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Calculate (7-i*sqrt(6))*(13+i*sqrt(6))

We expand the parentheses to get to the equation: 7 13-13 i sqrt(6)+7 i sqrt(6)-i i sqrt(36) which after some further calculations equals to: 91-6 i sqrt(6)+sqrt(36) [We got +sqrt of 36 because i i*=sqrt(-1)...
Answered by • Maths tutor
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Why is the derivative of ln(x) equal to 1/x.

This fact can be deduced several ways, and I would encourage tutees to find other methods, (such as using implicit differentiation, or the chain rule.) However one of the simplest explanations is given below...
CV
Answered by Christopher V. • Maths tutor
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The curve y = 2x^3 -ax^2 +8x+2 passes through the point B where x = 4. Given that B is a stationary point of the curve, find the value of the constant a.

y=2x 3 - ax 2 + 8x +2. If we are told that B is the stationary point of the curve, then it is at that point where the gradient of the curve is equal to 0. In order to find the gradient of the curve at this p...
FM
Answered by Frazer M. • Maths tutor
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A-level: solve 8cos^2(x)+6sin(x)-6=3 for 0<x<2(pi)

8(1-sin^2(x))+6sin(x)-6=38(1-sin^2(x))+6sin(x)-9=08sin^2(x)-6sin(x)+1=0(2sin(x)-1)(4sin(x)-1)=02sin(x)-1=0 4sin(x)-1=02sin(x)=1 4sin(x)=1sin(x)=1/2 sin(x)=1/4x=(pi)/6 , 5(pi)/6 , 0.253 , 2.89
KM
Answered by Katie M. • Maths tutor
5956 Views

Solve the equation 7^(x+1) = 3^(x+2)

1st we will log both sides of the equation7 (x+1) = 3 (x+2) becomes log7 (x+1) = log3 (x+2) NEXT we will use the power law which is log a (x) k =k log a (x)This turns log7 (x+1) = log3 (x+2) to (x+1) log7 = ...
AE
Answered by Anwulika E. • Maths tutor
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