Question

1.)The 2nd term of an exponential sequence is 9 while the 4th term is 81.Find the common ratio(r),the first term(a) and the sum of the first five terms of the sequence.
2.)Solve the inequality 3xsquare +10x-8<0 and show the range of values of x on a number line.
3.) If f(x)=2x-3 and g(x)=3x+p,for what value of constant P is (fog)=(gof)?
4.) Find the value of:i) Tan 300° ii.)Cos 135° iii.)Sin 225° iv)Cos 330° in surd form.
5.) Sketch and shade the required region of x-2y +1 less than or equals to 0.

Answer 1

1)
$ar = 9 \\ a {r}^{3} = 81 \\ {r}^{2} = 9 \\ r = 3 \\ a = 3$
Since the sequence is increasing , the common ratio can't be negative.

2)
$3 {x}^{2} + 10x - 8 < 0 \\ 3 {x}^{2} + 12x - 2x - 8 < 0 \\ 3x(x + 4) - 2(x + 4) < 0 \\ (x + 4)( 3x - 2) < 0$
Now using the curvy wave method, ( can't explain here as I can't draw a line), we get the values of x as
$- 4 < x < \frac{2}{3}$
3)

What is fog and gof???!!!

4)
$\tan(300) \\ = \tan(3 \times 90 + 30) \\ = \ - cot(30) \\ = - \sqrt{3} \\ \\ \cos(135) = \cos(90 \times 1 + 45) \\ = - \sin(45) = \frac{ - 1}{ \sqrt{2} } \\ \\ \sin(225) \\ = \sin(90 \times 2 + 45) \\ = - \sin(45) = \frac{ - 1}{ \sqrt{2} } \\ \\ \cos(330) \\ \cos( - 30) \\ = \cos(30) = \frac{ \sqrt{3} }{2}$
Since sine is positive in 1st and 2nd quadrant, cosine in 1st and 4th, and tangent in 1st and 3rd.