Prove the first half of the open-jaw inequality where the point G lies inside triangle DEF i.e. show that if x less than y => AC < DF.

Related BrainMass Solutions

• Metric space and triangle inequality.

  9070 Metric space and triangle inequality. Prove that in a metric space, if C lies between A and B and O is any other point, then OC<=OA + OB.

• Proof involving equilateral triangle

  90393 Proof involving equilateral triangle I need to see a construction and proof. Let (triangle DEF) be equilateral triangle and Q is a point inside. Prove that the sum of the three distances from Q to each side is equal to the altitude DD'.

• deriving the distance formula

  Synthetic proof: Consider the triangle ABC and let the midpoint of AB be F, and that of AC be E; then BE and FC intersect at G, say. It's enough to show that the line segment from A to the midpoint of BC -- call it D -- passes through G.

• Real analysis

  31259 Real Analysis Proof Function 29.2 Prove that |cos x - cos y| ≤ |x - y| for all x, y in R See attachment 29.2 Prove that |cos x - cos y| ≤ |x - y| for all x, y in R.

• Limit points

  2643 Limit points Prove that the point p is a limit point of the point set X if and only if each open point set containing p contains a point in X which is different from p. Prove without using sequences.

• Lorenz curve

  a) Show that the coefficient of inequality is twice the area between the Lorenz curve and the line y=x; that is, show that the coefficient of inequality = (2)the integral from 0 to 1 of [x-L(x)]dx.

• Lipschitz functions

  (a.C) To prove that M_K is the closure of the set D_K of all differentiable functions on [a,b] with |f^' (t)|≤K (a.5) we first note that since condition (a.4) follows from (a.5), so that D_K⊂M_K .

• Real analysis - Proving Closure of a Ball

  (2) In non-formal words, this neighborhood consists of points whose distance from y is smaller than half the distance from y to the boundary of the ball.

• Internal bisectors and incenter of a triangle

  (D is the point where e internal bisector of triangle ABC with in-center I prove that < BIC = 90 + ½ (< BAC) Response is in a file called 'Geometry.doc" (1) Need to prove, BD/DC = AB / AC Lets use the sin rule