A 13-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the house, the base is moving away at the rate of 5 ft/sec. a. What is the rate of change of the height of the top of the ladder? b. At what rate is the area of the triangle formed by the ladder, wall, and ground changing then? C. At what rate is the angle between the ladder and the ground changing then? 13-ft ladder X(t) a. The rate of change of the height of the top of the ladder is t/sec. (Simplify your answer.)

A 10​-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 6 ft from the​ house, the base is moving away at the rate of 24 ​ft/sec. a. What is the rate of change of the height of the top of the​ ladder? b. At what rate is the area of the triangle formed by the​ ladder, wall, and ground changing​then? c. At what rate is the angle between the ladder and the ground changing​ then? A coordinate plane has a horizontal x-axis and a vertical y-axis. A thin rectangle falling from left to right labeled 10 foot ladder starts on the y-axis at y(t) and ends on the x-axis at x(t). An arrow on the y-axis below y(t) is pointing down and an arrow on the x-axis to the right of x(t) is pointing to the right. The angle created between the segment and the x-axis is labeled theta. θ x(t)y(t)010-ft ladderxy   a. The rate of change of the height of the top of the ladder is nothing ​ft/sec. ​(Simplify your​ answer.)   b. The area is changing at…