I recently graduated from KU with a BS in Mechanical Engineering and a minor in Economics. I tutored Physics II and math up to Calculus III during my senior year at KU, and I tutored Calculus I at the University of South Dakota during my senior year of high school. I also have experience tutoring K-5th grade students through an after-school volunteering program during my time at KU.
I am looking to work in STEM education within a short-term contract. I excel at breaking down complex problems with visual and verbal aid in fields like math, physics, and engineering. I am willing to work in a more difficult subject if possible.
Two spheres, each of mass $m,$ can slide freely on a frictionless, horizontal surface. Sphere $A$ is moving at a speed $v_{0}=16 \mathrm{ft} / \mathrm{s}$ when it strikes sphere $B,$ which is at rest, and the impact causes sphere $B$ to break into two pieces, each of mass $m / 2 .$ Knowing that 0.7 s after $B$ the collision one piece reaches point $C$ and 0.9 s a after the collision the other piece reaches point $D,$ determine $(a)$ the velocity of sphere $A$ after the collision, $(b)$ the angle $\theta$ and the speeds of the two pieces after the collision.
Explain why, at a point that maximizes or minimizes $f$ subject to a constraint $g(x, y)=0,$ the gradient of $f$ is parallel to the gradient of $g .$ Use a diagram.
If $f(x, y)=x^{2}+y^{2}$ and $g(x, y)=2 x+3 y-4=0,$ write the Lagrange multiplier conditions that must be satisfied by a point that maximizes or minimizes $f$ subject to $g(x, y)=0.$
If $f(x, y, z)=x^{2}+y^{2}+z^{2}$ and $g(x, y, z)= 2 x+3 y-5 z+4=0,$ write the Lagrange multiplier conditions that must be satisfied by a point that maximizes or minimizes $f$ subject to $g(x, y, z)=0.$
Sketch several level curves of $f(x, y)=x^{2}+y^{2}$ and sketch the constraint line $g(x, y)=2 x+3 y-4=0 .$ Describe the extrema (if any) that $f$ attains on the constraint line.
Use Lagrange multipliers to find the maximum and minimum values of $f$ (when they exist) subject to the given constraint.$f(x, y)=x+2 y$ subject to $x^{2}+y^{2}=4$
