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1. Show that there do not exist integers x and y for which 110x + 315y = 12.
2. If a and b are odd integers, prove that a2 +b2 is divisible by 2 but is NOT divisible by 4. Hint:
Any odd number can be written 2k + 1 for some integer k.
3. Prove that for any prime number p, √ p is irrational. Hint: Follow the same method that was used to prove √ 2 is irrational, by first supposing √ p can be expressed as a=b.
#question when equation of tangent T=0 and why
Find all the local maximum and minimum values and saddle points of the function f(x, y) = x 2 - xy + y 2 + 9x - 6y + 10
how to prove Decidability Theorem of Logic
If the areas of the circular bases of a frustum of a cone are 4cm 2 and 9cm 2 respectively and the height of the frustum is 12cm. What is the volume of the frustum. (Ans:44cm 2 )
2/2
What is the slope and y intercept for (6,5) (-3,8)
Below is the sketch of a function f ( x ) . Sketch the graph of the derivative of this function f ′ ( x ) . Solution : At first glance it seems to an all however impossib
lbl 2 lcl 2 sin 2 θ
Example Factorize x 2 - 4x + 4. If we substitute x = 1, the value of the expression will be (1) 2 - 4(1) + 4 = 1 If we substitute x = -1, the value o
STATISTICS AND PROBABILITY : Statistics are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of
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