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Here is one from a textbook. Given sin x not = 0, and n is a natural number, prove that cos(x) cos(2x) cos(3x) ...... cos((2^(n-1))x) = (sin((2^n)x))/((2^n)sin(x)).

I'll take the meaning of 'transverse' as 'interchange x and y', i.e. reflect in the line y = x. In that case the foci are (0, -ae) and (0, ae).

:) :) :wave:

You find out the instantaneous motion of an object from its velocity, not from its acceleration. Since the velocity is not given, all the answers A to F are correct. Acceleration is related to the net force on the object according to Newton. If the acceleration is to the right, the net force...

This statement is false. Why?

I can spot three misses from the calculation. (1) Flux at start = 85 x 1.2 x 0.3 x 0.47 x cos 59 (2) Flux at end = 85 x 1.2 x 0.3 x 0.47 x cos 0 (3) Another possibility: Flux at end = 85 x 1.2 x 0.3 x 0.47 x cos 180

z^9 -1 = (z^3 - 1)(z^6 + z^3 + 1) .: the roots of z^6 + z^3 + 1 = 0 are among the roots of z^9 -1 = 0. The roots of z^9 -1 = 0 are 1cis(2npi/9) where n = 0, 1, 2, 3, ......, 8 or n = 0, +/-1, +/-2, +/-3, +/-4. .: the roots of z^6 + z^3 + 1 = 0 are 1cis(2npi/9) where n = 1, 2, 4, 5, 7, 8...

(i) Find the area of parabolic segment by integration = integ(-1, 2) of x + 2 - x^2 = 9/2 (ii) Area of triangle = area of trapezium under AB - area of trapezium under AP - area of trapezium under PB = (1/2)(1 + 4)3 - (1/2)(1 + t^2)(t+1) - (1/2)(t^2 + 4)(2 - t) =(3/2)(2 + t - t^2)...

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a - b = 0 is the correct answer.

I don't think it can be solved analytically (algebraically). If you look at the two graphs, they intersect at two points only around x = 0 and x = 1. These two values happen to satisfy the equation, so they are the only solutions. Use numerical methods for other similar equations. :) :) :wave:

Please correct my mistakes.

:) :) :wave:

1 --- > 4 x+1 So x + 1 > 0 and x + 1 < 1/4 So x > -1 and x < -3/4 i.e. -1 < x < -3/4 :) :) :wave:

:) :) :wave:

There is a net force acting on the car because the velocity is changing continuously as the car moves in a circle at constant speed. Changing velocity means acceleration and a net force is required according to Newton's second law. For constant speed the net force is always towards the centre of...

To summarise information -> to analyse information -> to solve problems and make decisions

Only the x-coordinate is given!

Please explain!

The x-intercept of the linear graph gives the x-coordinate of the turning point. So the given information (I was given one piece of information to find what C was, and that was the minimum/ turning point value of x, ie the x coordinate of the turning point of f(x) ) is redundant. To find the...