# How do you find the centroid of the quarter circle of radius 1 with center at the origin lying in the first quadrant?

Non-Calculus Solution:

Observation 1:

The centroid must lie along the line

By signing up, you agree to our Terms of Service and Privacy Policy

To find the centroid of the quarter circle of radius 1 lying in the first quadrant, you can use the formulas for the centroid of a region. For a quarter circle, the centroid lies along the axis of symmetry, which in this case coincides with the y-axis.

The x-coordinate of the centroid (¯x) for a quarter circle with radius r is given by the formula:

¯x = (4r) / (3π)

In this case, r = 1, so:

¯x = (4(1)) / (3π) = 4 / (3π)

Since the centroid lies along the y-axis, the x-coordinate is 0.

Therefore, the centroid of the quarter circle of radius 1 lying in the first quadrant is at the point (0, 4 / (3π)).

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you find the arc length of the curve #f(x)=x^3/6+1/(2x)# over the interval [1,3]?
- How do you find the arc length of the curve #sqrt(4-x^2)# from [-2,2]?
- Given the general solution to #t^2y'' - 4ty' + 4y = 0# is #y= c_1t + c_2t^4#, how do I solve the problem #t^2y'' - 4ty' + 4y = -2t^2 , y(1) = 2, y'(1) =0#?
- What is the general solution of the differential equation # dy/dx + 2y = 0#?
- What is a solution to the differential equation #dy/dx=ky#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7