Answer:
radius = 1.37 cm
height = 2.71 cm
Step-by-step explanation:
We are given volume = 16 m³.
Formula for volume of a cylinder is;
V = πr²h
Thus,
πr²h = 16
h = 16/πr²
Now formula for the surface area is;
S = 2πr² + 2πrh
Putting 16/πr² for h gives;
S = 2πr² + 2πr(16/πr²)
S = 2πr² + 2π(16/πr)
S = 2π(r² + 16/πr)
To minimize, we will find the derivative of S and equate to zero
S' = 2π(2r - 16/πr²) = 0
4πr - 32/r² = 0
4πr = 32/r²
r³ = 32/4π
r = ∛(32/4π)
r = 1.37 cm
From h = 16/πr²;
h = 16/(π × 1.37²)
h = 2.71 cm
Answer:
The answer is below
Step-by-step explanation:
The Royal Fruit Company produces two types of fruit drinks. The first type is 65% pure fruit juice, and the second type is 90% pure fruit juice. The company is attempting to produce a fruit drink that contains 85% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 80 pints of a mixture that is 85% pure fruit juice?
Answer: Let x be the number of pints of the first fruit juice (i.e 65%) and y be the number of pints of the second fruit juice (i.e 90%).
Since the total number of pints to make the 85% pure fruit juice is 80, it can be represented using the equation:
x + y = 80 . . . 1)
Also, x pints of the first juice = 0.65x, y pints of the second juice = 0.9y and 80 pints of the mixture to be produced = 80(0.85) = 68. Therefore:
0.65x + 0.9y = 68 . . . 2)
We have to solve equation 1 and 2 simultaneously, first multiply equation 1 by 0.65 to get equation 3:
0.65x + 0.65y = 52 . . . 3)
Subtract equation 3 from 2 and solve for y:
0.25y = 16
y = 16/0.25 = 64
y = 64 pints
Put y = 64 in equation 1:
x + 64 = 80
x = 80 - 64 = 16
x = 16 pints
Therefore 16 pints of the 65% pure fruit juice, and 64 pints of the 90% pure fruit juice is required to make 80 pints of 80% fruit juice.
Total members = 25
Number of males = 11
So, required ratio = 11/25
If I understand your question right, this is not necessary, but is very useful to keep problems organized.
