A rectangle is drawn as shown in the figure below. One side of the rectangle is on the y-axis and the right upper corner lies in the first quadrant on the line y = -12 x + 9. The rectangle extends below the x-axis to the line y = -4. Answer the following: a) Write the area of the rectangle as a function of x A(X) = b) For all first quadrant points on the given line, determine the maximum area enclosed by the rectangle. (Decimals in answers are marked incorrect.) Maximum area = square units (x, y)MY NOTES A business (Widgets, Inc) forms a linear model of its widget pricing function based on the following information: Let x represent the number of widgets sold and p(x) the price per widget in dollars. The firm begins by selling x = 250 widgets at a set price of $30 each. After holding a "sale", the firm proposes that a $10 discount on the price will yield an increase of 20 more widgets sold. This leads to a pricing model: P(x) = 30 -_ (x - 250) Use this to model to answer the following. (a) Based on the fact that the firm wants both sales and the price to be positive, what is the appropriate domain of the pricing function p(x)? Enter your answer using interval notation. Domain: (b) What is the revenue function? (revenue is total sales income) R ( X ) = (c) What sales price p yields maximum revenue? P dollars per widgetFarmer Brown has 900 yards of fencing with which to build a rectangular corral. He wants to divide it evenly into three pens, so he adds in two divider fences, as shown below. Ans a) Write the area of the corral as function of x X A(X) = X VI b) Determine the maximum area enclosed by the corral. (Decimal approximations are marked incorrect. ) 900 - 2. 900 Maximum area = 900 4 square yards 4 4 X yFlights of leaping animals typically have parabolic paths. The figure below illustrates a frog jump superimposed on a coordinate plane. The length of the leap is 9 feet, and the maximum height off the ground is 3d feet. In the graph, assumed = 1.5. Find a standard equation in the form y = a(x - h)2 + k for the path of the frog. NOTE: Simplify your work so that your leading coefficient is a negative fraction without any parentheses. X Frog's path d + 9 XAn object is thrown upward. The height, h, in feet, at time t, in seconds, is given by the formula h = -16+2 + 160 t Determine the time required for the object to reach a height of 40 feet on its way up. Enter an exact answer, not a decimal approximation. XA rectangular field with base x and height 2r is surmounted by two semicircular fields, as shown in the diagram below. The external perimeter of the fields (solid blue track) is 200 meters. Answer the following: a) Express the area A of the rectangular field (shaded green) as a function of r A (r ) = X b) Determine the maximum area enclosed by the rectangular field. (Type "pi" if you need it, or look in the MathPad Greek list. Decimal approximations are marked incorrect.) Maximum area = square meters X