in real-world problems it is often easier to calculate the rate of change of. Differentiation with respect to time or one of the other variables requires application of the chain rule, since most problems involve several variables. If the rate of change of the quantity x with respect to the time t is given. Because science and engineering often relate quantities to each other, the methods of related rates have broad applications in these fields. The rate of change is usually with respect to time. I thought about this explanation for a long time, and couldn't figure out why the distance from the tip of the shadow to the man was dependent while the distance from the tip of the shadow to the light post was independent.In differential calculus, related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known. If I remember correctly, he said that x and y represented variables that could independently changed, while y-x represented a value that couldn't be changed on its own. For example, if we consider the balloon example again, we can say that the rate of change in the volume, V, is related to the rate of change in the radius, r. While this answer does make sense to me, I can remember my teacher from last year giving a more logical explanation. Setting up Related-Rates Problems In many real-world applications, related quantities are changing with respect to time. The common sense method states that the volume of the puddle is growing by 2 in 3 /s, where. Suppose they are related by the equation 3P2. Example: RelatedRates 1 Suppose P and Q are quantities that are changing over time, t. I asked an online tutor why the variables had to be placed in the locations on the answer key, and he told me that it was because when differentiating to find the answer in part (a), you could not differentiate (x+y) because it had to be a specific variable. We can answer this question two ways: using 'common sense' or related rates. But it is much easier to mea- sure directly the rate of increase of the volume than the rate of increase of the radius. Chapter 3: Applications of Derivatives 3.2: Related Rates Related Rates - Introduction 'Related rates' problems involve nding the rate of change of one quantity, based on the rate of change of a related quantity.

After doing the calculations for part (a) several times, I found that I was unable to obtain the correct answer. I tried to complete the problem with the distance from the man to the light post designated as x, the distance from the tip of the shadow to the man as y, and the distance from the tip of the shadow to the light post as x + y.

Currently, the distance from the man to the light post is assigned the variable x, the distance from the tip of the shadow to the light post is assigned y, and the distance from the tip to the man is (y-x). At the same instant, the width is 2 inches and is decreasing at the rate of. At a certain instant, the length of a rectangle is 3 inches and is increasing at the rate of 1 inch per minute. My question isn't about the process of finding the answers, but more about why the answer key placed the variables where they did. Calculus AB Assignment Related-Rates Problems 1. (b) at what rate is the length of his shadow changing? (a) at what rate is the tip of his shadow moving? When he is 10 feet from the base of the light, For instance, if we pump air into a donut floater, both the radius and the balloon volume increase, and their growth rates are related.

A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground. Related Rates are calculus problems that involve finding a rate at which a quantity changes by relating to other known values whose rates of change are known.

Related rate calculus problems