Explanation Given: The amount of a tracer dye injected into the bloodstream decreases exponentially, with a decay constant of 3% per minute. Initially 6 cc are present. Concept used: Decline rate of sale gives us the idea that decline is with respect to time, which is proportional to the amount of sales. This makes the problem an ordinary differential equation of variable separable form. Calculation: The decline rate is proportional to the amount of sales. So taking the variable y as the amount of sales. Then, the problem can be expressed as, d y d t ∝ − y Removing the proportionality sign requires multiplying the right hand side of the above expression with a constant of proportionality with k Therefore, the differential equation can be expressed as, d y d t = − k y The decline rate is given as 3 % per minute. Therefore, the value of k is k = − 0 ⋅ 03 . Negative sign denotes the decrease in the amount of injection. Thus, the differential equation can be written as d y d t = − 0 ⋅ 03 y Separating the variables of the above differential equation as, d y y = − 0 ⋅ 03 d t Integrate both the sides. ∫ d y y = ∫ − 0 ⋅ 03 d t Evaluate the integral on both the sides

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 10.1, Problem 46E

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The amount of dye present after 10 minutes in cubic centimeters.

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Chapter 10.1, Problem 45E

Chapter 10.1, Problem 47E

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 10 Solutions

Calculus with Applications (11th Edition)

Ch. 10.1 - Find all solutions of the differential equation . Ch. 10.1 - Prob. 2YT Ch. 10.1 - Prob. 3YT Ch. 10.1 - Prob. 4YT Ch. 10.1 - Prob. 1WE Ch. 10.1 - Prob. 2WE Ch. 10.1 - Prob. 3WE Ch. 10.1 - Prob. 4WE Ch. 10.1 - Prob. 5WE Ch. 10.1 - Find the general solution for each differential...

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