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3 years ago

What is the value of x? Enter your answer in the box. x = ? in

Mathematics

1 answer:

Marina CMI [18]3 years ago

3 0

The answer is 18, its showing 5 as the base for the small triangle and 15 for the larger triangle, it would be safe to assume the same applies to the other sides as well. add 10 to the rest and multiply them and you get the correct area for a triangle.

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An open-top box with a square base is to have a volume of 4 cubic feet. Find the dimensions of the box (in ft) that can be made

Lemur [1.5K]

Answer:

The dimension of box= $2ft\times 2ft\times 1ft$

Step-by-step explanation:

We are given that

Volume of box=4 cubic feet

Let x be the side of square base and h be the height of box

Volume of box= $lbh=x^2h$

$4=x^2h$

$h=\frac{4}{x^2}$

Now, surface area of box,A= $x^2+4xh$

$A=x^2+4x(\frac{4}{x^2})=x^2+\frac{16}{x}$

$\frac{dA}{dx}=2x-\frac{16}{x^2}$

$\frac{dA}{dx}=0$

$2x-\frac{16}{x^2}=0$

$2x=\frac{16}{x^2}$

$x^3=8$

$x=2$

$\frac{d^2A}{dx^2}=2+\frac{32}{x^3}$

Substitute x=2

$\frac{d^2A}{dx^2}=2+\frac{32}{2^3}=2+4=6>0$

Hence, the area of box is minimum at x=2

Therefore, side of square base,x=2 ft

Height of box,h= $\frac{4}{2^2}=1 ft$

Hence, the dimension of box= $2ft\times 2ft\times 1ft$

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