Answer:
<h2>The area of the base is 144 square inches.</h2><h2>The area of each triangular face is 66 square inches.</h2><h2>Grabiel needs 408 square inches of paint.</h2>Step-by-step explanation:
The complete problem is attached.
Notice that the figure is a square pyramid, where its base dimensions are 12 inches by 12 inches, which represents an area of
The slant height of the pyramid is 11 inches, which allow us to find the area of each triangle face
But there are four triangle faces, so .
Therefore, the area of each triangular face is 66 square inches.
So, the total surface area would be the sum
Therefore, Gabriel needs 408 square inches to paint the whole model.
The average squared distance between the points is their variance
The average squared distance is 8/3
<h3>How to determine the average squared distance?</h3>The given parameters are:
R={(x,y): 0<=x<=2, 0<=y<=2}
The point = (2,2).
f(x,y) = (x-2)² + (y-2)²
The squared distance is calculated as:
D² = f(x,y) = (x-2)² + (y-2)²
Where the area (A) is:
A = xy
Substitute the maximum values of x and y in A = xy
A = 2 * 2
A = 4
The minimum values of x and y are 0.
So, the limits for the integrals are 0 to 2
The integral becomes
Expand
Evaluate the inner integral with respect to x from 0 to 2
Expand
Simplify
Expand
Evaluate the integral with respect to y from 0 to 2
Expand
D² = 32/3
The average squared distance (AD²) is calculated as:
AD² = D²/A
So, we have:
AD² = 32/3 4
Evaluate the quotient
AD² = 32/12
Simplify
AD² = 8/3
Hence, the average squared distance is 8/3
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