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).
since the ∡C = ∡B, that means their corresponding sides stemming from the vertex A are equal, namely AC = AB.
2x - 24 = x - 2
x = 22.
Answer:
The area of the piece of construction paper is 
Step-by-step explanation:
Length of construction paper =
=
Width of construction paper = 
= 
Area of construction paper =
Area of construction paper = 
=
Hence the area of the piece of construction paper is
The second quartile Q₂ is nothing but the Median.
This means that it median = 4.2
Answer:
Step-by-step explanation:
If taxes have been underpaid, it won’t matter to the IRS who is responsible. If the return was filed jointly, the government can go after both even if one didn’t personally earn one penny of the reported income.
Hence in the given case,
For the unpaid amount of $38,200 IRS can assess either Mr.peterson or Mrs.Peterson for the entire deficiency as both are jointly and severally liable for the tax paid before they got divorced.
