Q-3:a) A rectangle is to be inscribed in a semicircle of radius 2 m. What is...
A rectangle that is x feet wide is inscribed in a cirdle of radius 4 ft area of the rectangle as a function of x. b) Find the domain of the function. c) Graph the function with a graphing calculator d) What dimensions maximize the area of the rectangle? )Simplifty your answer.) b) Find the domain of the function. Choose the correct answer below ○ H. (xlxs64) c) Choose the correct graph below. The window settings for each graph are...
A rectangle is inscribed in a circle of radius 1 (see the figure). Let P = (x,y) be the point in quadrant that is a vertex of the rectangle and is on the circle. Psy) Answer the following questions (a) Express the area A of the rectangle as a function of X A(x) = ax/1-x² (b) Express the perimeter p of the rectangle as a function of x. p(x) = 2(2** 2/7-x) (c) Graph AA(X). For what value of A...
(1 point) Find the dimensions of the rectangle of largest area that can be inscribed in a circle of radius r. List the dimensions in non-decreasing order (the answer may depend on r).
7. Find the rectangle of largest area that can be inscribed under f(x)-9-x and above theX-axis. radvea ans) 7. Find the rectangle of largest area that can be inscribed under f(x)-9-x and above theX-axis. radvea ans)
1. Find the dimensions of the largest rectangle that can be inscribed in the right triangle ABC show in the illustration. A (0, 9) (x, y) 0 8 (12, 0)
10. (5 points) You want to maximize the area of an inscribed rectangle under the line 4 in the FIRST quadrant with the x-axis and the y-axis. Find the measurements of such rectangle so that you can have maximum area. Please draw the picture of the problem on X-y coordinate system to receive full credit. Yx) = -x +
Please do both 3. A rectangle has its base on the x-axis and it upper two vertices on the parabola y = 12 - x? What dimensions will maximize the area of the rectangle? 4. What are the dimensions of the right circular cylinder of greatest volume that can be inscribed in a sphere with radius 8 inches? OE (S! R4 135=61 rta 64 - 4
14. Cousider the following fiunction y()graphed on the interval (0, 10]. The graph between z = 5 and z = 7 is a semicircle having radius 1. (4,0) 2.2) 7,2) 10,0) -2 -f(a) Find the following values. (a) f24/5 f(x) do 23/5 12 (c) g f(x) dx= The area of a circle is πγ2.) (Hint: (d) f(x) dx 10 (e) Suppose that F(x) is the antiderivative of f(x), and assume that F(0) = What is F(2)? What is F(23/5)? F(2)...
4. On the segment CD we draw the semicircle (A, a) which is tangent to the semicircle (B, b). We also draw the semicircle (0, OC), and the perpendicular EF to CD. The segments FC,FD intersect the semicircles at points H, J. The circles (M.). (L. 2) are tangent to the semicircle (O), the segment FE, and the semicircles (A). (B), respectively. a) Show that OC = a + b. b) Show that FE is a common tangent to the...
Show work please Optimization problems 1. (5 points) Find two nonnegative numbers whose sum is 25 and so that the product of one number and the square of the other number is a maximum. 2. (5 points) Build a rectangular pen with two parallel partitions using 300 feet of fencing. What dimensions will maximize the total area of the pen? (5 points) An open rectangular box with square base is to be made from 48 ft.2 of material. What dimensions...