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Maths
A Level

An object of mass 3kg is held at rest on a rough plane. The plane is inclined at 30º to the horizontal and has a coefficient of friction of 0.2. The object is released, what acceleration does the object move with?

We need to use Newtons law F=ma going down the slope.
We can see that the only forces acting in this direction are the component of the weight and friction, so we have that: F = Wsin30 - μR = 3a

Answered by Asha D. Maths tutor
2927 Views

Show that (sec(x))^2 /(sec(x)+1)(sec(x)-1) can be written as (cosec(x))^2.

( sec2(x))/((sec(x)+1)(sec(x)-1))Then, by the rule of 'difference of two squares', we know that this equals= (sec2(x))/(sec2(x)-1)= (sec2x/tan2x)s...

Answered by Rishi S. Maths tutor
10211 Views

Find the values of A between and including 0 and 360 degrees for tan(2A) = 3tan(A)

You cannot work with this equation in the current form so you must use identities to find an equivalent form that you can work with. It is known that tan(2A) = 2tan(A) / 1-tan2(A) so set this e...

Answered by Daniel M. Maths tutor
3934 Views

Express the equation cosecθ(3 cos 2θ+7)+11=0 in the form asin^2(θ) + bsin(θ) + c = 0, where a, b and c are constants.

We must first use the identity cosecθ = 1/sinθ. Now the equation becomes (1/sinθ)(3 cos 2θ+7)+11=0. Since we know that the question is asking for the answer in the form of asin2θ + bsinθ + c = ...

Answered by George L. Maths tutor
5670 Views

Explain why for any constant a, if y = a^x then dy/dx = a^x(ln(a))

So let's start with taking the natural log on both sides of y=ax, giving us ln(y) = ln(ax). Using the laws of logarithms we can write this as ln(y) = xln(a).Next, we differentiate bo...

Answered by James M. Maths tutor
10174 Views

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