Thread: Confused on finding a function with multiple variables (Pizzabox)

1. Confused on finding a function with multiple variables (Pizzabox) (still confused)

Well the problem is this
1) Find a polynomial function p(x) that computes the volume of the box in terms of x. What is the degree of p?

2) Find a polynomial function q(x) that computes the exposed surface area of the closed box in terms of x. What is the degree of q? What are the explicit dimensions if the exposed surface of the area is 600 square inches?

I was having trouble with this, because there is 'x' in 2 sides.
At first I was thinking 50 + 20, but I don't know where that came from.
I was thinking that there was 3 'x' in one side, and 3 'x' in the other half
So it was like 2x^3? But I'm confused if that makes any sense at all.
May anyone help me start this off and explain the steps?

SOLVED
I understand the steps now and where the 600 came from

2. Re: Confused on finding a function with multiple variables (Pizzabox)

folded box length = $\displaystyle 20-2x$

folded box width = $\displaystyle \frac{50-2x}{2} = 25-x$

folded box height = $\displaystyle x$

3. Re: Confused on finding a function with multiple variables (Pizzabox)

Originally Posted by skeeter

folded box length = $\displaystyle 20-2x$

folded box width = $\displaystyle \frac{50-2x}{2} = 25-x$

folded box height = $\displaystyle x$
Oh.... I see now
Thanks
So to find the volume, would be multiplying the length, width, and height together right? (Since it's a rectangle?)
So (20-2x) * (25 - x) * (x), I think
500 - 20x - 50x + 2x^2
=500-70x+2x^2
Which, in order would be 2x^2 - 70x + 500
Though I am confused with to 'find the degree of 'p'
(70 +- sqrt 4900 - 40000)/2
Though that is wrong cause I can't get the square root of a negative number
I am confused on what is the 'degree'?
I thought it was like 90 degree, as in right angle, but that makes no sense, and I'm assuming it's not that type of degree.

4. Re: Confused on finding a function with multiple variables (Pizzabox)

V = (20-2x)(25-x)(x)

you forgot to multiply by the last x, the height

the degree of a polynomial is the highest power of x in the polynomial

5. Re: Confused on finding a function with multiple variables (Pizzabox)

Originally Posted by skeeter
V = (20-2x)(25-x)(x)

you forgot to multiply by the last x, the height

the degree of a polynomial is the highest power of x in the polynomial
Oh I get it now, thank you very much

6. Re: Confused on finding a function with multiple variables (Pizzabox)

So the second part is the surface area of a rectangle which is what I am on right now

7. Re: Confused on finding a function with multiple variables (Pizzabox)

Originally Posted by skeeter

folded box length = $\displaystyle 20-2x$

folded box width = $\displaystyle \frac{50-2x}{2} = 25-x$

folded box height = $\displaystyle x$
So I'm on the second part right now to find the surface area of the rectangle which is
2ab + 2bc + 2ac right?
a = 20-2x
b = 25-x
c = x
2(20-2x)(25-x) + 2(25-x)(x) + 2(20-2x)(2x)
=2(500-20x-50x+2x^2) + 2(25x+x^2) + 2(40x-4x^2)
=2(500-70x+2x^2) + 2(25x+x^2) + 2(40x-4x^2)
=1000-140x+4x^2+50x+2x^2+80x-8x^2
=1000-60x-2x^2
Though I think I messed up, it's suppose to be -50x instead of -60x, but I don't know how did I do it wrong
And how would you do "What are the explicit dimensions if the exposed surface of the area is 600 square inches?"

Also, how did you get (50-2x)/2
I understand the 50-2x, but all over the 2, how did you get that?

8. Re: Confused on finding a function with multiple variables (Pizzabox)

Originally Posted by Chaim
So I'm on the second part right now to find the surface area of the rectangle which is
2ab + 2bc + 2ac right?
a = 20-2x
b = 25-x
c = x
2(20-2x)(25-x) + 2(25-x)(x) + 2(20-2x)(2x)
=2(500-20x-50x+2x^2) + 2(25x+x^2) + 2(40x-4x^2)
=2(500-70x+2x^2) + 2(25x+x^2) + 2(40x-4x^2)
=1000-140x+4x^2+50x+2x^2+80x-8x^2
=1000-60x-2x^2
Though I think I messed up, it's suppose to be -50x instead of -60x, but I don't know how did I do it wrong
And how would you do "What are the explicit dimensions if the exposed surface of the area is 600 square inches?"

Also, how did you get (50-2x)/2
I understand the 50-2x, but all over the 2, how did you get that?
This is the part I am still confused with, help please?

9. Re: Confused on finding a function with multiple variables (Pizzabox)

Originally Posted by Chaim
So I'm on the second part right now to find the surface area of the rectangle which is
2ab + 2bc + 2ac right?
a = 20-2x
b = 25-x
c = x
2(20-2x)(25-x) + 2(25-x)(x) + 2(20-2x)(2x)
=2(500-20x-50x+2x^2) + 2(25x+x^2) + 2(40x-4x^2)
That middle term should be 25x- x^2.

=2(500-70x+2x^2) + 2(25x+x^2) + 2(40x-4x^2)
=1000-140x+4x^2+50x+2x^2+80x-8x^2
=1000-60x-2x^2
Though I think I messed up, it's suppose to be -50x instead of -60x, but I don't know how did I do it wrong
No, neither -50x nor -60 x. (-140+ 50+ 80)x= -10x. And with that "-x^2" in the middle term, you have (4- 2- 8)x^2= -6x^2. it should be 1000- 10x- 6x^2.

[quote] And how would you do "What are the explicit dimensions if the exposed surface of the area is 600 square inches?"
Solve 1000- 10x- 6x^2= 600 and use that value of x to find the three lengths.

Also, how did you get (50-2x)/2
I understand the 50-2x, but all over the 2, how did you get that?
The long side of the original rectangle was 50 and there are two sections of length x taken out so that leaves 50-2x. And both top and bottom are cut from that: each has length (50-2x)/2= 25- x.