A circle of radius r has area A = πr . If a random circle has a radius that is uniformly distributed on the interval (0, 2) what is the mean of the area of the circle?
A random circle is chosen with radius a random variable R having density function fR(r) = 6r(1−r) if 0< r <1 and fR(r) = 0 for r≥1.What is the expected value of R? What is the expected value of the area of the circle?
A microscopic particle cannon fires spherical particles of radius R, which is a continuous random variable with the PDF given by fR(r) := ( ar + b r ∈ [1, 2] , and 0 else It is further given that fR(2) = 1/2 . (a). Find a and b. (b) Let S = 4πR^2 be the surface area of a particle. Find E(S), the mean surface area. (c). Let V = 4/3 πR^3 be the volume of a particle. Find...
Question 11 A plastic rod has been bent into a circle of radius R-9.00 cm. It has a charge Q1-+6.23 pC uniformly distributed along one-quarter of its circumference and a charge Q2 - -6Q1 uniformly distributed along the rest of the circumference (see the figure). With V 0 at infinity, what is the electric potential (a) at the center C of the circle and (b) at point P, which is on the central axis of the circle at distance D...
5. A sector in a circle of radius r сm has area 6 cm² and the arc opposite @ has length a cm. Determine r and 0 (in radians) analytically and exactly. 7
Write a PYTHON program that will approximate the value of π. You can do this by computing π to be the ratio of the area of a circle to the area of the square that bounds that circle. Assume a circle of radius 0.5 enclosed by a 1x1 square. The area of the circle then is πr^2=π/4, since r=0.5=1/2 and the area of the square is 1. To approximate the ratio, take a large number of uniformly distributed random points....
Theorems prove the following 4.5 Area of circle 1 The area of a circle is a = πr, wherer is the radius of the circle Hint: Decompose and rearrange the area of a circle into something a little more familiar. 5.3 Parallel lines in Triangle Theorem I Let a ABC be a triangle with points Pand Q be points on AB and ac, respectively. In this case, AP - AQ If and only if P Q 11 BL. AP -...
Let A be the area of a circle with radius r. In = 3, find a when = = 1 Preview Points possible: 5 This is attempt 1 of 4.
h(t) be the radius of the circle at time t. (1 point) Let A- f(r) be the area of a circle with radius r and r Which of the following statements correctly provides a practical interpretation of the composite function f(h(t) ? Select all that apply if more than one is appropriate. | ■ A. The area of the circle which at time t has radius h(t) B. At what time t the area will be A-f(r). C. The area...
If the magnetic field is uniform over the area bounded by a circle with a radius R, the net current through the circle is? A) 0B) 2(pi)RB u0 C) (pi)R 2 B/ u0D) RB/2u0E) 2RB/ 0
A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 2 ft/min. What is the rate in the change of area at the instant that the radius is 23 ft? Write an equation relating the area of a circle, A, and the radius of the circle, r. (Type an exact answer, using a as needed.) Differentiate both sides of the equation with respect to t. dA dr dt dt (Type an exact...