45. (a) Find the point on the x-axis closest to the point (a, b, c). (b) Find a unit vector that points from the point you found in part 45(a) toward (a, b, c).

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A: Here, the given functions are: z=f(x,y)=(10+23x)ytan xx=13-e2e(t-1)+tan-1(t)y=(2-t)et-13(t-1)

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A: We will solve the integration. 

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A: We will use the concept of inverse of matrix and then letter coding to decode the message

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Q: -. .- --- .... ...

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A: To solve the integration of the integrand (x2+1)/(x-6)(x-5)2 , we use partial fraction form. 

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A: We have to find indefinite integral

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A: Given population of world in 2015  was 9.75 billionlet   for t=0 , we have year 2015

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A: Using error function erf(f) . 

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A: In order to solve this question we will use the concept of first principle which defines derivative.

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