The top of a 10-ft ladder is leaning against a wall, and the base of the ladder is on the ground. If the top of the ladder slides down the wall at a rate of 2 ft/sec, how fast (in ft/sec) is the bottom of the ladder moving along the ground when the bottom of the ladder is 5 ft from the wall?

Ladder is moving away from the wall with the speed of 3.464 ft/s

Step-by-step explanation:

Consider the figure attached

Given that top of ladder slides down with the speed of 2ft/sec, i.e

Length of ladder =10 ft

bottom of the ladder is 5 ft from the wall i.e b=5

By pythagorous theorem

Differentiating equation (1) w.r.to t

Negative sign shows that ladder is moving away from wall

-33 or 33

Step-by-step explanation:

The seventh term of an AP is written as:

The eleventh term of an AP is written as:

If the 7th term is 11 times the 11th term, then;

Expand to get:

We must have a=-52 and d=5

Or

a=52 and d=-5

For the first case, the 18th term is :

For the second case,