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A curve C is defined by the parametric equations x=(4-e^(2-6t))/4 , y=e^(3t)/(3t), t doesnt = 0. Find the exact value of dy/dx at the point on C where t=2/3 .

To solve this we must use the chain rule which is dy/dt * dt/dx. Firstly, we differentiate dy/dt. For this we must use the quotient rule, this gives us dy/dt=(9te^3t - 3e^3t)/9t^2. Now for dx/dt, by substitu...
LK
Answered by Lauren K. • Maths tutor
6588 Views

Find the roots of the following equation: x^2 + x - 6 = 0

Student should factorise equation to (x-2)(x+3) = 0 This gives roots of 2 and -3
AR
Answered by Adam R. • Maths tutor
2214 Views

How do I solve a simultaneous equation like this: 2x-5y=3, 3x+2y=14 ?

Solving a simultaneous equation finds the point(s) where two lines on a graph intercept. Therefore, one way of solving the equations is to plot the two lines onto the same graph and find the coordinates of t...
EG
Answered by Ellie G. • Maths tutor
10381 Views

Find the integral of tan^2x dx

You can not integrate tan 2 x but you can integrate sec 2 x Since sec 2 x = 1 + tan 2 x Then tan 2 x = sec 2 x-1 so the intragral of tan 2 x dx = the integral of (sec 2 x-1) dx = intrgral of sec 2 x dx + int...
NP
Answered by Nandini P. • Maths tutor
21441 Views

How do i solve two linear simultaneous equations 2x+y=7 & 3x-y=8 ?

To start with, try and spot whether or not two of the coeffecients (numbers next to the letters) are the same for either question (i.e. could be a 3x in one equation and a 3x in the other). This also works i...
TB
Answered by Tom B. • Maths tutor
4492 Views