Cou X 0 115 X 115 X Link X 115 X 5 6.2 F X G arct X P CSE: X * Cou X * 1 X *115 X New X Dow X 115 X C File | C:/Users/ryan/Downloads/1151M3_Sp22.pdf.pdf R Update E 1151M3_Sp22.pdf.pdf 5 / 5 67% + Math 1151 Midterm 3 Spring 2022 4) A rectangle in the first quadrant is constructed by taking a point (x, y) on the graph of the function f(x) =9-x2, drawing a line segment vertically downward to the x-axis and a line segment horizontally leftward to the y-axis, as in the picture below. Denote the length of the base (along the x-axis) of the rectangle by x, the height of the rectangle (along the y-axis) by y (in meters), and the PERIMETER of the rectangle by P. When x = 2 m (and only at that moment), the height y is shrinking at a rate of = m/s. Find the value of P by performing the steps below. (x, y) a) (1 point) Find a formula for the height, y, of the rectangle as a function of x. (This is denoted as y(x).) y ( x ) = _ 9 - x 2 b) (4 points) Find the value of at an Y = 9 - x 2 dy = - 2x . # - 0.5 = - 2.2. # [dx] 8 m/s [ at y = 2 m = 3 c) (2 points) Find a formula for the perimeter, P, of the rectangle as a function of x. (This is denoted as P(x).) P (x ) = _-2x + 2x + 9 d) (4 points) Find the value of ap [at ] x-2mm If = - 4x x + If + 2. 94 [-Off Jy = 2 m = - 4.2. 8 + 2. 8 = - #m/s - * m/s e) (4 points) Write a sentence to explain what the value found in (d) means about the rectangle. (Don't forget UNITS.) At the moment x = 2m, the perimeter of the rectangle is shrinking at rate of m/s . ed by 100000872644204 from CourseHero.com on 10-17-2023 14:09:03 GMT -05:00 60F Q Search 90 W 3:09 PM Funny 10/17/2023 20