Question

If 1000 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

Answer 1

The area of the base is x^2> The height is h. Each side of the box has area xh. There are 4 sides of the box so the total surface area of the box is x^2+4xh and that is equal to 1000. Solve that equation for h:

x^2+4xh = 1000 h = (1000-x^2)/4x so the Volume = x^2[(1000-x^2)/4x]

Simplify and get V = 250x-x^3/4
The volume will be a maximum when its first derivative is 0.

V' = 250-3/4x^2
Set to 0 and solve. x=18.26
Now plug into the volume function to find the maximum volume:

V=250(18.26)-(18.26)^3/4
V= 4564.35 - 1522.10 =3042.25

Answer 2

Thank you so much!!! Can you by any chance solve this problem as well? I would reallyyy appreciate it.
A cylinder is inscribed in a right circular cone of height 3.5 and radius (at the base) equal to 5.5. What are the dimensions of such a cylinder which has maximum volume?

Answer 3

I will try as soon as I get done watching Hannity's interview with Newt

Answer 4

Ok my assignment is due in less than an hour though. Again thanks a lotttt

Answer 5

5.5/3.5=r/(3.5-x) Solve for r r=(38.5-11x)/7
Plug into V formula v = pir^2h V= pi[(38.5-11x^2/7]^2(x)
=pix/49(1482.25x-847x^2+121x^3)
V' = pi/49(1482.25-1694x+363x^2)
Set to 0 and use the quadratic formula

Answer 6

I only need the final answer. No explanation needed.

Answer 7

Please and thank you so much. Really appreciate it.

Answer 8

you will get (1694+ - 847)/726
V = 15.7

Answer 9

I need the dimensions not the volume. Like what is the height and radius when the volume is maximized???

Answer 10

r=3.66

Answer 11

not correct :(

Answer 12

due in 5 mins
pls help

Answer 13

h=2.33

Answer 14

both incorrect...

Answer 15

How do you know?

Answer 16

i submit it online and it tells me if the answer is incorrect

Answer 17

but i can try again

Answer 18

Should be close

Answer 19

A baseball team plays in he stadium that holds 68000 spectators. With the ticket price at 9 the average attendence has been 29000. When the price dropped to 8, the averege attendence rose to 34000.
a) Find the demand function p(x), where x is the number of the spectators. (assume p(x) is linear).

Im really sorry im annoying you with all these questions but im stressed because its due now...

Answer 20

let me know if you find out the right answer.

Answer 21

ok do you know what the demand function is?

Answer 22

p(x)=5000x-16000 ???

Answer 23

p(x)=-5000x + 64000 I think the slope is negative

Answer 24

p(x) = -5000x +74000