Need help with some precalculus problems.

[imported_takuma]

I Homeschool and am taking precal now and its not to bad but there are these two pos problems nethier me nor my dad can solve. Anyway if someone could help me with them and explain it that would be great. Thanks.

A rectangular city block was 40 meters long and 20 meters wide. Two city streets were widened by the same amount, decreasing the adjacent length and width of the block. Find the area of the block as a function of the number of meters the streets were widened. Give the domain of the function.



1. {x | x < 20 or x > 40}
2. {x | 0 <= x < 20}
3. {x | 0 <= 20}
4. {x | 0 <= 40}





A sphere with a radius of 1 meter circumscribes a cylinder. Which of the following would be the volume of the cylinder expressed as a function of its radius?



1. V = p r^2 sqrt(1-r^2)
2. V = 2p r^2 sqrt(1-r^2)
3. V = p r^2 ? p r^4
4. none of the above

 

[zbalat]

Ask your mom.

 

[arcenite]

I doubt you're going to get any help this late. I am too tired to even read the whole thing.

 

[chrisms]

Sorry I quit math sophomore year of high school

 

[Goosemaster]

I am too tired

 

[Legendary]

Why are you doing precalculus homework on a friday night?

 

[chuckywang]

You need more info for the second question, such as the height of the cylinder. Are you sure you didn't mistype it?

 

[gar3555]

Originally posted by: Legendary
Why are you doing precalculus homework on a friday night?

what r u doing posting on AT on a Friday night?

 

[Mo0o]

Originally posted by: gar3555

Originally posted by: Legendary
Why are you doing precalculus homework on a friday night?

what r u doing posting on AT on a Friday night?

what r u doing posting on AT on a Friday night?

 

[JustAnAverageGuy]

I'm glad today was my last today and I'm on summer break now.

That hurts my head just reading that stuff.

 

[chuckywang]

For the first question: the area is (40-x)*(20-x) where x is the length widened. The domain of the function is 0 <= x <= 20.

I think. If I understood the question.

 

[Legendary]

Originally posted by: gar3555

Originally posted by: Legendary
Why are you doing precalculus homework on a friday night?

what r u doing posting on AT on a Friday night?

My poker game got cancelled and I missed the bus to the city.

 

[Epic Fail]

Originally posted by: chuckywang
For the first question: the area is (40-x)*(20-x) where x is the length widened. The domain of the function is 0 <= x <= 20.

I think. If I understood the question.

This is more like a verbal problem than math problem.

 

[chuckywang]

Originally posted by: yamadakun

Originally posted by: chuckywang
For the first question: the area is (40-x)*(20-x) where x is the length widened. The domain of the function is 0 <= x <= 20.

I think. If I understood the question.

This is more like a verbal problem than math problem.

Freaking OP signed off. I hate it when they do that.

 

[imported_takuma]

Originally posted by: chuckywang
You need more info for the second question, such as the height of the cylinder. Are you sure you didn't mistype it?

Yeah that is the exact question looking at it right now. the other stuff was normal and easy but these ones are some random hard crap.

Also thanks alot chuckywang.

 

[MaxFusion16]

Originally posted by: takuma

Originally posted by: chuckywang
You need more info for the second question, such as the height of the cylinder. Are you sure you didn't mistype it?

Yeah that is the exact question looking at it right now. the other stuff was normal and easy but these ones are some random hard crap.

Also thanks alot chuckywang.

you don't need the height of the cylinder, the height is dependent upon the radius. The cylinder is fitted inside a sphere of radius 1m, so if the radius of the cylinder increases, the height decreases to accomodate the sphere.

write out all the information you have, establish relationships, and you'll have the answer.

 

[TuxDave]

Originally posted by: takuma

Originally posted by: chuckywang
You need more info for the second question, such as the height of the cylinder. Are you sure you didn't mistype it?

Yeah that is the exact question looking at it right now. the other stuff was normal and easy but these ones are some random hard crap.

Also thanks alot chuckywang.

I think it's assuming a cylinder with maximum volume? So the height of the cylinder equals the diameter of the top and bottom?

 

[MaxFusion16]

samething for the first question,

draw a diagram if you must, but just write out all the pieces of information you have, sort them into equations based on relationship, and you'll have the answer.

these are precursors to differential calculus, not very difficult, good luck.

 

[chuckywang]

Originally posted by: MaxFusion16

Originally posted by: takuma

Originally posted by: chuckywang
You need more info for the second question, such as the height of the cylinder. Are you sure you didn't mistype it?

Yeah that is the exact question looking at it right now. the other stuff was normal and easy but these ones are some random hard crap.

Also thanks alot chuckywang.

you don't need the height of the cylinder, the height is dependent upon the radius. The cylinder is fitted inside a sphere of radius 1m, so if the radius of the cylinder increases, the height decreases to accomodate the sphere.

write out all the information you have, establish relationships, and you'll have the answer.

No, you still have to prove that when you decrease the height to accomodate for the radius increase of the cylinder that the volume of the cylinder stays the same. This, however, is not true. There can be multiple cylinders inscribed in a sphere with different volumes.

 

[MaxFusion16]

Originally posted by: chuckywang

Originally posted by: MaxFusion16

Originally posted by: takuma

Originally posted by: chuckywang
You need more info for the second question, such as the height of the cylinder. Are you sure you didn't mistype it?

Yeah that is the exact question looking at it right now. the other stuff was normal and easy but these ones are some random hard crap.

Also thanks alot chuckywang.

you don't need the height of the cylinder, the height is dependent upon the radius. The cylinder is fitted inside a sphere of radius 1m, so if the radius of the cylinder increases, the height decreases to accomodate the sphere.

write out all the information you have, establish relationships, and you'll have the answer.

No, you still have to prove that when you decrease the height to accomodate for the radius increase of the cylinder that the volume of the cylinder stays the same. This, however, is not true. There can be multiple cylinders inscribed in a sphere with different volumes.

that's right, but the question is not asking you to prove that the volume is constant, instead it's asking you to write an equation describing the relationship between the cylinder's volume and its radius with the given sphere as a constraint.

 

[chuckywang]

Originally posted by: MaxFusion16

Originally posted by: chuckywang

Originally posted by: MaxFusion16

Originally posted by: takuma

Originally posted by: chuckywang
You need more info for the second question, such as the height of the cylinder. Are you sure you didn't mistype it?

Yeah that is the exact question looking at it right now. the other stuff was normal and easy but these ones are some random hard crap.

Also thanks alot chuckywang.

you don't need the height of the cylinder, the height is dependent upon the radius. The cylinder is fitted inside a sphere of radius 1m, so if the radius of the cylinder increases, the height decreases to accomodate the sphere.

write out all the information you have, establish relationships, and you'll have the answer.

No, you still have to prove that when you decrease the height to accomodate for the radius increase of the cylinder that the volume of the cylinder stays the same. This, however, is not true. There can be multiple cylinders inscribed in a sphere with different volumes.

that's right, but the question is not asking you to prove that the volume is constant, instead it's asking you to write an equation describing the relationship between the cylinder's volume and its radius with the given sphere as a constraint.

Ah...I thought r=radius of sphere. I was wondering why it first gave the radius of the sphere as 1m, but then it said the radius was r.

 

[chuckywang]

Well, then problem no. 2 is easy.

h/2 = sqrt(1-r^2).

Therefore V=pi*r^2*h = pi*r^2*2*sqrt(1-r^2).

 

[Yossarian]

who are you supposed to cheat off of when you homeschool? btw if you had a real teacher you would be able to ask them for help

 

[imported_takuma]

Lol cheat. There are counssulars or something I could ask but this seemed easier. And it was.