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

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

the 8 in 8,420 is in the thousands place so it's value is 8 thousand.

the 8 in 6,870 is in the hundreds place so it's value is 8 hundred.

divide 8000 by 800 to find the answer:

8000 / 800 = 10

the 8 in 8,420 is 10 times greater than the 8 in 6,870