Please find the attachment.
Let x represent the side length of the squares.
We have been given that an open box is made from an 8 by ten-inch rectangular piece of cardboard by cutting squares from each corner and folding up the sides. We are asked to find the volume of the box.
The side of box will be
and
.
The height of the box will be
.
The volume of box will be area of base times height.
![\text{Volume of box}=(8-2x)(10-2x)\cdot x](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20box%7D%3D%288-2x%29%2810-2x%29%5Ccdot%20x)
Now we will use FOIL to simplify our expression.
![\text{Volume of box}=(80-16x-20x+4x^2)\cdot x](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20box%7D%3D%2880-16x-20x%2B4x%5E2%29%5Ccdot%20x)
![\text{Volume of box}=(80-36x+4x^2)\cdot x](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20box%7D%3D%2880-36x%2B4x%5E2%29%5Ccdot%20x)
Now we will distribute x.
![\text{Volume of box}=80x-36x^2+4x^3](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20box%7D%3D80x-36x%5E2%2B4x%5E3)
![V(x)=80x-36x^2+4x^3](https://tex.z-dn.net/?f=V%28x%29%3D80x-36x%5E2%2B4x%5E3)
Therefore, the volume of the box would be
.
Y = -x/3 + b1 = -3/3 + b
substitute values of point1 = -1 + b
then reduce2 = b
add one to both sides y = -x/3 + 2
Alright here goes, it’s 7.05024•10^11
Explination:
Maths…
Hope this helps!
-- You have two angles.
-- They're complementary . . . they add up to 90 degrees.
-- One is 4 times as big as the other one.
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-- The smaller angle has 1 share of the 90 degrees.
-- The bigger angle has 4 shares of the 90 degrees.
-- (The smaller one is 1/4 the size of the bigger one.
The bigger one is 4 times the size of the smaller one.)
-- When you add them together, you get 5 shares, totaling 90 degrees.
-- What's the size of each share ? It's 90/5 = 18 degrees.
-- The smaller angle gets one share . . . 18 degrees.
-- The bigger angle gets 4 shares. (4 x 18) = 72 degrees.
____________________________________
Check:
-- Is the small one 1/4 the size of the big one ? 18/72 = 1/4 Yes.
-- Are they complementary ? Do they add up to 90 degrees ?
18 + 72 = 90 Yes.
yay !