folded box length =
folded box width =
folded box height =
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
Thanks for all your help
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.
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?
That middle term should be 25x- x^2.
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.=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
[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.
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.Also, how did you get (50-2x)/2
I understand the 50-2x, but all over the 2, how did you get that?