A ladder 10 feet long is leaning against a vertical wall. The bottom of the ladder slides away from the wall at a rate of 2 ft/s. How fast is the top of the ladder sliding down the wall when the bottom of the ladder is 6 feet from the wall?
A 15-foot ladder leans against a wall, forming an angle θ with the ground. If the bottom of the ladder slides away from the wall at 3 ft/s when the bottom is 9 feet from the wall, at what rate is the angle θ changing (in radians per second) at that instant?
5
2.5
10
Consider the following problem, "The radius of a cylindrical water tank is fixed at 5 meters. Water is being pumped into the tank at a rate such that the height of the water is increasing at 0.3 m/min. At what rate is the volume of water in the tank increasing when the height is 4 meters?" Match the expressions on the left with the values on the right or state that they are unknown.
| Stavka koja se može prevući | arrow_right_alt | Odgovarajuća stavka |
|---|---|---|
| arrow_right_alt | ||
| arrow_right_alt | ||
| arrow_right_alt | ||
| arrow_right_alt | unknown |
The radius of a cylindrical water tank is fixed at 5 meters. Water is being pumped into the tank at a rate such that the height of the water is increasing at 0.1 m/min. Write the equation for the rate of change of the volume of the water in the tank when the water level is 10 meters.