Currently unavailable: for regular students
Degree: Mathematics (Bachelors) - Exeter University
Little bit about me:
I'm a first year maths student at Exeter. With a excitement for all things mathematics I have helped teach at many different levels in the past! I hope my patience, friendlieness and entusiasm comes across in the sessions.
The sessions will be primarily guided by what you want covered and your experiance with mathematics. Understanding why is much more important than just how to plug in the numbers and I will not only teach the applications but how they can be derived ( within reason, no need to stress over learning PhD level proofs!), but, most importanly help you to think like a mathematician!
If you have any questions feel free to message me and don't be afraid to book a free 'Meet the Tutor' session! If you could also let me know the exam board and any specific areas you are struggling with I would be very grateful!
Look forward to hearing from you!
|Further Mathematics||A Level||£20 /hr|
|Maths||A Level||£20 /hr|
|Further Mathematics||GCSE||£18 /hr|
Firstly we must change it into a form we can deal with. To do this we take the natural log (ln) of both sides.
ln(y)=x(ln(a)) using our rules of logs
From here we differentiate. The differential of ln(f(x)) is [(d/dx)f(x)]/f(x)
differentiating from above rule and ln(a) is just a constant so d/dx xln(a)= ln(a)
dy/dx=yln(a) times both sides by y
subbing in y=ax to get dy/dx in terms of xsee more
For this we are going to test our knowledge of discriminats and factorisation.
Firstly we will format the equation as (m+8)x2+8x+(m-7)=0
From here we can see it takes the form ax2+bx+c, and as we know the equation has two real roots we know that the discriminant D is greater than 0. Therfore b2-4ac>0
a=(m+8) b=8 c=(m-7)
82-4(m+8)(m-7)>0 Pluggin in a,b,c
64-4(m2+m-54)>0 expanding brackets and squaring 8
16-(m2+m-54)>0 dividing both sides by a factor of 4
0>(m2+m-54)-16 moving left handside to right handside by addition / subtraction
0>m2+m-72 collecting terms
We have now shown that (m+9)(m-8)<0 for the above equation when it has two real roots.see more