Answered: Use the total differential…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.3: The Natural Exponential Function

Problem 44E

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The kinetic energy E of an object varies jointly with the object’s mass m and the square of the object’s velocity v . An object with a mass of 50 kilograms traveling at 16 meters per second has a kinetic energy of 6400 joules. What is the kinetic energy of an object with a mass of 70 kilograms traveling at 20 meters per second?
If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.
A mass of 1.25 kg stretches a spring 0.08 mm. The mass is in a medium that exerts a viscous resistance of 45 NN when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object.Suppose the object is displaced an additional 0.05 mm and released.Find an function to express the object's displacement from the spring's natural position, in mm after tt seconds. Let positive displacements indicate a stretched spring, and use 9.8 ms2ms2 as the acceleration due to gravity.u(t) = 5·10−5(e−3t)sin(349.98t+π2)mIncorrect syntax error. Check your variables - you might be using an incorrect one. Submit QuestionQuestion 1
A mass of 1.25 kg stretches a spring 0.08 mm. The mass is in a medium that exerts a viscous resistance of 45 NN when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.05 mm and released. Find an function to express the object's displacement from the spring's natural position, in mm after tt seconds. Let positive displacements indicate a stretched spring, and use 9.8 ms2ms2 as the acceleration due to gravity.
Explain, in terms of linear approximations or differentials,why the approximation is reasonable. (1.01)6 ≈ 1.06
Differentiate the function. u= (1/t -1/square root of t)^2
Use the linearization of the function f(x) = x²/3 at x = 8 to approximate 7.72/3 Enter your approximation in the box below.
Using differentials, approximate the change in length of the space diagonal of a parallelepiped of length, width, and height given to be 2 units, 3 units, and 5 units, respectively, when the length increased by 0.1 unit and the width decreased by 0.2 unit, while keeping the height constant
Use differentials to approximate √16.5.
A water tank is being drained and has the shape of a rectanuglar box 7m long, 6m wide and 5m high. How fast is the water depth changing when the water depth is 0.9m? V= 42(60-t)^2
Do the b part
At time t seconds, the center of a bobbing cork is 2sin(2t) centimeters above or below water level. What is the velocity of the cork at t=0, pi/2, and pi?

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Use the total differential approximation to calculate sqrt((3.91)(9.11))