Answer:
The investment required is: $5687
Step-by-step explanation:
Future Amount A= $7000
Rate r = 6% =0.06
Time t = 4
Compounded Weekly = n= 52
We need to find Principal Amount P
The formula used is:
Putting values and finding P
So, The investment required is: $5687
Answer:
Minimum dimensions are r=3cm, h=9cm
Minimum Cost=$254.47
Step-by-step explanation:
Volume of a Cylinder=πr²h
Volume of the Open Top Cylinder=81π cm³.
Therefore:
πr²h=81π
The bottom costs $3 per cm² and the side costs $1 per cm².
Total Surface Area of the open top Cylinder= πr²+2πrh
Cost, C=3πr²+2πrh
As the Volume is fixed.
πr²h=81π
r²h=81
h=81/r²
Modifying C,
We differentiate C with respect to r
C'=
At the minimum cost, C'=0.
Next we solve C'=0 for r
6πr³-162π=0
6πr³=162π
r³=27
r=3
The dimensions of the cylinder at minimum cost are therefore:
r=3 cm
h=81/9=9cm
The minimum cost of the Cylinder
C=3πr²+2πrh
=(3XπX3²)+(2XπX3X9)
=$254.47