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We have claimed that a randomly generated point lies on the equator of the sphere independent of where we pick the North Pole. To test this claim randomly generate ten vectors in 128 dimensions whose coordinates have value ±1. Think of these ten vectors as ten choices for the North Pole. Then generate some additional random vectors with ±1 coordinates. For each of the new vectors determine how many of the original vectors they are close to being perpendicular to. That is, they lie close to the equator.
All the number sets we have seen above put together comprise the real numbers. Real numbers are also inadequate in the sense that it does not include a quantity which i
E1) Try and see the order in which different children fills numbers in the grid above. My claim is that all of them would fill in the ones, the fives and the tens first. Test my hy
Two sessions of swimming lessons were held at a pool. In the first session 40 students attended. Of these 40 students 60% were girls. How many girls attended the first session of s
2 of 10 =
Integration by Parts -Integration Techniques Let's start off along with this section with a couple of integrals that we should previously be able to do to get us started. Fir
how can a curve be divided in three equal part?
Simplify the Boolean function: F (w,x,y,z) = ∑ (0, 1, 2, 3, 4, 6, 8, 9, 12, 13, 14) (8) Ans: f(w, x, y, z) = ∑(0, 1, 2, 3, 4, 6, 8, 9, 12, 13, 14) The above
Solve 2 ln (√x) - ln (1 - x ) = 2 . Solution: Firstly get the two logarithms combined in a single logarithm. 2 ln (√x) - ln (x - l) = 2 ln ((√x) 2 ) ln (1 - x ) = 2
Prove that sec 2 θ+cosec 2 θ can never be less than 2. Ans: S.T Sec 2 θ + Cosec 2 θ can never be less than 2. If possible let it be less than 2. 1 + Tan 2 θ + 1 + Cot
As noted, Euler's method is little used in practice, as there are much better ways of solving initial value problems. By better, we mean, "able to achieve a result of the same prec
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