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mrs_skeptik [129]
3 years ago
5

From a square piece of cardboard paper of area size 9 m2 , squares of the same size are cut off from each corner of the paper. T

his allows for folding the paper to a box without a top. What values for the lengths of the squares only make sense? How do we have to choose the length of the squares to maximize the volume of the box? Verify that your answer is indeed a maximum.
Mathematics
1 answer:
levacccp [35]3 years ago
6 0

Answer:

Max vol = 2 cubic metres

Step-by-step explanation:

Given that from a square piece of cardboard paper of area size 9 m2 , squares of the same size are cut off from each corner of the paper.

Side of the square = 3m

If squares are to be cut from the corners of the cardboard we have the dimensions of the box as

3-2x, 3-2x and x.

Hence x can never be greater than or equal to 1.5

V(x) = Volume = V(x) = x(3-2x)^2\\= 9x+4x^3-12x^2

We use derivative test to find the maxima

V'(x) = 9+12x^2-24x\\V"(x) = 24x-24\\

Equate I derivative to 0

9+12x^2-24x=0\\x=1/2,3/2

If x= 3/2 box will have 0 volume

So this is ignored

V"(1/2) <0

So maximum when x =1/2

Maximum volume

=9(1/2)+4(1/2)^3-12(1/2)^2\\=2 cubic metres

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3 0
3 years ago
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-Dominant- [34]

Answer:

357

Step-by-step explanation:

A) We replace x = - 5 and u = 3 into -3x^3 -2y^2

and we have -3x^3 -2y^2= -3*(-5)^3 -2*3^2= -3*(-125)- 2*9

or -3x^3 -2y^2 = 375-18= 357

The answer is 357.

B) Replace h = -2 into h^2-3h+2

we have h^2-3h+2 = (-2)^2 -3*(-2) +2 = 4 +6 + 2= 12

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8 0
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7 0
2 years ago
PLEASE HELP DUE IN 30 MINUTES
Vladimir79 [104]
<span>(a) At the end of Month 0, about how many more insects were in Pod A than Pod B? Explain.
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(b) Find and compare the growth rates of each pod. Show your work.
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(44-20)/20 = 1.2
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3 years ago
in a class children, three quarters are chinese, one fifth are malay, and the rest are indian. what fraction of the class are in
Rudiy27

Answer:

\frac{1}{20}

or 5%

Step-by-step explanation:

Explanation:

3/4=15/20

1/5=4/20

So, rest of 'em 1/20

3 0
2 years ago
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