I need to answer more questions to pm so i’m doing this
Answer:
A) Radius: 3.44 cm.
Height: 6.88 cm.
B) Radius: 2.73 cm.
Height: 10.92 cm.
Step-by-step explanation:
We have to solve a optimization problem with constraints. The surface area has to be minimized, restrained to a fixed volumen.
a) We can express the volume of the soda can as:
This is the constraint.
The function we want to minimize is the surface, and it can be expressed as:
To solve this, we can express h in function of r:
And replace it in the surface equation
To optimize the function, we derive and equal to zero
The radius that minimizes the surface is r=3.44 cm.
The height is then
The height that minimizes the surface is h=6.88 cm.
b) The new equation for the real surface is:
We derive and equal to zero
The radius that minimizes the real surface is r=2.73 cm.
The height is then
The height that minimizes the real surface is h=10.92 cm.
Bonnie paid 1.6$ per pound and Dan paid 2$ per pound
So the answer is 2$
Answer:
2.52.
Step-by-step explanation:
If one number is x then the other = 3x/8.
Also x - 3x / 8 = 4.2
x - 0.375 x = 4.2
0.625x = 4.2
x = 4.2 / 0.625
x = 6.72.
So the lesser number is 6.72 * 0.375 = 2.52.
3( to the power of 4) times 5(to the power of 3)