Saturday

April 19, 2014

April 19, 2014

Posted by **Amber** on Tuesday, April 24, 2012 at 1:16am.

- Calc 1 -
**Steve**, Tuesday, April 24, 2012 at 5:04amif h is the height of the ladder on the wall, and x is the distance of the base of the ladder from the wall, then by similar triangles,

x/h = (x-3)/8

h = 8x/(x-3)

Now, the ladder length y is

y^2 = x^2 + h^2 = x^2 + 64x^2/(x-3)^2

2yy' = 2x + 128x/(x-3)^2 - 128x^2/(x-3)^3

y' = (2x(x-3)^3 + 128x(x-3) - 128x^2)/y(x-3)^2

That's messy, but we want y'=0, and as long as the denominator isn't 0, we just need

2x(x-3)^3 + 128x(x-3) - 128x^2 = 0

x = 3 + 4∛3 = 8.769

h = 8x/(x-3) = 12.161

so, y, the ladder, is 15 ft

**Related Questions**

calculus - A fence 8 feet tall stands on level ground and runs parallel to a ...

Calc Help Please - A fence 2 feet tall runs parallel to a tall building at a ...

Calc - A fence 5 feet tall runs parallel to a tall building at a distance of 5 ...

Pre-calc - a rectangular yard is to be enclosed by a new fence on 3 sides and by...

Pre-calc - a rectangular yard is to be enclosed by a new fence on 3 sides and by...

math - judy wants to fence the sides of the yard in front of her house . She ...

Calculus - A 17 foot ladder is leaning on a 6 foot fence. The base of the ladder...

Calculus - A 25 foot ladder is leaning on a 9 foot fence. The base of the ladder...

Geometry - Larry, Lionel, and Lester painted a fence. Larry painted the first 1/...

math - a fence post a 4-foot shadow at the same time that a tree next to it cast...