Jess & Mildred Fisher College of Science & Mathematics

Towson University Mathematics Club

Questions of the Week Answers #1

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?

Answer: Rabbit.



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