Vector a = (2, 1, 2) Vector b = (1, 2, 4) Vector p = (k, k, k)
Vector a to vector b = vector b - vector a = (1, 2, 4) - (2, 1, 2) = (1 - 2, 2 - 1, 4 - 2) = (-1, 1, 2) Vector a to vector p = vector p - vector a = (k, k, k) - (2, 1, 2) = (k - 2, k - 1, k - 2)
Vector a to b is perpendicular to vector a to p if the dot product of vector a to vector b and vector a to vector p is equal to zero. i.e. (-1, 1, 2) . (k - 2, k - 1, k - 2) = 0 -1(k - 2) + (k - 1) + 2(k - 2) = 0 -k + 2 + k - 1 + 2k - 4 = 0 2k -3 = 0 2k = 3 k = 3/2
The amount he pays is the number of shirts times 3 / 2 (or 1.5) unless the equation is f=3/(2s) where the cost would then be the number of shirts times two, divided by three
The x-intercepts are the values of x for which f(x) = 0. x^2 + 4 = 0 x^2 = -4 x= ±√(-4), which are not real numbers. f(x) does not have an x-intercept.
