My cat Pythagoras has purchased and installed in my back yard a large barrel with a 400-gallon capacity. It is initially half full of clean water. But he has three hoses feeding this barrel, each with a rate of flow of 2 gal./min. of water. Two provide the barrel with clean water, but the third contains a concentration of 2 g/gal. of liquid calculus text books. My other cat, Jolie, has decided to sabotage this process by puncturing a hole toward the bottom of this barrel that allows 4 gal./min. to leak. If we assume that there is a benevolent feline deity that blissfully stirs this barrel with a rather large spoon, then write a differential equation that mathematically models the rate at which the amount of liquid calculus text books changes in the barrel (at least up to the time it fills). Thereafter, solve this differential equation.

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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.