Answer:
B
Step-by-step explanation:
We will be using the formula in looking for the volume of the cylinder which is
V = πr²h
where:
r = radius
h = height
V = volume
but in the problem V and r have values already:
r = 8
V = 4019.2
plug this in the volume equation:
V = πr²h
= 4019.2 = π* 8² * h
= 4019.2 = 64πh
= 4019.2 / 64π = h
so the answer is: h = 4019.2 /201.06193
= 19.99 is the height of the cylinder.
the assumption being that the first machine is the one on the left-hand-side and the second is the one on the right-hand-side.
the input goes to the 1st machine and the output of that goes to the 2nd machine.
a)
if she uses and input of 6 on the 2nd one, the result will be 6² - 6 = 30, if we feed that to the 1st one the result will be √( 30 - 5) = √25 = 5, so, simply having the machines swap places will work to get a final output of 5.
b)
clearly we can never get an output of -5 from a square root, however we can from the quadratic one, the 2nd machine/equation.
let's check something, we need a -5 on the 2nd, so

so if we use a "1" as the output on the first machine, we should be able to find out what input we need, let's do that.

so if we use an input of 6 on the first machine, we should be able to get a -5 as final output from the 2nd machine.

D. works because if you work it out that means 2n=140 and then divide by 2 which means n=70 and the other number is 71
The Pythagorean theorem formula for a triangle is A^2 + B^2 = C^2 where A and B are the sides and C is the hypotenuse.
The sides of the triangle shown are AB and BC and the hypotenuse is AC,
so the correct answer would be:
(AB)2 + (BC)2 = (AC)2, because 25 + 144 = 169