[4] 3 A curve has equation y = cos x cos 2x . Find the x-coordinate of the stationary point on the curve in the interval 0 x 1, giving your answer correct to 3 significant figures. [6] 2 4 (i) Express 3 sin + 2 cos in the form R sin + , where R 0 and 0 90,...
We study the existence of nontrivial solution branches of three-coupled Gross–Pitaevskii equations (CGPEs), which are used as the mathematical model for rotating spin-1 Bose–Einstein condensates (BEC). The Lyapunov–Schmidt reduction is exploited to te
(9) The vector (,)a b = for which equation 0y ay by '''++=has the general solution 2212x x y C e C xe =+.(A)(4,4)-. (B)(4,4). (C)(4,4)-. (D)(4,4)--.(10) If (,)(0,1)lim (,)2x y f x y →=, then .(A)20 lim (,)2x f x x →=. (B)2 ...
A curve C has parametric equations 3 x = 2t – 1, y = 4t – 7 + , t 0. t Show that the Cartesian equation of the curve C can be written in the form 2x 2 ax b y = , x 1, x 1 where a and b are integers to be found. Specification reference (...
Answer to: Consider and find the following x = t + \ln (t) y = t - \ln (t) Find the following (a) \frac{dy}{dx} \frac{d^2y}{dx^2} (b) For...
Answer to: The slope of the tangent line to a curve is given by f'(x) = 4x^2 + 5x - 5. If the point (0, 6) is on the curve, find an equation of the...
Use the equation given to calculate the slope of a line tangent to y=4x2+3x at P(−3,27). mPQ=f(x1+h)−f(x1)hSlopes and Tangents:To find the slope o the curve, we can use two methods, one is the definition of the derivative met...
the x-component of the electric field and the y-component of the magnetic field must be continuous. Then at the interface of z = 0, E1x = E2x, H1y = H2y, one can get the following equations, Then the following equation can be obtained, Similarly, one can get the ...
If a function is given by the expression z=f(x,y) and we make f(x,y)= k, this equation corresponds to the points of the surface obtained by sectioning with the plane z=k, parallel to the coordinate plane z=0, that is to say, ...
and PANI as a potential structure for humidity sensing applications Mohamed Morsy 1,2*, Islam Gomaa 2, Abd Elhamid M. Abd Elhamid 3, Heba Shawkey 4, Mohamed Aly Saad Aly 5 & Amir Elzwawy 6 Humidity sensing has been offering a noticeabl...