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Problem 1. Find the maximum and the minimum distance from the origin to the ellipse x 2 + xy + y 2 = 3. Hints: (i) Use x 2 + y 2 as your objective function; (ii) You c
Grouping - situations in which we need to find the number of portions of a given size which can be obtained from a given quantity. (e.g., if there are 50 children in a class and t
Initial Condition(s) are a set of conditions, or a condition on the solution which will permit us to find out that solution which we are after. Initial conditions are frequently a
Fermat's Theorem : If f ( x ) contain a relative extrema at x = c & f ′ (c ) exists then x = c is a critical point of f ( x ) . Actually, it will be a critical point such that f
Find the amount of sheet metal need to form a conical funnel of base radius 30cm with a vertical height of 50cm, allowing for 0.5cm overlap. Find the total surface area?
Inverse Cosine : Now see at inverse cosine. Following is the definition for the inverse cosine. y = cos -1 x ⇔ cos y = x for
a) The distance d that can be seen from horizon to horizon from an airplane varies directly as the square root of the altitude h of the airplane. If d = 213 km for h = 3950
1. (‡) Prove asymptotic bounds for the following recursion relations. Tighter bounds will receive more marks. You may use the Master Theorem if it applies. 1. C(n) = 3C(n/2) + n
A business has the opportunity to expand by purchasing a machine at a cost of £80,000. The machine has an estimated life of 5 years and is projected to generate a cashflow of £20,0
sin30+cos30=
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