## Towson University Mathematics Club

### Upper Level Problem

Let $A = \int_0^1 \sqrt{1-x^3} \, dx, \quad B = \int_0^1 \sqrt{1-x^4} \, dx, \quad C = \int_0^1 \sqrt{1+x^5} \, dx.$ Order the numbers $$0, 1, 2, A, B, C$$ in ascending order.

Answer: $$0 < A < B < 1 < C < 2$$.

### Mid Level Problem

A box with an open top is to be made from a rectangular piece of cardboard with dimensions 20 in. by 35cm. by cutting out equal sqaures of side $$x$$ at each corner and then folding up the sides. Express the volume $$V$$ of the box as a function of $$x$$. Express the function and variable $$x$$ in terms of inches.

Answer: $$V(x)=x(20-2x)(7.87-2x), \; 0 < x < 3.935$$.

### Math Triva Question

Leonardo Pisano Bigollo; better known as Fibonacci, modeled the famous fibonacci sequence after the growth in population of which animal?