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
Read more about surface area at
brainly.com/question/76387
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Answer:
AB = 6.5
Step-by-step explanation:
C = 59°
AC = 7
CD = 6
AB = ?
Apply the Law of Cosines, which is AB² = AC² + CD² - 2(AC)(CD)*Cos(C)
AB² = 7² + 6² - 2(7)(6)*Cos(59)
AB² = 85 - 43.26
AB² = 41.74
AB = √41.74
AB = 6.5 (nearest tenth)
Answer:
I don't know..............
Answer:
2300
Step-by-step explanation:
We are given that
Out of 200 , four ducks are tagged.
We have to find the number of ducks in the preserve if 46 ducks are tagged.
Let x be the number of ducks in the preserve.
If number of tagged ducks increases then number of preserved ducks also increases.It is in direct proportion.
According to question
x=2300
