Math Problem Solving

Introduction to Related Rate Issues & solutions

The study of rates of change is called calculus. Related rates of issues in which rates of change are related by means of differentiation (The process of finding a derivative).

Standard example issues include water dripping from a cone - formed tank as well as a man’s shadow lengthening as they walks away from a street lamp. Calculus related rates issues are used to finding the rates of the changes of the two variables respect to time.

Example: A boy as well as a girl start from the same point. The boy walks S70o E at 2.6 m/sec. The girl walks south at 3.2 m/sec. At what rate is the distance between the boy & girl changing after 45 minutes?

Solution:

Let x be the distance the boy has travelled, y the distance the girl has travelled & z the distance between the boy & the girl. looking for math homework solver

Speed of the girl, (dx/dt) = 2.6 m/sec & the speed of the girl, (dy/dt) = 3.2 m/sec. The rate of change of the distance between the boy & girl is (dz/dt) after 45 minutes have passed. After t seconds, the distance boy has travelled is 2.6t while the girl’s distance is 3.2t.

So after 2700 seconds or 45 minutes, the boy’s distance is x = 2.6(2700) = 7020m & the girl’s distance y = 3.2(2700) = 8640m.

Use Free Math online study the cosine law to equate the variables.
z2 = x2 + y2 - 2xy cos θ