Aladder 25 feet long is leaning against the wall of a building. initially, the foot of the ladder is 7 feet from the wall. the foot of the ladder begins to slide at a rate of 2 ft/sec, causing the top of the ladder to slide down the wall. the location of the foot of the ladder at time t seconds is given by the parametric equations (7+2t,0).

The location of the foot of the ladder at time t is

Step-by-step explanation:

The wall, ladder and the ground makes a right angled triangle. Let the ground be x and the wall be y.

Then, by Pythagorean theorem, we have,

Also, given that the ladder is sliding at a rate of 2ft/sec.

The location of the foot of the ladder at time t is given by the parametric equations and thus, . Substituting these values in the equation , we get,

Subtracting on both sides,

Taking square root on both sides, we get,

Thus, the location of the foot of the ladder at time t is

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step-by-step explanation: