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.
you can make you,no,cab,cat,train,rack
A, b, c, d, g, j, k, l, o, p, q, r, s, t, u, v, x, y
A b c d g j k l o p q r s t u v w x y.
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).
3 Primary Colours - Blue, Red, and Yellow
It is spelled B-u-r-e-a-u-c-r-a-c-y.
No, at least not in R/B/Y/G/S/C/R/S/E. I dunno if they did some corruption in D/P to make this happen.
drop, bore, to, be... no word contains all of these letters.
h a p p y b I r t h d a y
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 is the next letter? A Z B Y C X D
Given the point P = (a, b) and slope m, the point-slope equation is(y - b) = m*(x - a)y - b = mx - may = mx - ma + bwhich can be re-written asy = mx + (b - ma) which is of the slope-intercept form y = mx + c in which c = b - ma.Given the point P = (a, b) and slope m, the point-slope equation is(y - b) = m*(x - a)y - b = mx - may = mx - ma + bwhich can be re-written asy = mx + (b - ma) which is of the slope-intercept form y = mx + c in which c = b - ma.Given the point P = (a, b) and slope m, the point-slope equation is(y - b) = m*(x - a)y - b = mx - may = mx - ma + bwhich can be re-written asy = mx + (b - ma) which is of the slope-intercept form y = mx + c in which c = b - ma.Given the point P = (a, b) and slope m, the point-slope equation is(y - b) = m*(x - a)y - b = mx - may = mx - ma + bwhich can be re-written asy = mx + (b - ma) which is of the slope-intercept form y = mx + c in which c = b - ma.
p-u-b-e-r-t-y
They are b, l, p, r, t and y (although the y acts as a vowel).
Wise you are, wise you be, I see you are too wise for me.
You need to use the sine rule. If the three angles are A, B and C and the sides opposite them are named a, b and c then, by the sine rule, a/sin(A) = b/sin(b) = c/sin(C) Therefore b = a*sin(B)/sin(A) = a*y where y = sin(B)/sin(A) can be calculated and c = a*sin(C)/sin(A) = a*z where z = sin(C)/sin(A) can be calculated. then perimeter = p = a + b + c = a + ay + az = a*(1 + y + z) therefore a = p/(1 + y + z) or a = p/[1 + sin(B)/sin(A) + sin(C)/sin(A)]. Everything on the right hand side is known and so a can be calculated. Once that has been done, b = a*y and c = a*z.