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Maths
A Level

Given that log3 (c ) = m and log27 (d )= n , express c /(d^1/2) in the form 3^y, where y is an expression in terms of m and n.

I find that a lot of maths at A-Level is unmotivated, and this causes a lot of unnecessary confusion. You can do this question, you just need to recognise the point of log and keep a level head. Log is d...

Answered by Gabriel V. Maths tutor
3572 Views

Write √80 in the form c√5, where c is a positive integer.

Firstly, we recall that √ab=√a x √b. Noticing that 80=16 x 5 then, we have that √80=√16 x √5. Since √16 = 4 then, we have that √80=4 x √5. So, giving the final answer in the form that the question asks: c...

Answered by Tutor524731 D. Maths tutor
6113 Views

A fair die has six faces numbered 1, 1, 1, 2, 2, and 3. The die is rolled twice and the number showing on the uppermost face is recorded. Find the probability that the sum of the two numbers is at least three.

There are a couple of ways to approach this. A grid showing all the possibilities can be drawn up, which would help to illustrate the solution a little more explicitly. For now, let's talk through the log...

Answered by Anthony S. Maths tutor
6829 Views

A block of mass M lies stationary on a rough plane inclined at an angle x to the horizontal. Find a general expression relating the coeffecient of friction between the block and the plane and the angle x. At what angle does the box begin to slide?

The first step to any problem is to draw a suitable diagram. Here we draw a free body diagram, marking the angle x, the friction force F, normal reaction force N and weight of the block Mg. "Stat...

Answered by Elliot G. Maths tutor
2286 Views

A particle, P, moves along the x-axis. At time t seconds, t > 0, the displacement, is given by x=1/2t^2(t ^2−2t+1).

Find the times when is instantaneously at rest.In order to solve this question we first have to multiply out in order to obtain the full expression of x which will be x = 1/2t^4 -2t^3+1/2t^2. N...

Answered by Aleksander K. Maths tutor
16648 Views

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