Finding the center of gravity of an object by calculus There is a circular iron sheet with uniform thickness, and its radius is 30 cm long. Now take any of its radius as the diameter of the small circle as a circle (the small circle is too large for the center of the circle), and cut off the small circle with a diameter of 30 cm. Find out how many cm is the distance between the center of gravity of the remaining part (crescent shaped) and the center of the large circle? Requirements: use calculus to solve, and give the detailed process Thank you very much.

Finding the center of gravity of an object by calculus There is a circular iron sheet with uniform thickness, and its radius is 30 cm long. Now take any of its radius as the diameter of the small circle as a circle (the small circle is too large for the center of the circle), and cut off the small circle with a diameter of 30 cm. Find out how many cm is the distance between the center of gravity of the remaining part (crescent shaped) and the center of the large circle? Requirements: use calculus to solve, and give the detailed process Thank you very much.

I don't know calculus, but this problem can also be solved by using the lever principle
Let the center of gravity of the small circle be O1, the center of gravity of the large circle be O2, and the center of gravity of the crescent shape be O3
It can be seen that O3 and O1 are on both sides of O2. The ratio of the mass of crescent shape to the mass of small circle is 3:1, then 3M * o3o2 = m * o2o1
Therefore, o3o2: o2o1 = 1:3
Because o2o1 = 15cm
So the center is huge, and the center of the circle = 5cm

Calculus, advanced mathematics Let y = (square of x) * ln (1 + x), find the derivative of order 50 of Y,

The first floor is misunderstood. The algorithm on the website quoted on the second floor is also wrong. Please see the following figure for details (it has been transmitted, please wait a few minutes)

An advanced calculus problem, A chain is hung on a frictionless nail. Suppose that at the beginning of the movement, one side of the chain drops 8 meters and the other side drops 10 meters. How long does it take for the whole chain to slide over the nail

Let me work out an equation for you   Take it yourself
Let the length of the chain end be s    G is the gravitational acceleration   T is the time

The area of a figure enclosed by a parabola and a straight line Parabola C: y = 2x ², Line L1, y = - 4x + 2, line L2, x = a, a ≠ - 1, find the area of the figure surrounded by parabola C and L1, L2

Use calculus to calculate. Do tangent assistance

If the function f (x) = log is a subtractive function with a as the base (3-ax) on the interval [0,2], then the value range of real number a

Because a > 0, the function g (x) = 3-ax is the subtraction function, and the function f (x) = log takes a as the base (3-ax) as the subtraction function. The principle of subtraction and increase must be a > 1, and then from X in the interval [0,2], there is always 3-ax > 0, so X

If f (x) = loga (x2 − ax + 1 2) If there is a minimum value, the value range of real number a is __

Let u = x2 ax + 1
2=（x-a
2）2+1
2-a2
4, then u has a minimum value of 1
2-a2
4，
To make the function f (x) = loga (x2 − ax + 1
2) If there is a minimum value, there must be
a＞1
one
2−a2
4＞0 ， The solution is 1 < a <
2．
That is, the value range of a is (1,
2）．
So the answer is: (1,
2）．