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    Minimum Distance

    Find all values of b such that the minimum distance from the point (2,0) to the line Y = (4/3)X + b is 5. d = 5 = ((Y - 0)[sup:u4ekfm1r]2[/sup:u4ekfm1r] + (X - 2)[sup:u4ekfm1r]2[/sup:u4ekfm1r])[sup:u4ekfm1r]1/2[/sup:u4ekfm1r] Squaring both sides, 25 = (Y - 0)[sup:u4ekfm1r]2[/sup:u4ekfm1r] +...
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    Find k so f(n^2 + k) = f(n)Xf(n + 1) for f(n) = n^2 - n + 2

    Let f(n) = n[sup:2bpiakor]2[/sup:2bpiakor] - n + 2 Find a value for k such that the equation f(n[sup:2bpiakor]2[/sup:2bpiakor] + k) = f(n) X f(n + 1) holds for all values of n. f(n[sup:2bpiakor]2[/sup:2bpiakor] + k) = (n[sup:2bpiakor]2[/sup:2bpiakor] + k)[sup:2bpiakor]2[/sup:2bpiakor] -...
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    Function: For f(x)=2x+3, find a, b so f(ax+b)=x is true for

    Let f(x) = 2x + 3 Find values for a and b such that the equation f(ax + b) = x is true for all values of x. 2(ax + b) + 3 = x So, how does one solve for three variables without some method of substitution? Or, have I missed the substitution possibilities?
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    Tangent to a Curve

    Find a point P on the curve y = x[sup:1o6xq0tm]3[/sup:1o6xq0tm] such that the slope of the line passing through P and (1, 1) is 3/4. p[sub:1o6xq0tm]1[/sub:1o6xq0tm] = (1, 1) p[sub:1o6xq0tm]2[/sub:1o6xq0tm] = (x, x[sup:1o6xq0tm]3[/sup:1o6xq0tm]) m = (y[sub:1o6xq0tm]2[/sub:1o6xq0tm] -...
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    Solving for X

    X^5 - 2X^3 - 2X = 0 I factored X out of the left side, X(X^4 - 2X^2 - 2) = 0 So one solution is X = 0, which obviously checks in the original equation. That leaves X^4 - 2X^2 - 2 = 0, And I have no idea what to do next
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    Factoring Problem

    Factor 8 - (a + 1)^3 I started cubing the (a + 1) binomial, resulting in 8 - (a^3 + 3a^2 + 3a + 1), and then subtracting to get 8 - a^3 - 3a^2 - 3a - 1, and then subtracting 1 from 8 I get, 7 - a^3 - 3a^2 -3a I do not see what to do next.
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