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:
Option B is not a justification
Step-by-step explanation:
Option A is a justification (to get two pair of similar triangles (ABC-ACD) and (ABC-BCD))
Option C is a justification (a^2 = cy, b^2 = cx, a^2 + b^2 = cy + cx)
Option D is a justification (a^2 + b^2 = cy + cx = c(y + x) = c^2)
=> Option B is not a justification
Answer: x = - 12/9 ( the equation is negative)
Step-by-step explanation:
\frac{5}{3}x+\frac{1}{3}=13+\frac{1}{3}x+\frac{8}{3}x
\frac{5}{3}x=3x+\frac{38}{3}
\frac{5}{3}x-3x=3x+\frac{38}{3}-3x
-\frac{4}{3}x=\frac{38}{3}
3\left(-\frac{4}{3}x\right)=\frac{38\cdot \:3}{3}
-4x=38
\frac{-4x}{-4}=\frac{38}{-4}
x=-\frac{19}{2}
Answer:
A
Step-by-step explanation:
all of them are positive✔︎
all of them are real numbers✔︎
