So check the picture below
notice, since you're cutting out a square, the sides must all be equal, thus the largest "x" can't be 2, half of 4, it has to be just less than 2 or it has no volume, so x<2, and can't be 0, because, you'd have no volume either, so x>0, so 0<x<2

anyway... so that'd be dv/dx... you can just run it through the quadratic formula to get the critical points, and run a first-derivative test on them, bearing in mind the range for "x", (0, 2)
Answer:
5in by 5in by 5in
Step-by-step explanation:
We are not told wat to find but we can as well find the dimension of the prism that will minimize its surface area.
Given
Volume = 125in³
Formula
V = w²h ..... 1
S = 2w²+4wh ..... 2
w is the side length of the square base
h is the height of the prism
125 = w²h
h = 125/w² ..... 3
Substitute eqn 3 into 2 as shown
S = 2w²+4wh
S = 2w²+4w(125/w²)
S = 2w²+500/w
To minimize the surface area, dS/dw = 0
dS/dw =4w-500/w²
0= 4w-500/w²
Multiply through by w²
0 = 4w³-500
-4w³ = -500
w³ = 500/4
w³ =125
w = cuberoot(125)
w = 5in
Get the height
125 =w²h
125 = 25h
h = 125/25
h = 5in
Hence the dimension of the prism is 5in by 5in by 5in
Answer:
Fraction: 7/9
decimal: 0.778
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
Answer:
Step-by-step explanation:
It appears to be the last step there that has evaded you. In the second line of work, you can see that what's in each set of parenthesis is exactly the same. Because of this, it is common and can be factored out. What's left is the 4x and the +5:
(5x - 3)(4x + 5)
That's factoring by grouping. It only works with polynomials that have an even number of terms so you can group them together in 2's.