Answer:


Step-by-step explanation:
Given
Represent volume with v, height with h and radius with r

Required
Determine the values of h and r that uses the least amount of material
Volume is calculated as:

Substitute 432π for V

Divide through by π

Make h the subject:

Surface Area (A) of a cylinder is calculated as thus:

Substitute
for h in 


Factorize:

To minimize, we have to differentiate both sides and set 

Set 

Divide through by 


Cross Multiply


Divide through by 2

Take cube roots of both sides
![r = \sqrt[3]{216}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B216%7D)

Recall that:




Hence, the dimension that requires the least amount of material is when


Answer:
log(6) = x
Step-by-step explanation:
4log(216)=12x
Divide both sides by 12
log(216)/3 = x
Use properties of logs
log(216^(1/3)) = x
Simplify
log(6) = x
4y+25=3y+20
4y+5=3y
***y=5***
so you plug y into both
4(5)+25 and 3(5)+20
45, 100, and 35 are the measurements of the angles.
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal or initial amount of money invested.
R represents interest rate
T represents time
Considering the investment on account A,
I = $6.94
R = 3.7%
T = 9 months = 9/12 = 0.75 years
6.94 = (P × 3.7 × 0.75)/100 = 0.02775P
P = 6.94/0.02775 = $250
Considering the investment on account B,
I = $13.80
R = 2.3%
T = 18 months = 18/12 = 1.5 years
13.8 = (P × 2.3 × 1.5)/100 = 0.0345P
P = 13.8/0.0345 = $400
To determine the account that earned more interest in the first month,
250/9 = $27.8
400/18 = $22.2
Account A earned you the most interest the first month because $27.8 is higher than $22.2
Answer:
z= 37/23
Step-by-step explanation: