Answer:


Step-by-step explanation:
Given

--- lower diameter
--- upper diameter
Solving (a): The curved surface area
This is calculated as:

Where
--- lower radius
--- upper radius
And
---- l represents the slant height of the frustrum





So, we have:




Solving (b): The volume
This is calculated as:

This gives:





For this case we must simplify the following expression:
![\sqrt [3] {64 * a ^ 6 * b ^ 7 * c ^ 9}](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B64%20%2A%20a%20%5E%206%20%2A%20b%20%5E%207%20%2A%20c%20%5E%209%7D)
We rewrite:

So:
![\sqrt [3] {4 ^ 3 * (a ^ 2) ^ 3 * (b ^ 2) ^ 3 * b * (c ^ 3) ^ 3} =\\\sqrt [3] {4 * a ^ 2 * b ^ 2 * c ^ 3) ^ 3 * b} =](https://tex.z-dn.net/?f=%5Csqrt%20%5B3%5D%20%7B4%20%5E%203%20%2A%20%28a%20%5E%202%29%20%5E%203%20%2A%20%28b%20%5E%202%29%20%5E%203%20%2A%20b%20%2A%20%28c%20%5E%203%29%20%5E%203%7D%20%3D%5C%5C%5Csqrt%20%5B3%5D%20%7B4%20%2A%20a%20%5E%202%20%2A%20b%20%5E%202%20%2A%20c%20%5E%203%29%20%5E%203%20%2A%20b%7D%20%3D)
By definition of properties of powers and roots we have:
![\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}](https://tex.z-dn.net/?f=%5Csqrt%20%5Bn%5D%20%7Ba%20%5E%20m%7D%20%3D%20a%20%5E%20%7B%5Cfrac%20%7Bm%7D%20%7Bn%7D%7D)
So:
![4a ^ 2b ^ 2 c ^ 3 \sqrt [3] {b}](https://tex.z-dn.net/?f=4a%20%5E%202b%20%5E%202%20c%20%5E%203%20%5Csqrt%20%5B3%5D%20%7Bb%7D)
Answer:
Option B
Answer:
AP = 22
Step-by-step explanation:
In a triangle, the centroid divides the median in the ratio 2:1.
It is given that AD is the median and AD = 33
It is also given that P is the centroid on the median AD.
Therefore, P divides AD in the ratio 2:1.

AP = 2k and PD = k
AD = 33
AP + PD = 33
2k + k = 33
3k = 33
k = 11
So, AP = 2k = 2(11) = 22
Most of the time its juss common sense where you can point the right measurement with just sense i guess
Answer:
f(x)= $70 - $1.5*x
Step-by-step explanation:
You know your friend spends $ 5 to enter the fair and $ 15 for food. So the total you spent is given by:
$5 + $15= $20
Knowing that the trips at the fair cost $ 1.50 per trip, and with x being the number of trips, then the cost after x trips will be:
$1.5*x
So the money spent after x rides can be expressed as:
$20 + $1.5*x
Knowing that your friend has $90 when he goes to the fair, to calculate the amount of money he has left after x rides, the amount taken to the fair and the amount spent is subtracted:
$90 - ($20 + $1.5*x)
$90 -$20 -$1.5*x
$70 - $1.5*x
By calling the function f(x) used to determine the amount of money left after x trips, you can finally express:
<u><em>f(x)= $70 - $1.5*x</em></u>