Linear Equations A 10 ft square concrete pad is on a constant plane, but is not

Question

Linear Equations A 10 ft square concrete pad is on a constant plane, but is not level. es x = 0 and y = 0, as indicated in the figure below The corner of the pad is at the The station and elevation or three points on the pad are surveyed. What equation in the form z Ax By + C describes the surface (ie, what values of A, B and C)? Set up a block to predict the elevation of any point on the pad given the x and y coordinates using the equation. Have the spreadsheet return the word "Off if the coordinales entered are not on the pad. Basically, add an if statement to check whether or not the x's and y's you enter are between 0 and 10 (10 ft wide slab). Note: this check is not exact, because it just checks whether or not the vertical projection of the plane are within the 10 ft range; if the slab is tited (as it is in our case), the actual dimensions of the pad will be longer than 10 ft but this provides a quick check. Use goal seek to determine the y coordinate on the plane if the x coordinate is 2 and the z coordinate is 12.88. Observations Point x (ft) 2.0 4.5 9.0 7.0 2.5 6.0 z (ft above datum) 12.0 10.0 11.5 Oa x=0 =0

Explanation / Answer

The three given points on the plane, P=(2,7,12), Q=(4.5,2.5,10) and R =(9,6,1.5)

PQ = 2.5i-4.5j-2k and PR = 7i-j-0.5k

PQ x PR = 0.25i-12.75j+29k

So equation of surface = 0.25(x-2)-12.75(y-7)+29(z-12)

which is x-51y+116z-1037=0

So, z=(1037-x-51y)/116

Give if to x- and y- values as 0<x<10 and 0<y<10.

Give goal seek as z=12.88 for x=2 (you will get y =9.0015)

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