A 10-foot ladder is leaning straight up against a wall when a person begins pulling the base of the ladder away from the wall at the rate of 1 foot per second. Calculate the true distance between the top of the ladder and the ground when the base of the ladder is 9 feet from the wall.

The true statement about the true distance between the top of the ladder and the ground when the base is 9 feets from the wall is - 9/√19

Let :

Ladder forms a right angle triangle as it leans against the wall :

Hence, we have :

Taking the implicit derivative of both sides:

2xdx/dt + 2ydy/dt = 0

xdx/dt + ydy/dt = 0

ydy/dt = - xdx/dt

dy/dt = (-xdx/dt) / y

When the ladder is 9 ft from the wall;

81 + y² = 100

y² = 100 - 81 = 19

y = √19

Substituting into the equation :

dy/dt = -9(1)/√19

Hence, dy/dt = - 9/√19

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Explanation:

Let the height of the ladder be L

Also:

When the ladder leans against the wall, it forms a triangle and the length of the ladder forms the hypotenuse.

So, we have:

--- Pythagoras Theorem

When the base is 9ft from the wall, this means that:

Substitute 9 for x and 10 for L in

Make the subject

Make y the subject

Hence, the true distance at that point is approximately 4.36ft

i think it’s a. this is because if they measured the mass of something with a mass of 150g, then their final answer would have to be approximately 150g. though all of their answers are almost 150, rosa and tran have the closest answers (or the exact answer) to the accurate one.

hi there!

out of the two, (b) precision would be more reasonable.   however, both a and b could be pretty reasonable.

-awesomerepublic   : )