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Any point on parabola, (k 2 ,k) Perpendicular distance formula: D=(k-k 2 -1)/2 1/2 Differentiating and putting =0 1-2k=0 k=1/2 Therefore the point is (1/4, 1/2) D=3/(32 1/2
NULL/ VOID/ EMPTY SET A set which has no element is known as the null set or empty set and is indicated by f (phi). The number of elements of a set A is indicated as n (A) and
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The calculation of the angles of a triangle are shown by 2x + 15, x + 20 and 3x + 25. Evaluate the measure of the smallest angle within the triangle. a. 40° b. 85° c. 25°
1. Consider the model Y t = β 0 + β 1 X t + ε t , where t = 1,..., n. If the errors ε t are not correlated, then the OLS estimates of β 0 and β
Given two functions f(x) and g(x) which are differentiable on some interval I (1) If W (f,g) (x 0 ) ≠ 0 for some x 0 in I, so f(x) and g(x) are linearly independent on the int
a, b,c are in h.p prove that a/b+c-a, b/a+c-b, c/a+b-c are in h.p To prove: (b+c-a)/a; (a+c-b)/b; (a+b-c)/c are in A.P or (b+c)/a; (a+c)/b; (a+b)/c are in A.P or 1/a; 1
prove that every non-trivial ingetral solution (x,y,z)of the diophantine equation Xsquare +Ysquare=Zsquare satisfies gcd(x,y)=gcd(x,z)=gcd(y,z)
trigonometric ratios of sum and difference of two angles
Parametric Equations and Polar Coordinates In this part we come across at parametric equations and polar coordinates. When the two subjects don't come out to have that much in
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