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3 years ago

10

Jennifer got a box of chocolates. The box is a right triangular prism shaped box. It is 7 inches long, and the triangular base m

easures 2 in x 3in x 4in. What is the surface area of the box of chocolates?

1 answer:

Dafna1 [17]3 years ago

4 0

The surface area would be 68 squared inches. I hope this helps!

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12. To create an open-top box out of a sheet of cardboard that is 6 inches long and

dimulka [17.4K]

Answer:idk

Step-by-step explanation:

Use photomath

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3 years ago

A piece of cardboard is 15 inches by 30 inches. A square is to be cut from each corner and the sides folded up to make an open-t

solmaris [256]

Answer:

Maximum volume = 649.519 cubic inches

Step-by-step explanation:

A rectangular piece of cardboard of side 15 inches by 30 inches is cut in such that a square is cut from each corner. Let x be the side of this square cut. When it was folded to make the box the height of box becomes x, length becomes (30-2x) and the width becomes (15-2x).

Volume is given by

V = $V = Length\times Width\times Height\\V = (30 - 2x)(15-2x)x= 4x^3-90x^2+450x\\So,\\V(x) = 4x^3-90x^2+450x$

First, we differentiate V(x) with respect to x, to get,

$\frac{d(V(x))}{dx} = \frac{d(4x^3-12x^2+9x)}{dx} = 12x^2 - 180x +450$

Equating the first derivative to zero, we get,

$\frac{d(V(x))}{dx} = 0\\\\12x^2 - 180x +450 = 0$

Solving, with the help of quadratic formula, we get,

$x = \displaystyle\frac{5(3+\sqrt{3})}{2}, \frac{5(3-\sqrt{3})}{2}$ ,

Again differentiation V(x), with respect to x, we get,

$\frac{d^2(V(x))}{dx^2} = 24x - 180$

At x =

$\displaystyle\frac{5(3-\sqrt{3})}{2}$ ,

$\frac{d^2(V(x))}{dx^2} < 0$

Thus, by double derivative test, the maxima occurs at

x = $\displaystyle\frac{5(3-\sqrt{3})}{2}$ for V(x).

Thus, largest volume the box can have occurs when $x = \displaystyle\frac{5(3-\sqrt{3})}{2}}$ .

Maximum volume =

$V(\displaystyle\frac{5(3-\sqrt{3})}{2}) = (30 - 2x)(15-2x)x = 649.5191\text{ cubic inches}$

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3 years ago

The sum of twice a number and 13 is 75

Nina [5.8K]

So what they are saying is the sum of 2x +13=75
Therefore we can just solve for 2x, our unknown value.
2x+13=75 now subtract 13 and divide by 2 from both sides of equation to not change the equation
x+13-13=75-13
This leaves us with
x=(75-13)/2=31 therefore x=31 or our unknown value is 31.

I hope this helped. Any questions please just ask. Thank you.

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3 years ago

HELP PLEASE AND NO LINKS!!

Alinara [238K]

Answer: 112

Step-by-step explanation:

educated guess

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3 years ago

What is 18 divided by 1/10 as a fraction

scoray [572]

Answer:

180

Step-by-step explanation:

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3 years ago

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