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When the equation of a circle is in this format:

(x - h)² + (y - k)² = r²     ,

The center of the circle is (h, k) and the radius is r.

So...if the equation of a circle is:

(x + 3)² + (y - 6)² = 81

h = -3

k = 6

r² = 81

r   = \(\sqrt{81}\)

r   = 9

The center of the circle is (-3, 6) and the radius is 9.

slope = (change in rise) / (given change in run)

A horizontal line rises 0 ..so

slope = 0 / (given change in run)

And, 0 divided by anything = 0...

Therefore,

slope = 0

We can use the inverse sine to solve this

arcsin (32 / 58)  = x ≈ 33.49°

You have to give a table of rates on this one as you did on the $479,000 house. I gave you a "tentative" answer to that one. But, I may be wrong!.

32  = .40x      divide both sides by .40

32 / .40  = x  = 80

I will take a crack at it, but Melody can correct me:

Up to $5,000 is Nil

$5,000 to $75,000, or on $70,000 is $1.50 per $100. So, $70,000/$100 x $1.50=$1,050.

$75,000 to $479,000,or on $404,000 is $1,050 + $3.50 x $404,000/100 =$15,190. So, the total will be:

$1,050 + $15,190 = $16,240 - transfer duty to the Government.

y  = -x ( x + 2) (x - 3)

The zeroes are  at x = -2, x = 0  and x  = 3

From (-inf, -2) the graph will be > 0

From (-2, 0) the graph will be < 0

From (0, 3) the graph will be > 0

And from (3, inf) the graph will be < 0

A minimum turning point will occur on ( -2, 0)  and a maximum turning point will occur between (0, 3)

We could use Calculus to find these turning points but look at the graph here : https://www.desmos.com/calculator/1qkjsbo1r3

It shows that the max turning point occurs at x ≈ 1.786  ≈ 1.8

On What?

Go to Wolfram/Alpha engine and see if it can help you. Check it here:

http://www.wolframalpha.com/input/?i=MacLaurin+series+for+sin(x%5E2)

ok thanks MELODY please help!!!

Here's a formula if you are interested:

\(s = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \mu)^2}\)

Huh? Let me explain what you should do:

1. Calculate the mean of the data

2. For each number in the data, subtract it from the mean and then square it

3.  Calculate the mean of those square differences

4. Calculate the square root of what you just calculated

Good luck!

Go online to this link and study it carefully:

https://www.mathsisfun.com/data/standard-deviation-formulas.html

Now you got it!!. But, since Melody is Australian, she is in a much better position to calculate the "transfer duty". So, Melody, if you see this, please help this young person! Thanks.

oops sorry the amount is $479,000

and sorry its $479,000

0/0 = undefined

Not more than $5,000 Nil More than $5,000 up to $75,000 $1.50 for each $100, or part of $100, over $5,000 $75,000 to $540,000 $1,050 plus $3.50 for each $100, or part of $100, over $75,000 $540,000 to $1,000,000 $17,325 plus $4.50 for each $100, or part of $100, over $540,000 More than $1,000,000 $38,025 plus $5.75 for each $100, or part of $100, over $1,000,000 Additional duty of 3% applies to acquisitions of residential land by foreign persons (including companies and trusts) from 1 October 2016. Find out more about the additional foreign acquirer duty.

Is that it?

Thanks CPhill !!! 

Ok, that is fine. But, what are the rates and percentages that calculate "Transfer duty to the Government"? Look it up in your textbook or assignment. It generally goes something like this:

From 0 - $100,000 is 1%, From $100,000 - $200,000 is 2%, over $200,000 is at 3%......etc. 

Very impressive, hectictar.....I suspect that your answer is exactly correct.....!!!

This is what I came up with, though this might not be the intended approach!

I found and labeled the y-intercept and x-intercept of line A, then used that to label the lengths of the blue and pink lines. I labeled the green line "1s" and the orange line "2s" because the slope of line A is 2. So, for every 1 unit line A goes right, it goes up 2 units. " s " is the unknown scale factor.

the x-coordinate of P = blue line + green line

Let's just look at this right triangle:

We can use the Pythagorean theorem to solve for s.

\((\frac52+1s)^2+(2s)^2=10^2 \\ \frac{25}{4}+5s+5s^2=100 \\ s^2+s+\frac14=20-\frac54+\frac14 \\ (s+\frac12)^2=19 \\ s=\pm\sqrt{19}-\frac12 \\ s=\sqrt{19}-\frac12\)

So...

the x-coordinate of P  \(=\frac52+\sqrt{19}-\frac12 \\~\\ = 2+\sqrt{19}\)

a = -4

b = -1

c = -6

The discriminant is always b² - 4ac, so it's:

   (-1)² - 4(-4)(-6)

= 1 - 4(24)

= 1 - 96

= -95

If the discriminate is <0, the quadratic formula becomes unsolvable, which means there are no values of n which satisfy this equation.

A good resource to use is WolframAlpha when checking your answers for these problems.

Here is the site with this function as the input. You'll notice the graph never touches the x-axis which means that y can never equal zero and the problem has no solution.

-4n²-n-6=0

The discriminant is given by  b^2 - 4ac  =   (-1)^2 - 4(-4)(-6)  =  1 - 96  = -95

A discriminant < 0    means that we have non-real solutions