- #1

oreon

- 10

- 0

Hi Everybody

I have two max and min word questions,I didnt understand well how to solve this type question,thats why, I would like you to help me and show me how to solve these questions.I know some beginning steps and know all solution way.But the problem is I don't know how to use or do those steps.Could you show me but not only show also teach me with explaining the steps sothat I can see what you did.I will have a small test tomorrow, and there will be afew min max questions.I want a learn how to those and after you show me, I will work on similar questions like them.

I will wait your responde and helps...

Here are two questions.

----------------------

1)My first question is:

A silo has a hemisphrerical roof,is cylindrical sided and has a circular floor, all made of steel. find the dimensions of a silo with a volume of 755 cubic meters that uses the least amount of steel to build. justify your answer with calculus. so it is asking minimize surface area.

note:there is a picture of a silo but there isn't anything on the picture except there is r on the top and on the bottom.also there is a h left side of silo.

My approach is=

So the two parameters are the height, h, of the silo, and

the radius, r, of the silo. The volume will be the volume

of the cylinder plus the volume of the hemisphere:

V = (2/3)pi r^3 + pi r^2 h

So V is given in the problem, allowing me to solve

for h in terms of r.

The total area is the sum of the area of the hemisphere and

the area of the cylindrical part:

A = 2pi r^2 + 2pi rh

Substitute for h in the area equation, then take the

derivative to find dA/dr. Set it to zero and solve for r.

Then back-substitute to find h.

2)Second question is:

A rectangular garden laid out along your neighbor's lot line contains 432 square meters area.it is to be fenced on all sides. If the neighbor pays for half the cost of the shared fence and fencing costs $35 per meter. what should the dimensions of the garden be so that YOUR COST is a minimum? justify your answer with calculus. so it is asking minimize cost of fence ,

not minimum perimeter.

note:there is a rectangular picture. top side of rectangular is your fence,

left side is shared fence, right site is your fence and there is y and at the bottom your fence and there is x.

My approach is=

The parameters are length, L, and width, W. Let W be

along the shared lot-line.

A = LW

Where area, A, is given in the problem. From this I think I can find L in terms of W, or vice versa but I don't know how to do it right:)

C = 35 (2L + 1.5W)

Thank you very much for your helps.

I have two max and min word questions,I didnt understand well how to solve this type question,thats why, I would like you to help me and show me how to solve these questions.I know some beginning steps and know all solution way.But the problem is I don't know how to use or do those steps.Could you show me but not only show also teach me with explaining the steps sothat I can see what you did.I will have a small test tomorrow, and there will be afew min max questions.I want a learn how to those and after you show me, I will work on similar questions like them.

I will wait your responde and helps...

Here are two questions.

----------------------

1)My first question is:

A silo has a hemisphrerical roof,is cylindrical sided and has a circular floor, all made of steel. find the dimensions of a silo with a volume of 755 cubic meters that uses the least amount of steel to build. justify your answer with calculus. so it is asking minimize surface area.

note:there is a picture of a silo but there isn't anything on the picture except there is r on the top and on the bottom.also there is a h left side of silo.

My approach is=

So the two parameters are the height, h, of the silo, and

the radius, r, of the silo. The volume will be the volume

of the cylinder plus the volume of the hemisphere:

V = (2/3)pi r^3 + pi r^2 h

So V is given in the problem, allowing me to solve

for h in terms of r.

The total area is the sum of the area of the hemisphere and

the area of the cylindrical part:

A = 2pi r^2 + 2pi rh

Substitute for h in the area equation, then take the

derivative to find dA/dr. Set it to zero and solve for r.

Then back-substitute to find h.

2)Second question is:

A rectangular garden laid out along your neighbor's lot line contains 432 square meters area.it is to be fenced on all sides. If the neighbor pays for half the cost of the shared fence and fencing costs $35 per meter. what should the dimensions of the garden be so that YOUR COST is a minimum? justify your answer with calculus. so it is asking minimize cost of fence ,

not minimum perimeter.

note:there is a rectangular picture. top side of rectangular is your fence,

left side is shared fence, right site is your fence and there is y and at the bottom your fence and there is x.

My approach is=

The parameters are length, L, and width, W. Let W be

along the shared lot-line.

A = LW

Where area, A, is given in the problem. From this I think I can find L in terms of W, or vice versa but I don't know how to do it right:)

C = 35 (2L + 1.5W)

Thank you very much for your helps.

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