3. A simple pendulum is a weight on the end of a string or rod, which when given an initial push, swings back and forth under the influence of gravity. The period T of a pendulum is the time taken for two swings (left to right and back again). The formula for the period is T = 27 dT (a) Find d g where is the length of the pendulum (in meters) and g is the acceleration due to gravity (in m/sec²). Note that g is a positive constant. lo zulev lie (b) When the length of the pendulum increases, does the period increase or decrease? Justify your answer. al beur nob

please solve this problem with step by step calculations

A nkcschools.instructure.com Near the surface of any planet, the distance D fallen by a rock in time t is given by ct(this is a consequence of Newton's 2nd law of gravitation). Here we will D = measure D in feet and t in seconds. (a) A rock is dropped from two different heights. It takes the rock 5 times as long to hit the ground from the taller height. How do the heights compare? The taller height is times as tall as the other. (b) On Venus, a rock dropped from 70 feet above the surface takes 2.2 seconds to strike the ground. What is the value of c for Venus? Round your answer to 2 decimal places. (c) Another rock is dropped on Venus. How far has it fallen after 4 seconds? Round your answer to 2 decimal places and include an appropriate label.

The electric power P (in W) as a function of the current i (in A) in a certain circuit is given by P = 12i2 + 60i. Find the instantaneous rate of change of P with respect to i for i = 0.75 A. The instantaneous rate of change of P is WIA for i = 0.75. (Simplify your answer.)

A buoy bobs up and down on ocean waves. It’s heigh is measured by the function h(t)= 3 cos (t) where h(t) is measured in feet and t is measured in seconds. What is the rate of change (in ft/s) of the heights of the buoy at t= 3pi/2

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I = 4t? dt

V 5. A sensor is attached to a spring and its velocity is given by the function (4)2 cos(2t) feet per second where t is in seconds. Find the distance traveled by the sensor from 0 to 7 seconds.