#17Jon Glauber

THE QUESTION

• A 13-ft ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of 2 ft/s, how fast will the foot be moving away from the wall when the top is 5 ft above the ground?

What we know

• We know that:Y=5

X=12

Dy/dt=-2

Dx/dt= ?

135

We also know that an equation for this diagram is X² + Y² = 13²

12

We found out that X= 12 because of the Pythagorean Theorem.

Step 1: Take the derivative of the equation

X² + Y² = 13²

2x(dx/dt) + 2y(dy/dt) =0

Step 2: Plug in

• The derivative is: 2x(dx/dt) + 2y(dy/dt) =0• Y=5• X=12• Dy/dt=-2

2(12)(dx/dt) + 2(5)(-2) =0

Step 3: Solve for dx/dt

• 2(12)(dx/dt) + (2)(5)(-2) = 0 24(dx/dt) – 20 = 0 24(dx/dt) = 20 So…..

dx/dt = ……...

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