Leap Frog Solutions 2013
... Solution. The polynomial has a real root if and only if its discriminant is non-negative, i.e., if a2 − 4b2 ≥ 0. Since a, b > 0, this is equivalent to a ≥ 2b. Now note that for two elements of the set above, we have a ≥ 2b ⇐⇒ a > b, so our polynomial has a real root if a > b and no real root if a < ...
... Solution. The polynomial has a real root if and only if its discriminant is non-negative, i.e., if a2 − 4b2 ≥ 0. Since a, b > 0, this is equivalent to a ≥ 2b. Now note that for two elements of the set above, we have a ≥ 2b ⇐⇒ a > b, so our polynomial has a real root if a > b and no real root if a < ...
Maths-Y09-LP1 Higher (Set 1-3)
... Know that squaring a linear expression is the same as expanding double brackets; Expand the product of two linear expressions, i.e. double brackets working up to negatives in both brackets and also similar to (2x + 3y)(3x – y). ...
... Know that squaring a linear expression is the same as expanding double brackets; Expand the product of two linear expressions, i.e. double brackets working up to negatives in both brackets and also similar to (2x + 3y)(3x – y). ...
A GENERALIZATION OF FIBONACCI FAR
... µn = ϕ2n+1 + O(1) is the mean number of summands for m ∈ [Fn , Fn+1 ) and σn2 = 5(ϕ+2) is the variance (see [KKMW] for the calculation of the variance). Henceforth in this paper whenever we say the distribution of the number of summand converges to a Gaussian, we mean in the above sense. There are m ...
... µn = ϕ2n+1 + O(1) is the mean number of summands for m ∈ [Fn , Fn+1 ) and σn2 = 5(ϕ+2) is the variance (see [KKMW] for the calculation of the variance). Henceforth in this paper whenever we say the distribution of the number of summand converges to a Gaussian, we mean in the above sense. There are m ...
