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Prove that 2^(80)+2^(n+1)+2^n is divisible by 7 for n belongs to the natural number.

We will prove that 2^(n+2)+2^(n+1)+2^n is divisible by 7 using formula to multiply powers with the same base:a^(b) * a^(c) = a^(b+c)Now looking at our expression we can write:2^(n+2) + 2^(n+1) + 2^n = 2^n...

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Find the equation of the tangent to the circle (x-3)^2 + (y-4)^2 = 13 that passes through the point (1,7)

Start with a sketch. We can see that the radius from the point (1,7) to the centre of the circle (3,4) is perpendicular to the tangent. The gradient of the radius is (4-7)/(3-1) = -3/2. We know that two p...

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Solve the quadratic inequality x^2+x-6>/= 0.

First equate the equation to zero and solve it. To solve the quadratic equation, find the multiples that make '-6' and within this which have a total sum of 1. By this method we can figure out the two bra...

Answered by Anannya M. • Maths tutor

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x/(2x-3) + 4/(x+1) =1 [5 mark question]

We have 2 fractions we want to get rid off to make it easier, so what we do is multiply both sides by the things we want to get rid off.In this case we multiply both sides by (2x-3)(x+1)This gives us x(x+...

Answered by Abdul Jalil A. • Maths tutor

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use the substitution u=2+ln(x) to show that int(e,1(ln(x)/x(2+ln(x)^2))dx)=p+ln(q) , where p and q are rational numbers.

So u=2+lnx, therefore du/dx=1/x , we can work out the new upper and new lower limit by substitute in e and 1 into 2+lnx , and we get 2+ln(e)=3 , 2+ln(1)=2Rearrange the differential we get dx=xdu , substit...

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