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N = 2a + b. a is a 2 digit square number, b is a 2 digit cube number. What is the smallest possible value of N?

First, the smallest values of a and b must be found and then substituted into the equation for N.

To find a.

A square number is a number that is the result of multiplying an...

Answered by Oliver G. • Maths tutor

3485 Views

Work out the value of 125 to the power of -2/3.

We want to find 125^-2/3. To do this, we will need to use lots of power rules that we have learnt.

Firstly, when we put a power to another power, we multiply the two powers. For...

Answered by Joe R. • Maths tutor

36298 Views

At t seconds, the temp. of the water is θ°C. The rate of increase of the temp. of the water at any time t is modelled by the D.E. dθ/dt=λ(120-θ), θ<=100 where λ is a pos. const. Given θ=20 at t=0, solve this D.E. to show that θ=120-100e^(-λt)

When solving any differential equation, the first method to consider is the seperation of variables. This is the simplest method and, conveniently, it works in this case. To seperate variables:1. Put all ...

Answered by Edmond W. • Maths tutor

8771 Views

A rollercoaster stops at a point with GPE of 10kJ and then travels down a frictionless slope reaching a speed of 10 m/s at ground level. After this, what length of horizontal track (friction coefficient = 0.5) is needed to bring the rollercoaster to rest?

Recognise that the intial potential energy and kinetic energy at 10 m/s position should be identical due to the frictionless slope.

mgh = 0.5mv²

Answered by Daniel M. • Maths tutor

4796 Views

Solve 4cos(2x )+ 2sin(2x) = 1 given -90° < x < 90°. Write 4cos(2x )+ 2sin(2x) in the form Rcos(2x - a), where R and a are constants.

Step 1: Recognise 4cos(2x )+ 2sin(2x) must be put into the form given in the question form i.e. Rcos(2x - a) as it contains only one trigonometric function

Step 2: Calculate values of R and a

Answered by Prannay K. • Maths tutor

16994 Views

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