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The sides of a triangle are x^(2 )+x+1, 2x+1,x^2-1, prove that the largest angle is 120 degrees, and find range of x. Ans) The biggest side is x^(2) + x + 1so findout the angle opposite to that byCos(A) = (b^2 + c^2-a^2)/2*b*cwhich gives Cos(A) = -1/2 ie 120degress
1. Finding the shortest path btween any two points on the surface of a sphere but use the method of the euler equations with an auxiliarty condition imposed? Question2:
Lucas purchased his motorcycle for $5,875.98 and sold it for $7,777.77. What was his profit? To ?nd out the pro?t, you must subtract what Lucas paid for the motorcycle from the
1) find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2)compute the work done by the force field F(x,y,z) = x^2I + y j +y k in moving
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Proof of: if f(x) > g(x) for a x b then a ∫ b f(x) dx > g(x). Because we get f(x) ≥ g(x) then we knows that f(x) - g(x) ≥ 0 on a ≤ x ≤ b and therefore by Prop
Equal groupings - when we want to find how many objects there are in several equal-sized sets. (e.g., if there are 3 baskets, each with 4 bananas, 4 oranges and 4 apples, respec
Theorem If {a n } is bounded and monotonic then { a n } is convergent. Be cautious to not misuse this theorem. It does not state that if a sequence is not bounded and/or
10 puzzles
how do you do divideing with a remaider
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