Question

a metal plate, with constant density 5 g/cm^2, has a shape bounded by the curbe y = x^2 and the x-axis, with 0<= x <= 3 and the x, y in cm

a) find the total mass of the plate
mass =

b) sketch the plate. using your sketch, is x less than or greater than 3/2?

c) find x
x =

Answer 1

Answer:

a) 45 g

b) greater (make the graph youself on desmos or something)

c) 9/4

Step-by-step explanation:

area = integral 0 to 3 of x^2 dx = [1/3x^3] 0 to 3 = 9

mass = density * area = 5 * 9 = 45 grams

area = y*deltax = x^2*deltax

x = integral 0 to 3 of 5x^3 dx / mass = (405/4) / 45 = 9/4