You are the coordinator for a program that is going to take place at night in a rectangular amphitheater in the mountains. You will have no access to any electricity, but you must be able to illuminate the entire grounds. You know the intensity of the light from a lantern varies inversely as the square of the distance from the lantern. Suppose the intensity is 90 when the distance is 5 m. a. Write an equation to model the situation. b. Solve for the constant of variation. c. Write the equation to model the situation using the constant () of variation. d. You have been given lanterns with 40 light intensity. Use your equation to solve for the distance from the lantern. e. You need to illuminate 225 km. How many meters do you need to light? f. How many lanterns will you need?

Askydiver weighing 140 lb (including equipment) falls vertically downward from an altitude of 19,000 ft and opens the parachute after 18 s of free fall. assume that the force of air resistance, which is directed opposite to the velocity, is of magnitude 0.55|v| when the parachute is closed and is of magnitude 14|v| when the parachute is open, where the velocity v is measured in ft/s. assume that acceleration due to gravity has magnitude 32 ft/s/s; remember that weight is the product of mass and gravitational acceleration. (a) find the speed of the skydiver when the parachute opens. (b) find the distance fallen before the parachute opens. (c) what is the limiting velocity vl after the parachute opens? (d) determine how long the sky diver is in the air after the parachute opens. (e) plot the graph of velocity versus time from the beginning of the fall until the skydiver reaches the ground.

In which situation has the independent variable for the experiment been changed? check all that apply. changed from counting the number of duckweed at day 0 and day 14 to counting them every day changed from testing duckweed growth in beakers to testing duckweed growth in large outdoor tanks changed from testing the effect of ph on duckweed growth to testing the effect of light levels on duckweed growth changed from testing the effect of acid ph on duckweed growth to testing the effect of basic ph on duckweed growth

The electric field inside a cell membrane is 8.0mn/c. what's the force on a singly charged ion in this field?