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2 answers:
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You have
so showing that
As
Answer:
a. -5 ft per sec
b. 59.5 ft² per sec
Step-by-step explanation:
a. Suppose l represents the ladder, x represents the height of the top of ladder from the base of house and y represents the distance of base of ladder from the base of house.
By the Pythagoras theorem,
Differentiating with respect to t ( time ),
But, height of ladder, l = 13 ft = constant,
We have,
y = 5, ,
Again by equation (1),
From equation (2),
Hence, the rate of change of the height of the top of the ladder is -5 ft per sec.
b. Now area of the triangle = 1/2 × base × height
Differentiating with r. t. t,
= 59.5 ft² per sec
Hence, area of the triangle is changing with the rate of 59.5 ft per sec.
