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What are 5 forms of equations of lines?
Standard form: ax + by + c = 0 (a, b, c constants, x and y variables)Slope intercept form: y = mx + c (m, c constants, x and y variables)Two points form: given P = (a, b) and Q = (c, d)(y - b)*(x - a) = (d - b)*(c - a ) (a, b, c, d constants, x and y variables)Parametric equation x = a + r*cos(t), y = b + r*sin(t) (a, b, t constants, x and y variables)X = A + k*B (X, A and B vectors, k scalar, X and k variables).The standard form, parametric equation and vector form have simple analogies for 3 or more dimensions.
What words can you make using the letters a b c g i j k n o p r t u y?
you can make you,no,cab,cat,train,rack
What letters don't have parallel lines?
A, b, c, d, g, j, k, l, o, p, q, r, s, t, u, v, x, y
What capital letters don't have parallel lines?
A b c d g j k l o p q r s t u v w x y.
If for a triangle abc tan a-b plus tan b-c plus tan c-a equals 0 then what can you say about the triangle?
tan (A-B) + tan (B-C) + tan (C-A)=0 tan (A-B) + tan (B-C) - tan (A-C)=0 tan (A-B) + tan (B-C) = tan (A-C) (A-B) + (B-C) = A-C So we can solve tan (A-B) + tan (B-C) = tan (A-C) by first solving tan x + tan y = tan (x+y) and then substituting x = A-B and y = B-C. tan (x+y) = (tan x + tan y)/(1 - tan x tan y) So tan x + tan y = (tan x + tan y)/(1 - tan x tan y) (tan x + tan y)tan x tan y = 0 So, tan x = 0 or tan y = 0 or tan x = - tan y tan(A-B) = 0 or tan(B-C) = 0 or tan(A-B) = - tan(B-C) tan(A-B) = 0 or tan(B-C) = 0 or tan(A-B) = tan(C-B) A, B and C are all angles of a triangle, so are all in the range (0, pi). So A-B and B-C are in the range (- pi, pi). At this point I sketched a graph of y = tan x (- pi < x < pi) By inspection I can see that: A-B = 0 or B-C = 0 or A-B = C-B or A-B = C-B +/- pi A = B or B = C or A = C or A = C +/- pi But A and C are both in the range (0, pi) so A = C +/- pi has no solution So A = B or B = C or A = C A triangle ABC has the property that tan (A-B) + tan (B-C) + tan (C-A)=0 if and only if it is isosceles (or equilateral).
