)/pi
r = sqrt(9)*sqrt(3pi)/pi
r = 3*sqrt(3pi)/pi
Note: the same issue comes up as before in part a)
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Part c)
Answer: sqrt(19pi)/pi
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Work Shown:
r = sqrt(A/pi)
r = sqrt(19/pi)
r = sqrt(19)/sqrt(pi)
r = (sqrt(19)*sqrt(pi))/(sqrt(pi)*sqrt(pi))
r = sqrt(19pi)/pi
Answer:
I cant tell is the 'x' is supposed to be a variable or a multiplication sign. IF its a multiplication sign then the answer is -30. Btu if its a variable then its in its simplest form there isn't any way to solve that equation.
Answer:
f(x) = 52
Step-by-step explanation:
f(x) does the same things as y, so when you get your answer, think of it as the value for y when x = - 4
The second thing you should know is that wherever you see an x on the right, you put in - 4
Let x = - 4
y = 2x^2 - 3x + 8
y = 2(-4)^2 - 3(-4) + 8
y = 2*16 - (-12) + 8
y = 32 + 12 + 8
y = 52
Be careful how you hand - 3x when -4 is put in for x. -3(-4) = 12 not - 12
f(-4) = 52
