Answer: A(t) = (6.4 ft^2/min)*t
Step-by-step explanation:
We know that Emily paints at a constant rate, and she can paint 32 ft^2 in 5 minutes.
Then if we take the quotient of these two quantities, we will find the amount she can paint in one minute, this is:
32ft^2/5min = (32/5) ft^2/min = 6.4 ft^2/min.
Then if she paints for t minutes, the area that she can cover can be written as:
A(t) = (6.4 ft^2/min)*t
This is the linear equation we wanted to find.
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:
The picture of the question in the attached figure
we know that
The surface area of a cylinder is given by the formula
simplify
we have
assume
substitute
Answer:
data set 3 would have the least mean absolute deviation among the three sets since there is less spread of the data and the data values in set-3 lie close to the mean.
Step-by-step explanation:
The mean absolute deviation is a measure of spread of the data.
If the data values in the given data set are widely spread then we obtain a higher mean absolute deviation.
if the data values of a given data set are close to each other i.e there is a less spread of the data and hence the mean absolute deviation will be low as the data values will lie close to the mean.
We are given three data set as:
set- 1 42, 48, 50, 88, 49
set- 2 63, 29, 35, 28, 30
set- 3 2, 5, 3, 8
Hence, we could observe that the data values in set 1 and set 2 are widely spread.
In set-1 the data value 88 is much higher value as compared to other data values.
Similarly in set-2 the data value 63 is again a much higher value as compared to other data values.
Whereas in set-3 the data values are all closely related and there is not much spread in the data.
Answer: - 19
Step-by-step explanation: