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3 years ago

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Johnathan has been driving at a constant speed for 4 hours, during which time he traveled 240 miles Johnathan world like to know

how long it will take him to complete the remaining 360 miles, assuming he maintains the same constant speed.

1 answer:

valentinak56 [21]3 years ago

8 0

30000000000000000000000000000000000

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kramer

Answer:

$18.73ft^3$

Step-by-step explanation:

Let

Side of square base=x

Height of rectangular box=y

Area of square base=Area of top= $(side)^2=x^2$

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Cost of top=$5 square ft

Cost of sides=$4 per square ft

Total cost=$204

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Substitute the values of y

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Differentiate w.r.t x

$V'(x)=\frac{1}{8}(102-21x^2)=0$

$V'(x)=0$

$\frac{1}{8}(102-21x^2)=0$

$102-21x^2=0$

$102=21x^2$

$x^2=\frac{102}{21}=4.85$

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It takes positive because side length cannot be negative.

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$V''(x)=\frac{1}{8}(-42x)$

Substitute the value

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Hence, the volume of box is maximum at x=2.2 ft

Substitute the value of x

$y=\frac{102-7(2.2)^2}{8(2.2)}=3.87 ft$

Greatest volume of box= $x^2y=(2.2)^2\times 3.87=18.73 ft^3$

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