3. A simple pendulum is a weight on the end of a string or rod, which whengiven 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 rightand back again). The formula for the period isT = 27dT(a) Find d9where is the length of the pendulum (in meters) and g is the accelerationdue to gravity (in m/sec2). Note that g is a positive constant.lo zulev lie(x)) (8)(b) When the length of the pendulum increases, does the period increaseor decrease? Justify your answer.(0)al bar nob

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Answered: 3. A simple pendulum is a weight on the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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The height h of the right triangle in the figure below increases at a rate of 10 cm/s, while the base remains constant at x =15 cm. How fast is the angle theta changing when h = 8 ? Round the final answer to three decimal places and give units with your answer. Show all work in the space provided and place your final answer in the answer blank below. I could not add a photo of the right triangle, so please picture a left facing right triangle. I labeled the 3 sides and 3 angles third angle third side side h Angle theta right angle Side x
The formula for kinetic energy is: K = 0.5 mv, where m is mass in kilograms, v is velocity in m/s, and K stands for the energy in Joules. If m = 30 kg, and v = 13 m/s, how fast is K changing if v is changing at the rate of 9 m/s? Assume m is constant. %3D Rate (in Joules/sec) = Number (Enter your answer rounded to 4 decimal places)
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1. The period T of oscillation (in seconds) of a simple pendulum of length L (in feet) is given by T = 2n 32 a.) What is the rate of change of T with respect to L when L = 8 inches? b.) What is the average rate of change of T from L = 2 inches to L = 8 inches?
please solve this problem with step by step calculations
e An airplane flying on a straight flight path will be exactly above a radar tracking station, which is 5,000 km below the path. When the distance of the plane from the station is 40,000 km, this distance decreases at the rate of 8,000 km/hr. At what rate is the plane flying at that instance? novi f. A truck travelling southwards at 40 kph and a car traveling eastward at a rate of 60 kph are headed for an intersection. At what rate are the vehicles approaching each other when the truck is 1 km from the intersection while the car is 2 km from the intersection? g. Water is being poured at the rate of 5 m³/sec into an inverted conical tank of radius 10 m and altitude 20 m. How fast is the water level rising when the water level is at 8 m? (Note: Here you will be using the concepts of similar triangles in order to rewrite the radius in terms of the height.) itoun bont h. A particle is moving along the curve with equation y = 3-x. At the point (2, 1), it was observed that the x-coordinate…
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3
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I = 4t? dt

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