Initial value: 1. rate of change: 3 over 5.
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).
This problem is a more like of a percentage increase problem. First, subtract 11 hours by the original hours which is 10 hours. Using mental math, subtracting 11 by 10 would be 1, obviously. Take the outcome of 1 and divide it by the hours he did last week which is 10. 1 divided by 10 would be equal to .1. Convert the decimal to a percentage and then you would get 10% and add it to 100%. So, yes, he is in fact correct.
Y = -1 is a horizontal line going through "-1" on the y axis
Note that the point (1,2) is exactly 3 units of distance above the line y = -1
When we reflect across this line, the point (1,2) will just move straight down to exactly 3 units of space below the line y = -1. Since we are not shifting left or right, the x coordinate of our original point will not change. The y coordinate of our original point will now need to be reduced by 6(3 units down to get to the line of reflection and then 3 more down to get to the image location)
The coordinates of the image point will be (1, -4)
Now we need to do the same process with (1, -4) being reflected across y=1
Note (1,-4) is 5 units of distance below the line y = 1 , so we need to reflect the point upward so that the image point is located exactly 5 units of distance above the line y = 1 Again, the x coordinate does not change, and our final image coordinates are (1, 6)
I guess more simply stated, if you're just looking for the number in the green box it would be " 1 " .. Reflecting points across horizontal lines only result in changes of the "y" coordinate since there is no shift left or right.
Answer: 1/2
Step-by-step explanation:
The sample space when a six sided die is thrown once is :
{ 1,2,3,3,5,6}
The even numbers are :
{2,4,6}
Therefore :
P(even) = n(even) / total number
That is
P(even) = 3/6
P(even) = 1/2
