EXAMPLE 4 Find the moments of inertia Ix, Iy, and I0 of a homogeneous disk D with density rho(x, y) = rho, center the origin, and radius a. SOLUTION The boundary of D is the circle x2 + y2 = a2 and in polar coordinates D is described by 0 ≤ θ ≤ 2π, 0 ≤ r ≤ a. Let's compute I0 first: I0 = D (x2 + y2)rho dA = rho 2π 0 a 0 r2 r dr dθ = rho 2π 0 dθ a 0 r3 dr = 2πrho a 0 = . Instead of computing Ix and Iy directly, we use the facts that Ix + Iy = I0 and Ix = Iy (from the symmetry of the problem). Thus Ix = Iy = I0 2 = .

Design a number line containing five (5) points2.benin, one of the smallest countries in africa, has a total area of 43,475 square miles. the population of the country was recently estimated at 10,160,555. about 3,657,790 people live in rural areas. the country has only about 870 miles of surfaced roads. a. round off the total population to the nearest hundred thousand people. b. round off benin’s area in square miles to the nearest thousand. c. round off the number of miles of surfaced roads to the nearest ten. d. round off the number of people who live in rural areas to the nearest million.

Svetlana's hair is 4 4 centimeters ( cm cm) long. her hair grows 1 . 5 cm 1.5cm per month. svetlana wants her hair to be less than 1 6 cm 16cm long. write an inequality to determine the number of months, m m, svetlana can allow her hair to grow so that it is less than 1 6 cm 16cm long.

Tim open up a new saving account with a $50 deposit and plant to deposit $20 per week into the same account.write an expression to represent the total amount in his savings account.