The impact crater of a small metal ball of 63.7 grams (0.0637kg) is dropped from 8 different heights, ranging from 0.20m to 0.90m was observed. A mean was measured for the craters diameter. Using the equation E=mg$\Delta$h given that we have m, and g is a constant of 9.81 we can find the kinetic energy of the ball on impact. The relationship between crater diameter, D, and impact energy, E, is given by D=kE$^n$ where K is constant and n is found by the gradient of the graph and is also constant. This can be modified to give $\log D = n\log E + \log k$.
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This problem is an applied optimization problem. The problem is to minimize
the area of the triangle formed by a tangent line to the function y = 1⁄9 x2.
The triangle is defined by the origin, the x-intercept of the tangent line, and the
y-intercept of the tangent line. Only triangles formed in the first quadrant are
A template for a proof submitted as homework with student name, today's date, assignment number, assignment statement, and proof.
Includes a function for aligning equals signs and has a box for the QED at the end of the proof.