Search our library of Maths A Level questions

Top answers

Maths

A Level

How would you differentiate ln(x^2+3x+5)?

Here we need to use the chain rule because we have a function (natural log) of another function (x^2+3x+5). Let u=x^2+3x+5, and differentiate lnu with respect to u, this gives us 1/u. Then we different...

Answered by Oli H. • Maths tutor

23406 Views

Given y=(1+x^3)^0.5, find dy/dx.

In order to solve this question, we need to use the chain rule when differentiating. The chain rule formula is dy/dx= (dy/du)(du/dx). Let u=1+x³Differentiating with respect to x gives du/dx...

Answered by Rebecca M. • Maths tutor

5447 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 ...
EW
Answered by Edmond W. • Maths tutor
8365 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

DM
Answered by Daniel M. • Maths tutor
4367 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
PK
Answered by Prannay K. • Maths tutor
16208 Views
←
647
648
649
650
651
→

Popular Requests

Maths tutor Chemistry tutor Physics tutor Biology tutor English tutor GCSE tutors A level tutors IB tutors Physics & Maths tutors Chemistry & Maths tutors GCSE Maths tutors

Terms & Conditions|Privacy Policy

CLICK CEOP
Internet Safety

Payment Security

Cyber
Essentials

Cookie Preferences

Search over 10,000 free study notes

Top answers

How would you differentiate ln(x^2+3x+5)?

Given y=(1+x^3)^0.5, find dy/dx.

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)

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?

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.

We're here to help

Company Information

Popular Requests

© MyTutorWeb Ltd 2013–2025

CLICK CEOP