Mathematical oncologists sometimes approximate tumors with the bumpy sphere model given by the family of curves: p = a + b[cos(m*theta)*sin(n*phi)] which gives different shapes and sizes of spheres with bumpy surfaces for different values of real scalars a, b, m, and n are real numbers. An example of a bumpy spere is shown in the image below. For further research into injecting nanoparticles to kill cancerous cells, a biopsy was conducted on an extracted tumor from a patient’s brain. The research team has tasked you to advise on the mathematical specifications of the biopsied specimen. TASKS Show that the bumpy sphere given by the equation above is itself contained inside a smooth sphere of radius a+b. Find the values of theta and phi where the two spheres intersect.

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.