You are to construct a€cylindrical can out of tin that encloses a volume of exactly 100 cubic inches. to three significant figures, which dimensions (r and h) will give you the tin can that requires the least amount of metal?

The formula for volume of cylinder is:

V = π r^2 h

since volume is 100 cubic inches, so:

100 = π r^2 h

Rewriting in terms of h:

h = 100 / π r^2

The least amount of metal means least amount of surface area needed. The surface area of cylinder is:

A = 2 π r h + 2 π r^2

insert the value of h in terms of r:

A = 2 π r (100 / π r^2) + 2 π r^2

A = 200 r-1 + 2 π r^2

Take the 1st derivate and set to 0, dA/dr = 0:

dA/dr = - 200 r-2 + 4 π r

0 = - 200 r-2 + 4 π r

200 / r^2 = 4 π r

r^3 = 50 / π

r = 2.52 inches

So height h is:

h = 100 / π r^2

h = 100 / π (2.52)^2

h = 5.01 inches

Answers:

r = 2.52 inches

h = 5.01 inches

a revenue

step-by-step explanation:

a.) revenue   - income from selling goods and services

b.) assets - property owned by a person or company

c.) money - something traded for goods and services

d.) accounting- keeping of financial records

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1