(i) Find the shortest distance from the origin to the line 3x + y = 6 and give the coordinate of the point P on this line that is closest to the origin. - Hint: Optimize the (distance) formula D = √√(x - xo)² + (y yo)² which measures the distance between a point (x, y) and the reference point (xo, yo). (ii) Show that the origin lies on the line perpendicular to 3x + y = 6 at the point P.

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A: Let's find t for the given  terminal points.

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A: We can prove the given the result by differentiating the given function.

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A: To solve: The equation log3x-9+k=2-log3x-1+k. Given: The value of k=3 Concept used;…

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A: The given integral,        ∫01ex1+exdx

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A: Given: y(3)-2y''+y'=1+xexAuxilliary equation: m3-2m2+m=0Therefore, m=0,1,1Complimentary…

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A: 5. Given that, the points are 1,3,0 and 2,4,4. Note that, the symmetric equation of the a straight…

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A: polynomial can have constants (like 4), variables (like x or y) and exponents (like the 2 in y2),…

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A: Solve the following

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