Top answers

Explain why the equation tanx + cotx = 1 does not have real solutions.

First of all, we need to express tangent and cotangent in terms of sine and cosine using the identities: tanx = sinx / cosx and cotx = cosx / sinx. Substituting these expressions into the initial equation we...
SV
17836 Views

Differentiate the function y = (x^2)/(3x-1) with respect to x.

This requires use of the quotient rule: d/dx[f(x)/g(x)] = [g(x)f'(x) - g'(x)f(x)]/[g(x)^2]dy/dx = ([(3x-1)*2x] - 3x^2)/[(3x-1)^2],= (3x^2-2x)/[(3x-1)^2], =[x(3x-2)]/[(3x-1)^2]
TS
Answered by Ted S. • Maths tutor
7256 Views

A curve has equation y = x^3 - 3x^2 -24x + 5, find the x co-ordinates of the two stationary points of the curve and hence determine whether they are maximum or minimum points.

y = x 3 - 3x 2 - 24x + 5, First, calculate the derivative of y and find its roots when y = 0:dy/dx = 3x 2 - 6x -24 = 0 -> x 2 - 2x - 8 = 0 -> (x+2)(x-4) = 0Therefore the coordinates of the stationary p...
TS
Answered by Ted S. • Maths tutor
8527 Views

Sphere A (mass m), moving with speed 3v, collides with sphere B (mass 2m) which is moving in the opposite direction with speed v. The two spheres then combine, calculate the resulting velocity of the combined spheres.

Sphere A has mass m and velocity +3v so its initial momentum is 3mv. Sphere B has mass 2m and velocity -v so its initial momentum is -2mv. Therefore we can say:3mv - 2mv = M c v c , where M c and v c are the...
TS
Answered by Ted S. • Physics tutor
3259 Views

Why is it important that the baryon and lepton numbers of an interaction are conserved?

Conservation Laws are useful because they establish fixed rules that physical interactions must follow, which helps physicists to better understand these processes. In particular, they provide a picture of w...
TS
Answered by Ted S. • Physics tutor
4019 Views