Question 4. You may use a calculator on both parts of this question. Part A. Imagine an elliptical oil slick that at some moment in time is 3 meters long and 2 meters wide. At this instant, it's length is increasing at a rate of 2 centimeters per minute, and its width at a rate of 1 centimeter per minute. How fast is the oil slick's area increasing? Helpful information: The area of an ellipse is given by the equation A πα5, where A is area, and a and b are the lengths of the semi-major and semi-minor axes respectively. What does that mean? The long axis of an ellipse is called its major axis; the short axis is called the minor axis. Half of these axes, i.e., the lines from the center of the ellipse to its edge in the longest and shortest dimensions, are the semi-major and semi-minor axes. Part B. If the oil slick is a constant 1 millimeter thick, how fast (in units of volume per minute, e.g., cubic centimeters per minute) is oil entering the slick at the moment described in Part A? More helpful information: The volume of such an oil slick is simply its thickness times its area.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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