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When studying anything in Mathematics, it is very easy to get lost in the technical details and lose sight of what everything really means on a conceptual level - that's why these kinds of questions are s...

x = sinhy=> dx/dy = coshycosh²y - sinh²y = 1=> sqrt(1 + sinh²y) = coshythus dx/dy = sqrt(1 + sinh²y)and dy/dx = 1/sqrt(1 + sinh²y)hence dy/dx =...

All coefficients of z are real, therefore one root must be the complex conjugate so β = 1-3i.It is known that Σαβ = 18 (the coefficient of z), so we can get an equation in the third root, γ, as follows: Σ...

Firstly we can use the fact that cosx is the real part of e^ix. This means that the series above is the real part of the infinite series 1 + 1/2e^ix + 1/4e^2ix + ...... This means that we have an infinite...

Start by determining dot product. a.b = 1x0 + 4x6 + 8*-3 = 0as a.b = |a||b|cos(theta)cos(theta) = 0therefore theta = 90 degTherefore vectors are perpendicular