Explanation Given: From Example 6, the desired differential equation is h ′ ( t ) = − k h , where t ≥ 0 , k = a A 2 g and g = 9.8 m / s 2 is the acceleration due to gravity. Initial condition is h ( 0 ) = H . The solution of the above initial value problem is h ( t ) = ( H − k t 2 ) 2 (1) Calculation: The water height function is obtained as follows, Given that, H = 1.96 m , A = 1.5 m 2 , a = 0.3 m 2 . Here, k = a A 2 g = 0.3 1.5 2 ( 9.8 ) = 0.2 × 4.427 = 0.88 Substitute the values in equation (1), h ( t ) = ( 1

Calculus: Early Transcendentals (2nd Edition)

2nd Edition

ISBN: 9780321947345

Author: William L. Briggs, Lyle Cochran, Bernard Gillett

Publisher: PEARSON

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter D1.1, Problem 33E

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To find: The water height function as well as determine the approximate time when the tank is first empty and graph the solution.

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Chapter D1.1, Problem 32E

Chapter D1.1, Problem 34E

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Calculus: Early Transcendentals (2nd Edition)

Ch. D1.1 - Prob. 1E Ch. D1.1 - Prob. 2E Ch. D1.1 - Prob. 3E Ch. D1.1 - If the general solution of a differential equation...Ch. D1.1 - Does the function y(t) = 2t satisfy the...Ch. D1.1 - Does the function y(t) = 6e3t satisfy the initial...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...Ch. D1.1 - Verifying general solutions Verify that the given...

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The water height function as well as determine the approximate time when the tank is first empty and graph the solution.

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To find: The water height function as well as determine the approximate time when the tank is first empty and graph the solution.

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