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First multiply top and bottom by conjugate of denominator, (7-3√5), and expand(3 + 2√5)(7 - 3√5)/(7 + 3√5)(7 - 3√5)(21 + 14√5 - 9√5 - 30)/(49 + 3√5 - 3√5 - 45)Simplify top and botton(-9 + 5√5)/4Write in r...

(1+6x)^3 = 1+3(6x) +(3)(2)(36x^2)/2 + (3)(2)(1)(216x^3)/6
= 1+18x+108x^2 + 216x^3

In this sequence, there is no common difference between one term and the next making it more challenging to solve. However, if you look at the terms closely, you can see that each term is the sum of the p...

Question is asking for gradient at x = 0, y = ln2. e^2y = 5 - e^-x. Differentiation with respect to x: 2e^2y * dy/dx = e^-x . dy/dx = e^-x / 2e^2y. At x = 0, y = ln2 ~ dy/dx = e^0 / 2e^2ln2 = 1 / 2e^ln4 =...

1a) 1000/7=142.8.... Therefore there are 142 multiples of 7 between 1 and 1000
Therefore the sum of series from 1 to 142 is 1/7th of the solution
Calculation:70.5142143=71071
...