**An arithmetic series has five term a and common difference d.**

The sum of the first 31 terms of the series is 310. **a)** Show that a + 15d = 10

*> S31 = 31/2 ( 2a + (31-1) d)*

> 31( a + 15d ) = 310

> a + 15d = 310/31; a + 15d = 10 **b)**Given also that the 21st term is twise the 16th term, find the value of d.

???

The clues allow you to solve the simultaneous equations for "d" subtract the left from the right use your first result....clue1 **c)**the nth term of the series is un. Given that

K

Sum un = 0, find the value of K.

n = 1

???

Inside the brackets is zero, so
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**Find the value of x in each of the following:** **(A)**. log9x = 0

**(B)**. log9x = 1/2

of coz i noe how to do it on the calculator with the answers

1 for

**(A)** and

3 for

**(B)**, but how do i get it withour a calculator??

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**A curve has equation y = 1/x^3 + 48x.** **a)** Find dy/dx.

*>> dy/dx = -3x^-4 + 48* **b)** Hence find the equation of each of the two tangents to the curve that are parallel to the x-axis.

*>> -3x^-4 + 48 = 0*

>> x^-4 = 16

>> x = +-1/2 **c)** Find the equation of the normal to the curve at the point (1,49)

???????????

The slope of the tangent at x=1 is The normal is perpendicular to the tangent, hence invert and negate the tangent slope The slope of the normal is -1/45 and the normal contains the point (1,49) Hence, the normal equation at that point is