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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 $\log D = n\log E + \log k$.

Overleaf and the American Society of Civil Engineers (ASCE) have created this template for authors submitting manuscripts to all 35 ASCE Journals. The template allows authors to easily prepare and edit their manuscripts using Overleaf. Once complete, authors can submit the source files downloaded from Overleaf.
To begin writing online, click the “Open as Template” button above. The Overleaf/ASCE template will load. Additional guidelines for preparing submissions are included within the template.
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Overleaf & the American Society Of Civil Engineers (ASCE)

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
of concern.

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.