An espresso stand finds that its weekly prot is a function of the price, a, it charges per cup. If a is in dollars, the weekly prot is 13(3) = 430032 + 9570:: 531's dollars. {a} What is the maximum weekly prot. 3 (Round to the nearest oent and do not include any commas in your answer.) {bi What price per cup that produces that maximum prot? $ [Hound to the nearest cent.) [c] Iul'd'hioh of the two functions below gives a function that has the same maximum profit? A\" ' \\"J' "" B. PT: 2) {d} Based on the function in your answer to to) above. what price per cup of produces that maximum profit? $ {Round to the nearest cent.) (e) Which of the two functions below gives gives a function where the price per cup that produces the maximum prot remains unchanged? A. 13(2) + 80 B. Pris + 80) (t) Based on the function in your answer to {3) above. what is that maximum weekly profit? $ {Round to the nearest cent.) The equation of the line that goes. through the point (3, 8) and is perpendicular to the line 4:: + 53; = 4 can be written in the form 3; 2 ma: + b. where m: b: \fUse interval notation to indicate the domain and range of y = vx2 - 25. Domain: I E Range: y E Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively.The equation of the Iinethat goes through the paint (6, 8) and is parallel to the line 3:: + 43; = 3 can be written in the form 3; 2 ma: + b. where m: b: C+7 Use interval notation to indicate the domain of f (@) = x2 + 4x + 4 Answer: I E Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively.Consider the quadratic function w(x) = -2x2 - 18x + 33. (a) The vertex of this parabola is at the point? Note: State the result in the form of a point (h, k) (b) What is the axis of symmetry for this parabola? Note: Enter an equation for a vertical line of symmetry, not just a number.Consider the quadratic equation v(t) = t' + 14t -9. a) What are the coordinates of the vertex? Note: State result in the form of a point (h, k). b) What is the axis of symmetry? Note: Enter an equation for a vertical line of symmetry, not just a number.Use interval notation to indicate the domain of f(@) = V I'- 17. Answer: I E Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively.Consider the function f() = 2x- + 10x - 1. (a) What is the y-intercept of the graph? y = (b) What are the x-intercepts of the graph? = = Note: If there are multiple answers, separate them by commas. If there are none, type none.Use interval notation to indicate the domain of f() = Vx2-8x. Answer: I E Note: Input U, infinity, and -infinity for union, oo, and -oo, respectively.Biologists have noticed that the chirping of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 113 chirps per minute at 71 degrees Fahrenheit and 170 chirps per minute at 86 degrees Fahrenheit. (a) Find a linear equation that models the temperature T' as a function of the number of chirps per minute N. T(N) = (b) If the crickets are chirping at 158 chirps per minute, estimate the temperature: T =The equation of the line that goes through the point {5, 9} end has slope % can be written in the form 3; = me: + b, where: The equation of the line that goes through (4, 4) and (6, 11) can be written in the form y = max: + b, where