1. The roof of a square floor (20m x 20m) base structure can be modelled as...

 

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1. The roof of a square floor (20m x 20m) base structure can be modelled as z(x, y) where (x, y) is the coordinate of the floor with (0,0) as the coordinate of the centre of the floor. (d) (e) EVEN number (2, 4, 6, 8, 0) (f) ODD number (1, 3, 5, 7, 9) Selection sin nx y² z(x, y) = A + ( (a) (b) To show the 3D graph of the roof, the function z(x, y) above the floor region - A≤x≤A and-B≤y≤B (c) Double Integral ) B000 ВО COS TTX y² z(x, y) = B + ( -- ) A000 Wolfram Alpha Method Write down the selection of function z(x, y) according to the input variables of A and B. АО Determine the value of the upper and lower limits of a, b, c, and d. Calculate the volume of the structure by using double integrals. d S.S. z(x, y) dx dy Z(x,y) dy dx Change Order of Double Integral Determine the value of the upper and lower limits of e, f, g, and h. Calculate the volume of the structure by using both double integrals. [ So Math Integration Method Determine the structure's volume using the math integration method for part 1(c). d So So z(x, y) dx dy Comments on the results for parts 1(c), 1(d) and 1(e). 1. The roof of a square floor (20m x 20m) base structure can be modelled as z(x, y) where (x, y) is the coordinate of the floor with (0,0) as the coordinate of the centre of the floor. (d) (e) EVEN number (2, 4, 6, 8, 0) (f) ODD number (1, 3, 5, 7, 9) Selection sin nx y² z(x, y) = A + ( (a) (b) To show the 3D graph of the roof, the function z(x, y) above the floor region - A≤x≤A and-B≤y≤B (c) Double Integral ) B000 ВО COS TTX y² z(x, y) = B + ( -- ) A000 Wolfram Alpha Method Write down the selection of function z(x, y) according to the input variables of A and B. АО Determine the value of the upper and lower limits of a, b, c, and d. Calculate the volume of the structure by using double integrals. d S.S. z(x, y) dx dy Z(x,y) dy dx Change Order of Double Integral Determine the value of the upper and lower limits of e, f, g, and h. Calculate the volume of the structure by using both double integrals. [ So Math Integration Method Determine the structure's volume using the math integration method for part 1(c). d So So z(x, y) dx dy Comments on the results for parts 1(c), 1(d) and 1(e).