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katrin2010 [14]

3 years ago

8

A gift box has a volume of 450 cubic inches. The width of the box is 4 inches less than the length. The height is twice the widt

h. What is the width in inches of the gift box?

1 answer:

VashaNatasha [74]3 years ago

5 0

Answer:

width = 5 in

length = 5+4=9 in

height = 2(5)= 10 in

Step-by-step explanation:

A gift box has a volume of 450 cubic inches.

Let 'w' be the width of the box

The width of the box is 4 inches less than the length.

$length = w+4$

The height is twice the width.

$height = 2 \cdot width$

height = 2w

Volume of box = length times width times height

$V=(w+4)(w)(2w)$

$450=(w+4)(w)(2w)$

$450=2w^3+8w^2$

$2w^3+8w^2-450=0$

$\quad 2\left(w-5\right)\left(w^2+9w+45\right)=0$

$w-5=0$

w=5

$\quad\left(w^2+9w+45\right)=0$ , this gives two complex values

so width = 5

length = 5+4=9

height = 2(5)= 10

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3 years ago

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dmitriy555 [2]

Answer:

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Step-by-step explanation:

Hi there!

We are given:

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Therefore, the ratio of their circumferences would be:

$\displaystyle\frac{\pi}{4\pi}$ ⇒ $\displaystyle\frac{1}{4}$ when simplified

The formula for circumference is $C=2\pi r$ , where <em>r</em> is the radius. To find the ratio of the circles' radii, we must identify their radii through their given circumferences.

If the circumference of Circle K is $\pi$ , or $1\pi$ , then its radius is $\displaystyle\frac{1}{2}$ .

If the circumference of Circle L is $4\pi$ , then its radius is $\displaystyle\frac{4}{2}$ , which is 2.

Therefore the ratio their radii would be:

$\displaystyle\frac{\frac{1}{2}}{{2}}$ ⇒ $\displaystyle\frac{1}{2}*\frac{1}{2}$ ⇒ $\displaystyle\frac{1}{4}$ when simplified

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$A=\pi r^2$

First, let's find the area of Circle K:

$A=\pi (\displaystyle\frac{1}{2})^2\\\\A=\displaystyle\frac{1}{4}\pi$

Now, let's find the area of Circle L:

$A=\pi (2)^2\\A = 4\pi$

Therefore, the ratio of their areas would be:

$\displaystyle\frac{\frac{1}{4}\pi}{4\pi}$ ⇒ $\displaystyle\frac{\frac{1}{4}}{4}$ ⇒ $\displaystyle\frac{1}{4} * \frac{1}{4}$ ⇒ $\displaystyle\frac{1}{16}$ when simplified

I hope this helps!

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The length of a pipe that weighs 45 pounds is cut into 2 pieces. One piece is 3 feet long and weighs 18 pounds. What is the leng

muminat

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