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Oh ok thanks!

(√6 - √2)/4 =?

can't be simplified

√(2 - √3)/2 (6 - 2√12 + 2)/16 =?

\(\frac{\sqrt{(2 - \sqrt3)}}{2}\times \frac{ (6 - 2\sqrt{12} + 2)}{16} \\ =\frac{\sqrt{(2 - \sqrt3)}}{2}\times \frac{ (8 - 2\sqrt{12} )}{16} \\ =\frac{\sqrt{(2 - \sqrt3)}}{1}\times \frac{ (4 - \sqrt{12} )}{16} \\ =\frac{\sqrt{(2 - \sqrt3)}}{1}\times \frac{ (4 - 2\sqrt{3} )}{16} \\ =\frac{\sqrt{(2 - \sqrt3)}}{1}\times \frac{ (2 - \sqrt{3} )}{8} \\ =\frac{(2 - \sqrt3)^{0.5}}{1}\times \frac{ (2 - \sqrt{3} )}{8} \\ =\frac{(2 - \sqrt3)^{1.5}}{8} \qquad or\\ =\left(\frac{2 - \sqrt3}{4}\right)^{1.5} \\\)

(2 - √3)/4 8 - 4√3 =?

\(\frac{(2 - \sqrt3)}{4 8} - 4\sqrt 3 \\ =\frac{(2 - \sqrt3)-4*48\sqrt3}{4 8} \\ =\frac{2 - \sqrt3-192\sqrt3}{4 8} \\ =\frac{2 -193\sqrt3}{4 8} \\ \)

4(2 - √3) 8 - 4√3 = 8 - 4√3

\(4(2 - \sqrt3) 8 - 4√3 = 8 - 4\sqrt3\)

This doesn't make sense.

expand;

2.5 - 3.5x = 8 - 4x - 6

take x to one side;

2.5 - 8 + 6 = 3.5x - 4x

collect;

0.5 = -0.5x

times 2;

1 = -1x

x = -1

ta dah!

How do you find the common ratio of the series 

 Where the first term is 1?

That series is not a geometric progression so it does not have a common ratio.

If a series is a GP then      \(\frac{t_2}{t_1}=\frac{t_3}{t_2}=\frac{t_4}{t_3}.......=\frac{t_{n}}{t_{n-1}}\)

If a series really is a GP and the first term is 1 then the the common ratio would be T2

how do i solve: ^2log(-2x+3) - ^2log(x+1)>0

rearrange:

\(\begin{array}{rcll} ^2log(-2x+3) - ^2log(x+1) &>& 0 \\ \log_{2}{ (-2x+3) } -\log_{2}{ (x+1) }&>& 0 \\ \log_{2}{ \left( \frac{-2x+3}{x+1} \right) } &>& 0 \quad & | \quad 2^{()}\\ \frac{-2x+3}{x+1} & > & 2^0 \quad & | \quad 2^0 = 1\\ \frac{-2x+3}{x+1} & > & 1\\ \end{array}\)

\(\boxed{~ \begin{array}{rcll} \dfrac{-2x+3}{x+1} & > & 1 \qquad D = R ~ \backslash ~ \{-1\}\\ \end{array} ~}\)

\(\small{ \begin{array}{ccc|ccc} \hline \text{denominator } x+1 > 0 && & \text{denominator } x+1< 0 && \\ \\ \hline -2x+3~ >~ 1\cdot(x+1) &&& -2x+3 {\color{red}~<~} 1\cdot(x+1)&& \\ \\ \begin{array}{ccc|c} x+1 &>& 0 & -1 \\ -2x+3 &>& x+1 & +2x-1\\ \hline \end{array} &&& \begin{array}{ccc|c} x+1 &<& 0 & -1 \\ -2x+3 &<& x+1 & +2x-1\\ \hline \end{array} \\\\ \begin{array}{ccc|c} x &>& -1 & \\ 2 &>& 3x & :3\\ \hline \end{array} &&& \begin{array}{ccc|c} x &<& -1 & \\ 2 &<& 3x & :3\\ \hline \end{array} \\\\ \begin{array}{ccc|c} x &>& -1 & \\ \frac23 &>& x & \\ \hline \end{array} &&& \begin{array}{ccc|c} x &<& -1 & \\ \frac23 &<& 3x & \\ \hline \end{array} \\\\ \mathbf{ -1 < x < \frac23 }&& & \text{no solution}&& \end{array} }\)

In the equation, cos θ = 20.8/33.6, θ =

Since you are finding an angle you need to use inverse cos or arc cos.

On the web2 calc you do it like this

[2nd] [acos]  (20.8/33.6) =

Make sure it is set to degrees or radians as needed... :)

Thanks for your help. Although I don't actually want to entirely copy your answer but just get an idea on how to work out the questions. Seeing as this is the last questions in my assignment and don't want to cheat myself into getting better marks then what I would probably originally get. Your help was much appreciated though! :)

cos θ = 20.8/33.6

Use the cosine inverse to find θ

arccos ( 20.8 / 33.6)   = θ   = about  51.75°

The number 'a' represents the number of accounts held in a large advertising firm. The number grows according to the rule a=75+3t (the 't' is raised) where 't' is the number of years from the year 2010.

\(a=75+3^t\)

a) How many accounts did the firm have in the year 2010

t=0

\(a=75+3^0=75\)

In 2010 there were 75 accounts

b) How many accounts were there in 2015

t=5

\(a=75+3^5=75+243=318\)

c) How many years will it take for the number of accounts to exceed 1000?

\(75+3^t>1000\\ 75-75+3^t>1000-75\\ 3^t>925\\ 3^6=729\qquad 3^7=2187\\ \mbox{925 will be exceeded in the 7th year}\\ \)

You can do this last question with logs but there was really no need to here because the answer was so little.

btw, I DO NOT want you to tell me the answer; only to give me clues or bits for me to figure out for myself or simply break down the worded questions for me. Thanks :)

Sorry, I didn't see your instruction until I had nearly finished. ://

Answers if specified like this:

Fraction form:

9π/4 or (9/4) π or (2 1/4) π

Decimal Form:

7.0685834705770348

1.5π² = 1.5 * (π²)

(1.5π)² = 1.5²π²

            = 2.25π²

^Thanks,

^Guest.

^{To avoid confusion, change it to equation form and if you need to add brackets, add.}

500 = 400(1.05)^x     divide both sides by 400

5/4   =  (1.05)^x

1.25  = (1.05)^x      take the log of both sides

log(1.25)  = log(1.05)^x     and we can write

log(1.25) = x * log(1.05)      divide both sides by log(1.05)

log(1.25) / log(1.05)  = x  =   about   4.5735

Here's what I got:

Decimal:

±9.899494934...

Simplified Form:

7√(2)

The size of an interior angle of a n-sided polygon is 14 times of its exterior angle.Find the value of n

HOW TO SOLVE?

The Exterior Angles of a Polygon add up to \( 360^{\circ} \qquad sum_e = 360^{\circ}\)
Sum of Interior Angles \( = (n-2) × 180^{\circ}\qquad sum_i = (n-2) \cdot 180^{\circ}\)

\(\begin{array}{rcll} sum_i &=& 14 \cdot sum_e \\ (n-2) \cdot 180^{\circ} &=& 14 \cdot 360^{\circ} \quad & | \quad :180 \\ n-2 &=& 14 \cdot \frac{ 360^{\circ} } { 180^{\circ} } \\ n-2 &=& 14 \cdot 2 \\ n-2 &=& 28 \quad & | \quad +2 \\ \mathbf{ n } & \mathbf{=} & \mathbf{30} \\ \end{array}\)

Nice graph, Melody......what did you use to create that???

The easiest way to see this is to imagine that something costs, lets say $100

A 22%  discount means  that the item now sells for 78%  of its original cost = $78

And.......another 15% discount means that the item now sells for 85% of the $78  = $66.30

So  the combined discount =  (100 - 66.30)%   =  33.7%

A simple method to figure this is :    1 - (1-.22)(1-.15)  = .337   = 33.7%

a submarine dives 100 m from sea level,rises 60 m then dives 25 m.what is its final position?

-100 +60 -25

You see if you can see the answer

The length of the hypotenuse, c, is obtained from Pythagoras's theorem:

c^2 = a^2 + b^2   where a and b are the legnths of the other two sides of the right-angled triangle.

Here:  a = 4.94  and b = 5.35

c^2 = 4.94^2 + 5.35^2

So  c = sqrt(4.94^2 + 5.35^2)   or  c ≈ 7.2819

The interior angle is given by : (n-2) (180)/ n

And the exterior angle is given by :  360/n

And we have that

(n - 2) (180) / n  =  14* 360/ n      [multiply both sides by n  and simplify ]

180n -360  =  5040    add 360 to both sides

180n = 5400     divide both sides by 180

n = 30

A squared plus B squared equals to C squared. 

So 4.94*4.94+5.35*5.35=7.281902224007131

just round it off to how many decimals or significant figures you need for your assignment :) Hope you find it useful

-5/4

if r = 35 find value of sin r

\(\sin{(35^{\circ})} = 0.57357643635\)

how to solve

9x^4=100

\(\begin{array}{rcll} 9\cdot x^4 &=& 100 \quad & | \quad :9 \\ x^4 &=& \frac{100}{9} \\ x^4 &=& \frac{10^2}{3^2} \\ (x^2)^2 &=& \frac{10^2}{3^2} \\ (x^2)^2 &=& \left( \frac{10}{3} \right)^2 \quad & | \quad \sqrt{} \\ x^2 &=& \frac{10}{3} \quad & | \quad \pm \sqrt{} \\ x &=& \pm\sqrt{ \frac{10}{3} } \\ x_1 &=& + 1.82574185835\\ x_2 &=& - 1.82574185835\\ \end{array}\)

Add them all up and then divide by how many numbers that there are.

ab          or                ba  

that is 2 ways

Write a quadratic equation that has 6 and 2 solutions.

Find the equation with 1 as the coefficient of the quadratic term.

The equation is ___=0

\((x-6)\cdot(x-2) = 0\)