Answer:
64 and 81
Step-by-step explanation:
67 is in between the two numbers and the square roots of those are 8 and 9. this shows that the square root is in between 8 and 9.
To determine the centroid, we use the equations:
x⁻ =
1/A (∫ (x dA))
y⁻ = 1/A (∫ (y dA))
First, we evaluate the value of A and dA as follows:
A = ∫dA
A = ∫ydx
A = ∫3x^2 dx
A = 3x^3 / 3 from 0 to 4
A = x^3 from 0 to 4
A = 64
We use the equations for the centroid,
x⁻ = 1/A (∫ (x dA))
x⁻ = 1/64 (∫ (x (3x^2 dx)))
x⁻ = 1/64 (∫ (3x^3 dx)
x⁻ = 1/64 (3 x^4 / 4) from 0 to 4
x⁻ = 1/64 (192) = 3
y⁻ = 1/A (∫ (y dA))
y⁻ = 1/64 (∫ (3x^2 (3x^2 dx)))
y⁻ = 1/64 (∫ (9x^4 dx)
y⁻ = 1/64 (9x^5 / 5) from 0 to 4
y⁻ = 1/64 (9216/5) = 144/5
The centroid of the curve is found at (3, 144/5).
Answer:
Step-by-step explanation:
4 lines of symmetry
We have two sides and one angle opposite to one of the known sides.
Begin with applying the Law of Sines to find angle A:

= <span>

Then, solve for sin A:
</span>sin A =

Now, plug in numbers:
sin A = 19 × sin(38) / 10 = 1.17
We know that it does not exist an angle whose sin is bigger than 1, therefore
no triangle is formed.