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Maths
A Level

Use the geometric series formula to find the 9th term in this progression : 12 18 27...

Formula for nth term in a geometric progression = ar^n-1

workings:  

a=12

r=1.5  because 18/12 = 1.5

Thus, using ar^n-1  -->   12 * 1.5^8 = 307.54... or 308 (to 3sf)

...

PF
Answered by Philip F. Maths tutor
7839 Views

How would you show that a vector is normal to a plane in 3D space?

There are 2 main methods for finding a normal vector.

  1. If you know two vectors that lie in the plane e.g. (a,b,c) and (d,e,f), we can find a normal vector by calculating the vector/cross p...

FK
Answered by Fionn K. Maths tutor
23262 Views

Find the gradient of the exponential curve y(x)=(9e^(7x))/(12e^(2x)) at x=2/5

According to the quotient rule, when y(x)=f(x)/g(x), y'(x)=(f'(x)g(x)-g'(x)f(x))/g(x)2

f(x)=9e7x f'(x)=63e7x, g(x)=12e2x g'(x)=24e2x

y...

CM
Answered by Connor M. Maths tutor
2790 Views

Use the double angle formulae and the identity cos(A+B)≡cos(A)cos(B)−sin(A)sin(B) to obtain an expression for cos 3x in terms of cos x only

To answer, you need to know and be able to use your trigonometric formulae including the double angle formulae on data sheet.

1: cos(3x)=cos(2x+x) = cos(2x)cos(x) - sin(2x)sin(x)        split the 3...

SH
Answered by Sam H. Maths tutor
15075 Views

how do I differentiate?

look at the power of term and multiply the coefficient of that term by the value of the power, then reduce the value of the terms power by 1. for example after differentiation 5Xbecomes 20X

SL
Answered by Stefen L. Maths tutor
2720 Views

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