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FrozenT [24]
4 years ago
10

A box is made from material that has a dimension 24 by 48. The box is to be form by cutting squares from each of the four edges

of the material. What are the dimensions of the box such that the volume is maximum

Mathematics
1 answer:
avanturin [10]4 years ago
6 0
(Refer to image for diagram.)

Volume is length*width*height
So V(x)=x(48-2x)(24-2x)
⇒V(x)=4x(24-x)(12-x)
⇒V(x)=4x(288-36x+x^{2})
⇒V(x)=4(288x-36x^{2}+x^{3})
Differentiate: V'(x)=4(288-72x+3x^{2})
For maximum, set V'(x)=0
⇒4(288-72x+3x^{2})=0
⇒96-24x+x^{2}=0
⇒x=\frac{24+-\sqrt{(-24)^2-4(96)}}{2}
⇒x=\frac{24+-\sqrt{576-384}}{2}
⇒x=\frac{24+-\sqrt{192}}{2}
⇒x=\frac{24+-8\sqrt{3}}{2}
⇒x=12+-4\sqrt{3}

Since theshorter side of the original rectangle is 24=2*12, x
⇒x=12-4\sqrt{3} is the height

For the longer side of the base:
48-2x=48-2(12-4\sqrt{3})=48-24+8\sqrt{3}=24+8\sqrt{3}
For the shorter side of the base:
24-2x=24-2(12-4\sqrt{3})=24-24+8\sqrt{3}=8\sqrt{3}

The dimensions are 8\sqrt{3}×(24+8\sqrt{3})×(12-4\sqrt{3})

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5 0
3 years ago
Tyler can rake 1/3 of a yard in 1/5 of an hour.How many yards can he rake in one hour?
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5/3 yards

Step-by-step explanation:

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8 0
3 years ago
I need to find the mean and the mode. What is the mode?
denis-greek [22]
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6 0
3 years ago
Read 2 more answers
What is...<br><br> 7 4/7 + 14 4/5<br> Thank you so much!
SCORPION-xisa [38]
7+4/7+14+4/5
=7+14+4/7+4/5
=21+(4*7+4*5)/35
=21+48/35
=22+13/35
=22\frac{13}{35}
7 0
4 years ago
2, 4 and 6 are consecutive even numbers.
AURORKA [14]

Answer:

Alice: 82, 84, 86

Pat: 103, 105, 107

Step-by-step explanation:

Alice:

x + (x+2) + (x+4) = 252

3x + 6 = 252

3x = 246

x = 82 so Alice's last term is 82+4 = 86

Pat:

y + (y+2) + (y+4) = Pat's Total

Pat's last term is (y+4) so

Alice's last term + 25 = Pat's last trem

86 + 25 = 111 = y+4

y = 107

7 0
3 years ago
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