How do you solve this problem carefully?

Question

This is a particle motion problem. A point moves smoothly along the curve y=x^(3/2) in the first quadrant in such a way that its distance from the origin increases at the constant rate of 11 units per second. Find dx/dt when x=3.
This is a Calculus problem. The answer is dx/dt=4 units/second. I want you to explain the answer. Thank you so much. I appreciated it.

Answer 1

y = x^(3/2): distance from origin is r = √(x^2 + y^2) = √(x^2 + x^3)

dr/dt = dr/dx dx/dt = (1/2) (x^2 + x^3)^(-1/2) . (2x + 3x^2) dx/dt
So when x = 3, dr/dt = (1/2) (36)^(-1/2) (33) dx/dt = 11/4 dx/dt. Since dr/dt = 11, this means 11 = 11/4 dx/dt, so dx/dt = 4.

Answer 2

a million) There are 6 numbers on a cube. So total no. of trials is 6. There are 3 strange numbers on a cube - a million,3,5 danger = no. of trials wherein an experience got here approximately / total no. of trials = 3 / 6 = a million/2 So there's a million/2 danger of having an strange style. 2) total no. of marbles = 6+5+3+7 = 20 marbles no. of green marbles = 6 danger = no. of green marbles / total no. of marbles = 6/20 = 3/10 So there is 3/10 danger of having a green marble. 3) danger = no. of black marbles / total no. of marbles = 7/20 So there is 7/20 probabilty of having a black marble. 4)On a coin there's a million head and a tail. So danger of having atleast a million heads = a million/ 2 ( 2 because of the fact coin is flipped two times) wish you understood it.