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A cricket player is capable of throwing a ball at velocity v. Neglecting air resistance, what angle from the horizontal should they throw at to achieve maximum distance before contact with the ground? How far is that distance?

Assume angle of throw theta. Resolving vertical and horizontal components: Vvert=v.sin(theta) and Vhoriz=v.cos(theta).From 'suvat' equations, time to vertical stationary t=v/a. This must be doubled to find t...
BW
Answered by Benjamin W. • Maths tutor
3996 Views

f(x) = e^(sin2x) , 0 ≤ x ≤ pi (a). Use calculus to find the coordinates of the turning points on the graph of y = f(x)

First, understand the concept of a turning point (zero gradient, implying first derivative is zero at the turning point)How do we differentiate exponentials ( if f(x) = e^g(x) then f'(x) = g'(x)*e^g(x) ) Oka...
MW
Answered by Marco W. • Maths tutor
6960 Views

Find the integral of (cosx)*(sinx)^2 with respect to x

This is a common example of an integral that is a product of two functions whose derivatives are related. As we know the derivative of sinx is cosx, we can use substitution to easily solve this - let our U= ...
HS
Answered by Harry S. • Maths tutor
7652 Views

express 9^(3x+1) in the form 3^(ax+b)

9 3x+1 =(3 2 ) (3x+1) =3 6x+2
HD
Answered by Harry D. • Maths tutor
3740 Views

The equation 5x sqaured + px + q , where p and q are constants, has roots α and α + 4. (a) Show that p squared = 20q +400.

a+a+4 = -p/5a+2 = -p/10(a+2)sqaured = q/5 +4p sqaured/100 = q/5 +4p sqaured = 100(q/5 +4)implies p squared = 20q+400
AT
Answered by Ahmed T. • Maths tutor
6536 Views