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Cardioids and Limacons
These can be split up into the following three cases.
1. Cardioids: r = a + a cos θ and r = a + a sin θ.
These encompass a graph that is vaguely heart shaped and all time contain the origin.
2. Limacons along with an inner loop : r = a + b cos θ and r = a + b sin θ along with a < b .
These will have an inner loop and will always contain the origin.
3. Limacons with no an inner loop : r = a + b cos θ and r = a + b sin θ with a > b .
These do not contain an inner loop and do not consist of the origin.
Find the Quadratic polynomial whose sum and product of zeros are √2 + 1, 1/ √2 + 1 Ans: sum = 2 √2 Product = 1 Q.P = X 2 - (sum) x + Product ∴ x 2 - (2 √2 )
How could 2+2 will be Equal to 5
Prove that a simple graph is connected if and only if it has a spanning tree. Ans: First assume that a simple graph G has a spanning tree T. T consists of every node of G.
3x3
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find the equation to the sphere through the circle xsqaure+ysquare+zsquare+=9 , 2x+3y+4z=5
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Let A be an n×n matrix. Then Show that the set U = {u?R^n : Au = -3un} is a Subspace of R^n
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