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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 solutionCalculation:70.5142143=71071...
From x : y = 7 : 4 work out an expression for x: x = y (7/4) and substitute into x + y = 88: y(7/4 + 1) = 88y( 11/4) = 88 y = 88 (4/11) = 8 x 4 = 24substitute this into x + y = 88 to get x = 88 - 24 = 64....
sin^2(x) = (1 - cos(2x))/2 and cos^2(x) = (1 + cos(2x))/2so sin^4(x) = 0.25(1 - 2cos(2x) + cos^2(2x)) = 0.25(1 - 2cos(2x) + 0.5 + 0.5cos(4x))integrate = 3x/8 - sin(2x)/4 + sin(4x)/32
Find the lowest common multiple of 2 and 3, which is 6. Multiply each term in the first equation by 3, and each term in the second equation by 2 to produce two equations with the same coefficient of x (wh...
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