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show that the circle described on any focal chord of the parabola touches the directrix
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
Prove that A tree with n vertices has (n - 1) edges. Ans: From the definition of a tree a root comprise indegree zero and all other nodes comprise indegree one. There should
The sum of the diameters of two circles is 2.8 m and their difference of circumferences is 0.88m. Find the radii of the two circles (Ans: 77, 63) Ans: d 1 + d 2 = 2.8 m=
Sherman took his pulse for 10 seconds and counted 11 beats. What is Sherman's pulse rate in beats per minute? A 10 second count is 1/6 of a minute. To find out the number of be
how to make a venn diagram?
As we saw in the previous section computing Laplace transforms directly can be quite complex. Generally we just utilize a table of transforms when actually calculating Laplace tran
Determine the inverse of the following matrix, if it exists. We first form the new matrix through tacking onto the 3 x 3 identity matrix to this matrix. It is, We
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Equation of line joining(0,0)and point of intersection of X2+Y2+2XY=4 , 3x2+5y2-xy=7 is solution) The two equations above represent pair of straight lines. We can complete the sq
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