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How are Judges appointed to the Supreme Court?

Judicial Appointment is a two tier process which begins once a vacancy occurs in the Supreme Court, either through a judge retiring, like David Souter, or dying like Antonin Scalia. The first tier is p...

HV
Answered by Harry V. Politics tutor
5049 Views

Integrate 1/(5-2x) for 3≤x≤4

You must be careful with these sorts of questions as although 1/(5-2x) is equivalent to (5-2x)^-1, when you integrate you would add one to the power and divide by the new power. But if you were to add one...

ES
7096 Views

Using the addition formula for sin(x+y), find sin(3x) in terms of sin(x) and hence show that sin(10) is a root of the equation 8x^3 - 6x + 1

First we state the formula for sin(x+y)

sin(x+y) = sin(x)cos(y) + cos(x)sin(y)

Letting y = 2x

sin(x+2x) = sin(x)cos(2x) + cos(x)sin(2x)

Now sin(2...

KR
Answered by Kyle R. Maths tutor
22321 Views

Using Integration by Parts, find the indefinite integral of ln(x), and hence show that the integral of ln(x) between 2 and 4 is ln(a) - b where a and b are to be found

Using integration by parts, we can re-write the integral of ln(x) as (xln(x) - int(x(1/x))) = x*ln(x) - x

Therefore, evaluating between 2 and 4 gives us (4ln(4) - 4) - (2

KR
Answered by Kyle R. Maths tutor
4004 Views

Given that d/dx(cosx)=-sinx show that d/dx(secx)=secx(tanx)

let y=sec(x) = 1/(cos(X)) = cos(x)-1

Thus dy/dx = -1(cos(x))-2(-sinx) = sin(x)/(cos(x))2

= 1/cos(x)  x  sin(x)/cos(x)

=sec(x)t...

OD
Answered by Owain D. Maths tutor
13169 Views

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