Let x be the width of the cardboard, then the length is x+15. If 5 unches square is cut from each corner, then the new length is x+15-5·2=x+5 and the new width is x-5·2=x-10. The height of the formed box is 5 in. Now you can find the box volume:

$V=\text{ width }\cdot \text{ length }\cdot \text{ height },\\ V=(x-10)\cdot (x+5)\cdot 5,\\ V=5(x^2-5x-50)$ .

If the volume of the box is 1,250 cubic inches, then

$5(x^2-5x-50)=1250,\\ x^2-5x-50=250,\\ x^2-5x-300=0,\\ D=(-5)^2-4\cdot (-300)=25+1200=1225,\\ \sqrt{D} =35,\\ x_{1,2}=\dfrac{5\pm 35}{2} =20,-15$ .

The length of the box is x+5=20+5=25 in. (the negative x is extra, because the length couldn't be negative).

Answer: the length of the box is 25 inches.

7 0

3 years ago

Find the volume of a cone with a base radius of 5 yd and a height of 6 yd.

wariber [46]

Answer:

157.08 yd3

Step-by-step explanation:

7 0

3 years ago

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Last friday tony worked for seven and a half hours. Express this time as a fraction of the day.

tangare [24]

I got it to be .3125 or 31%. just convert that to a fraction and you got it. sorry I forget how to put that decimal into a fraction it's been a year:)

8 0

3 years ago