Question

an open paper bag with a height of y feet and a square base with a side length of x feet is shown (the top of the bag is open). the total surface area of the outside of the bag is 4 square feet.

1. what is the equation for the total surface area,T, of the outside of the bag interms of x and y? since the total surface area of the outside of the bag is 4 square feet, what is the equation for y in terms of x?

2. what is the equation for the volume, V, of the bag in terms of x and y? using the equation for y in terms of x from part (a), what is the equation for V(x), the volume of the bag, in te

Answer 1

total surface area of bag = area base + 4 times area of each side
= x^2 + 4xy = 4
4xy = 4 - x^2
y = (4-x^2)/ 4x

Answer 2

Volume of the bag = x^2 * y cu ft

Answer 3

4. what is the dimensions, x, of the base of the bag that will provide the greatest volume? what is the maximum voume of the bag? (a graphing calculator should be used to determine these answers?)
5. if the volume of the bag is 1/2ft^2, what is one possible value for x? write the equation that will be used to solve the problem and then use a graphing calculator to determine the answer

Answer 4

to get volume of bag in terms of x you plug y = (4-x^2)/ 4x into volume:

V = x^2* (4x-x^2) / 4x = x(4x=x^2)/4

Answer 5

sorry - thats V = x(4x-x^2) / 4

Answer 6

thank you! :D youre a lifesaver!

Answer 7

2. what is the equation for the volume, V, of the bag in terms of x and y? using the equation for y in terms of x from part a, what is the equation for V(x), the volume of the bag, in terms of x only?
3. in the context of the problem, what is the domain of V(x)

Answer 8

this simplifies to V = x^2 - x^3/4

if you draw the graph on ur calculator it will have two turning points one will be the maximum volume and you can find the value of x corresponding to this using the Gsolv function

Answer 9

domain of V(x) is values of valid x in this case it s
0 < x,< 4

Answer 10

if volume of the bag = 1/2
we have
1/2 = x^2 - x^3/4

x^3 / 4 - x^2 + 1/2 = 0
the equn. can be solved using eqaution function of your calculator
one possible value of x is 0.789

(the value for x which gives maximum valume is 2.667)

Answer 11

thank you!!!!