Question:

Finding integers/equations? Point of tangency!? Urgent help needed please!?

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1)Find an integer, x, greater than 4 where the sum of x consecutive integers is divisible by x

2) Show that the equation above gives the correct slope for the line tangent to a circle with a radius of 13 at the point (-5,12)

So I'm thinking, the circle's center is at (0,0) because then the point of tangency will be (-5,12) exactly...But I don't know what to do

For #1, I got 5n+10....is that right or wrong

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  1. q1

    let the numbers be n+1 till n+x.

    then the sum is

    = nx + x(1+x)/2

    when the sum is divided by x, it will become n + (1+x)/2.

    so if (x+1) has to be even, then x must be an odd integers, greater than 4.

    x = 5, or any odd integers greater than 5.

    q2

    m = -1/(12/-5) = 5/12

    point of tangency is (-5,12), yes.

    y - 12 = 5(x + 5)/12

    y = 5x/12 + 169/12

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