Fazle R. A 13-ft ladder is leaning against a house. the distance from the bottom of the ladder to the house is 7-ft less than the distance from the top of the ladder to the ground .how far is the bottom of the ladder from the house. More 1 Expert Answer
(x-7)^2 +x^2 = 13^2 x^2 -14x +49 +x^2 = 169 2x^2 -14x -120 = 0 x^2 -7x- 60 =0 (x-12)(x+5) = 0 x =12 feet x-7= 5 feet from the bottom of the ladder to the house the ladder forms a 5-12-13 right triangle 5^2 +12^2 = 13^2 25+144= 169 Still looking for help? Get the right answer, fast.ORFind an Online Tutor Now Choose an expert and meet online. No packages or subscriptions, pay only for the time you need. Solution : `x^(2)+y^(2)=169` <br> `rArr " " 2x(dx)/(dt)+2y(dy)/(dt)=0` <br> `rArr "" ((dy)/(dt))=((dx)/(dt))(x-x)/(y)=5 xx(-12)/(5)=-12 ft//s` <br> `A=(1)/(2) xy` <br> `rArr " " (dA)/(dt)=(y)/(2)(dx)/(dt)+(x)/(2)(dy)/(dt)=(5)/(2) xx 5+ (12)/(2) xx-12` <br> `=(25-144)/(2)=-59.5 ft^(2)//s` <br> ` y=x tan theta` <br> `rArr " " (dy)/(dt)=(tan theta)(dx)/(dt)+x sec^(2) theta (d theta)/(dt)` <br> `rArr " " -12 = 5 xx (5)/(12) + 12 xx (169)/(12^(2)) (d theta)/(dt)` <br> `rArr " " (169)/(12) (d theta)/(dt) =-12 -(25)/(12)` <br> ` rArr " " (d theta)/(dt)=(144)/(169)-(25)/(169)=-1 "rad"//s`
Question 1033516: Q5 A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house, the base is moving at the rate of 5 ft/ sec. a. How fast is the top of the ladder sliding down the wall then? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? c. At what rate is the angle between the ladder and the ground changing then? Answer by addingup(3677)  You can put this solution on YOUR website! |
A 13 ft ladder is leaning against a house
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