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There will be intersection when x^2 + 4x + 3 = kx + 2. Our goal is to find the values of k which would only give one solution to this quadratic equation, which would make the lines 'tangent' to each other...

2x²(x² + 2 - 16x)

First, convert the units so you can compare more easily. 

0.72m = 72cm = 720mm

So 1 shelf is 720mm and 1 textbook is 30mm wide. 

To find the maximum number of books that can be stored...

Degrees are a made up unit; mathematicians simply decided that a complete revolution of a circle has 360 degrees, without that number actually meaning anything. Tecnically any number could have been picke...

In plain english, we need to show that there is a value of x, which we call "a", in the interval 1 < a < 2 where f(a)=0. To prove this we start by letting x = 1: f(1) = 3 - 5(1) + 1^3<...