An 600 mH inductor and a 3 W resistor are connected in series with a 1200-V dc power suppl, Quizzes of Physics

Download An 600 mH inductor and a 3 W resistor are connected in series with a 1200-V dc power suppl and more Quizzes Physics in PDF only on Docsity! A piece of rope that is 18 feet long is cut into pieces. One piece is used to form a circle and the other used to form a square. Write a function f representing the area of the circle as a function of the length of one side of the square s. Hint : If C is the diameter of the circle and P is the perimeter of the square, then C + P = 18. Answer f(s) = (9-2s)2/π , the area of the circle as a function of the length of one side of the square. Explanation Let Length of the rope= 18 ft C = circumference of circle P = perimeter of square s = side of the square r = radius of the circle Required f(s) = ? , Area of circle as a function of the length of one side of the square Solution C = 2πr , circumference of a circle P = 4s , perimeter of a square C+P = 18 ; substitute the formulas 2πr + 4s = 18 ; get the expression for radius,r ; 2πr = 18-4s r = (18-4s)/2π ; simplifying by dividing by 2 r = (9-2s)/π >>equation 1 Solve for the area of circle as a function of the length of one side of the square, f(s) ; f(s) = πr2 ; substitute equation 1 to the r = π((9-2s)/π))2 = π (9-2s)2/π2 = π (81-36s+4s2)/π2 f(s) = (81-36s+4s2)/π f(s) = (9-2s)2/π , the area of the circle as a function of the length of one side of the square.