I am 20 years old, and will be graduating Fall 2021 with a degree in Secondary Education with a Math emphasis. This last school year, I was an Academic Peer Mentor, and my job was to support first-year college students to be successful in their classes. Part of this was tutoring in classes I'd already taken, mainly Calculus.
Graph the curves in Exercises $37-46$ . a. Where do the graphs appear to have vertical tangents?b. Confirm your findings in part (a) with limit calculations. But before you do, read the introduction to Exercises 35 and 36.$$y=x^{2 / 3}-(x-1)^{1 / 3}$$
ALGEBRA $A B C D$ is a rectangle. If $A C=30-x$ and $B D=4 x-60$ find $x$(FIGURE CANT COPY)
ALGEBRA MNQR is a rectangle. If $N R=2 x+10$ and $N P=2 x-30$ find $M P$(FIGURE CANT COPY)
Find each value or measure.x(FIGURE CANT COPY)
FRAMING Mrs. Walker has a rectangular picture that is 12 inches by 48 inches. Because this is not a standard size, a special frame must be built. What can the framer do to guarantee that the frame is a rectangle? Justify your reasoning.
COORDINATE GEOMETRY Quadrilateral EFGH has vertices $E(-4,-3), F(3,-1)$$G(2,3),$ and $H(-5,1) .$ Determine whether $E F G H$ is a rectangle.