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Mathematics

1 answer:

balu736 [363]3 years ago

8 0

Answer: 3

Step-by-step explanation:

At x = -2, y = 3

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If an open box has a square base and a volume of 115 in.3 and is constructed from a tin sheet, find the dimensions of the box, a

Karolina [17]

Let h = height of the box,
x = side length of the base.

Volume of the box is $V=x^{2} h = 115$ .
So $h = \frac{115}{ x^{2} }$

Surface area of a box is S = 2(Width • Length + Length • Height + Height • Width).
So surface area of the box is
$S = 2( x^{2} + hx + hx) \\ = 2 x^{2} + 4hx \\ = 2 x^{2} + 4( \frac{115}{ x^{2} } )x$
$= 2 x^{2} + \frac{460}{x}$
The surface are is supposed to be the minimum. So we'll need to find the first derivative of the surface area function and set it to zero.

$S' = 4x- \frac{460}{ x^{2} } = 0$
$4x = \frac{460}{ x^{2} } \\ 4x^{3} = 460 \\ x^{3} = 115 \\ x = \sqrt[3]{115} = 4.86$
Then $h= \frac{115}{4.86^{2}} = 4.87$
So the box is 4.86 in. wide and 4.87 in. high.

5 0

3 years ago

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Which is the side length of a cube with a volume of 2744 cm3?<br><br> Please help

Elis [28]

$\sf~V=a^3$

Plug in what we know:

$\sf2744=a^3$

Find the cube root of both sides:

$\sf~a=\sqrt[3]{2744}$

Simplify:

$\sf~a=\boxed{\sf14}$

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2 years ago

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Graph the exponential function<img src="https://tex.z-dn.net/?f=%20f%28x%29%3D%5Cfrac%7B1%7D%7B2%7D%5E%7Bx%7D%20%20" id="TexForm

tatyana61 [14]

$f(x)=\left(\dfrac{1}{2}\right)^x\\\\for\ x=-3\to y=\left(\dfrac{1}{2}\right)^{-3}=2^3=8\to(-3,\ 8)\\\\for\ x=-2\to y=\left(\dfrac{1}{2}\right)^{-2}=2^2=4\to(-2,\ 4)\\\\for\ x=-1\to y=\left(\dfrac{1}{2}\right)^{-1}=2^1=2\to(-1,\ 2)\\\\for\ x=0\to y=\left(\dfrac{1}{2}\right)^0=1\to(0,\ 1)\\\\for\ x=1\to y=\left(\dfrac{1}{2}\right)^1=\dfrac{1}{2}\to\left(1,\ \dfrac{1}{2}\right)\\\\for\ x=2\to y=\left(\dfrac{1}{2}\right)^2=\dfrac{1}{4}$