Two triangles are congruent if one angle of one triangle is equal in measure to the corresponding angle of the other triangle.
2 answers:
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The center of mass is mathematically given as
Determine the center of mass in one dimension:
Represent the masses at the respective distances.
We calculate the total mass of the system.
Step 03: Calculate the moment of the system.
we calculate the center of mass.
Read more about the center of mass.
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You set up was almost accurate. Remember the arc length formula:
If f'(y) is continuous on the interval [a,b], then the length of the curve x = f(y), a ≤ y ≤ b should be;
L = ∫ᵇ ₐ √1 + [f'(y)]^2 * dy
We have to find the length of the curve given x = √y - 2y, and 1 ≤ y ≤ 4. You can tell your limits would be 1 to 4, and you are right on that part. But f'(y) would be rather...
f'(y) = 1/(2√y) - 2
So the integral would be:
∫⁴₁ √1 + (1/(2√y) - 2)² dy
Using a calculator we would receive the solution 5.832. Their is a definite curve, as represented below;
