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Find the equation of the normal of the curve xy-x^2+xlog(y)=4 at the point (2,1) in the form ax+by+c=0

differentiating: xy'+y-2x+(x/y)y'+log(y)=0rearranging: y'=y(2x-y-log(y))/x(1+y)at (2,1): y'=3/4 so gradient of normal at (2,1) is -4/3so the equation of the normal is y-1=(-4/3)(x-2)which is equivalent to 4x...
SL
Answered by Sam L. • Maths tutor
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Solve the simultaneous equations y = x^2 +3x and y = x+8

Because both of the equations are equal to y, the first thing we do is make them equal to each other:x^2 + 3x= x + 8We then want to rearrange the equation so that everything is on the same side of the equals...
JW
Answered by Jessica W. • Maths tutor
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Solve the equation 2log (base 3)(x) - log (base 3)(x+4) = 2

First express as a single logarithm as follows. The number in front of the logarithm remembering log rules can be rewritten as the power of the number in the bracketsSo rewriting the LHS log 3 (x 2 ) - log 3...
TS
Answered by Theranjit S. • Maths tutor
9331 Views

solve the simultaneous equations: 3x + 5y = 4 ; 7x - 3y = 8

first recognise that if you double the first equation the both equations will be equal to 8.so now we have 6x + 10y = 8 ; 7x - 3y = 8now we can set the equations equal to each other to get 6x + 10y = 7x - 3y...
EW
Answered by Elizabeth W. • Maths tutor
4345 Views

differentiate: y=[xcos(x^3)]/[(x^4 + 1)^3] with respect to x

This question is on the trickier side as it is heavily computational and requires a good knowledge of the differentiation rules however it is a good way to practise using multiple rules at once.First we will...
EW
Answered by Elizabeth W. • Maths tutor
3119 Views