The minimum surface area that such a box can have is 380 square
<h3>How to determine the minimum surface area such a box can have?</h3>
Represent the base length with x and the bwith h.
So, the volume is
V = x^2h
This gives
x^2h = 500
Make h the subject
h = 500/x^2
The surface area is
S = 2(x^2 + 2xh)
Expand
S = 2x^2 + 4xh
Substitute h = 500/x^2
S = 2x^2 + 4x * 500/x^2
Evaluate
S = 2x^2 + 2000/x
Differentiate
S' = 4x - 2000/x^2
Set the equation to 0
4x - 2000/x^2 = 0
Multiply through by x^2
4x^3 - 2000 = 0
This gives
4x^3= 2000
Divide by 4
x^3 = 500
Take the cube root
x = 7.94
Substitute x = 7.94 in S = 2x^2 + 2000/x
S = 2 * 7.94^2 + 2000/7.94
Evaluate
S = 380
Hence, the minimum surface area that such a box can have is 380 square
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Answer:
21C
22D
23B
24C
25A
Step-by-step explanation:
Answer:
The remainder is -2.
Step-by-step explanation:
According to the Polynomial Remainder Theorem, if we divide a polynomial P(x) by a binomial (<em>x</em> - <em>a</em>), then the remainder of the operation will be given by P(a).
Our polynomial is:
And we want to find the remainder when it's divided by the binomial:
We can rewrite our divisor as (<em>x</em> - (-1)). Hence, <em>a</em> = -1.
Then by the PRT, the remainder will be:
The remainder is -2.
Answer:
I tried my best to made the graph
3/-1/2
2/0/1
4/-2/3
2/0/1
1/+1/0
0/+2/1
Answer:
(-1, 4)
Step-by-step explanation:
Use of the coordinate plane.
The vertex of the parabola is 1 to the left and up 4.
Think of the vertex as where the curve starts.
