Making an Interactive SHOCKWAVE CALCULATOR with Desmos

Making an Interactive SHOCKWAVE CALCULATOR with Desmos
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https://www.youtube.com/watch?v=cgFbclatvPc
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# https://www.desmos.com/calculator/gnuwnpopmg
# The "mach" speed of the object (speed of the object divided by the speed of sound).  Play with the slider.
v_{mach}=1.3
# Angle.  Notice what happens when v_mach approaches 1 (when the object slows down to the speed of sound).
\theta_{angle}=\frac{360}{\pi}\arcsin\frac{1}{v_{mach}}
# Other stuff
a=\left[1,\ ...,\ n\right]
n=12
\left(x-\frac{a}{n}\right)^{2}+y^{2}=\left(\frac{a}{v_{mach}n}\right)^{2}
\left(x-k\right)^{2}+y^{2}=\left(\frac{k}{v_{mach}}\right)^{2}
k=0.75
\left|y\right|\sqrt{v_{mach}^{2}-1}=x