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:
168 units cubed
Step-by-step explanation:
so we know it's base times height right
so like identifying the base doesn't matter as long as you're smart enough to figure how to calculate then whatever lol
so like the base let's just say it's the triangle because that's probably what you're struggling on
so the base of the triangle is like what lol 6 * 8 / 2 = 48 / 2 = 24 so then you have the base multiply by the third dimension
24 * 7 = 140 + 28 = 168 so yeaaaaaaa and it's cubed because it's three dimensional
Answer:
$29, that is the answer for this question
Slope = (-14-1)/(7-1) = -15/6
y = mx + c
y = -15/6 x + c
at (1,1)
1 =-15/6(1) + c
c = 1 + 15/6 = 21/6
y = -15/6 x + 21/6 or
6y = -15x + 21
→ a
the equation is y = mx ( where m is the slope / constant of variation )
calculate m using the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁) = (0, 0 ) and (x₂, y₂ ) = (4, 1) ← 2 points on the line
m = 
=
