Melody

Use the ordered pairs to write a function rule. Give the rule in the slope-intercept form.

(–12, 1.5), (−1, –1.25), (5, –2.75), (8, −3.5)

The last row was added later as a check,

You are told to give the rule in gradient and y intercept form so that immediately says it is a line and will be written in  the form   y=mx+b

Choose ANY 2 points to find the gradient m.  I'll use the last 2

\(m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{-3.5-\;-2.75}{8-5}=\frac{-0.75}{3}=-0.25\)

y = -0.25x + b

Now sub in any of the points to get the y intercept.  I'll use (-1, -1.25)

-1.25=-0.25*-1+b

-1.25=  0.25 +b

-1.25-0.25=b

b = -1.5

y = -0.25x - 1.5

or

y=-x/4  - 1.5

I have checked each of the points on the table above to make sure that the equation works for all points

You mean that you have 

\(sin\theta=\frac{\sqrt2}{2}\)

And the answer is  theta =45 or 135 degrees.    

Yes so far that is true.  

Well it depends on the question which one is correct.  Often they are both corrects.

Like 

\(x^2=9\\ x=+3\;\;or\;\;x=-3\)

Both answers are true.  Maybe other factors may rule one of the answers out but they are both true.

Maybe if you give a specific question I may be able to help more.    ://

Hi guest, you ahve answered  9 divided by 4

NOT

9 divided by a quarter.

The question is asking you how many quarters are there in 9.

There are 4 quarters in 1 so how many quarters must there be in 9 ?

Use the web2 calc - or any calc for that matter.

The meaning is not clear anyway ://

10-[50/ (-2*25)-7]*2

Maybe you mean

10-[50/ (-2*25)-7] ^ 2         The hat (caret) is the symbo for 'to the power of'

You can enter it just lke that :)

Are you still here?  I do not want to wait till h**l freezes over. ://

Anyway.

I will assume that the hutticvane travels at 20.88 km/hour

Now   20.88 km per one hour is the same as         1 hour per 20.88 km

so

\(\frac{1hour}{20.88km}\times \mbox{distance travelled=time taken in hours}\)

I got t he answer straight up but I want you to tell me what it is. :)

Try googling

"Distance from Cuba to Key West" and see if you can get an answer.

I will have a look as well but you should learn how to get this kind of info so I will help you find it if you have problems. :)

 My answer is different from our guests.  We may have made different assumption, I don't know.  

The US government issued a Bond on June 1, 2010 to mature June 1, 2030. The coupon on this bond was 4% paid semi-annually on June 1 and on December 1. I wish to buy this bond on Monday, Nov. 2, 2015 at a yield of 3%. What is the Price that I should pay, as well as the accrued interest on this bond? Thank you.

Assumptions  

1)  The 4% and 3% are 6 monthly rates (not annual rates)

2)  Face value = Redeption value = $100

so

F=C=$100

r=4% =0.04

I = Fr = 100*0.04 = $4    That is, a $4 is paid every 6 months

--------------

i= 3% = 0.03

Because you want less interest than the coupon rate this means that you are prepared to pay a premium - this means that you are prepared to pay more than $100 for the bond.

Now, you are buying the bond in  the middle of a coupon cycle so you need to first work out how much you would pay for it at the beginning of that cycle.

It is easiest for you to draw up a rough time line to display what is happening.

Now the beginning of the cycle BEFORE is 1st June 2015

The next period will begin on 1st Dec 15  (but we do not need that just yet)

From the 1st june15 till 1st June 30 is 15 years which is 30 rate perids

n=30

First off you need to work out the price that will yeild 3% back to that date.

\(P_1=C+\left[(I-Ci)\times \frac{(1-(1+i)^{-n}}{i}\right]\\ P_1=100+\left[(4-100*0.03)\times\frac{1-(1.03)^{-30}}{0.03}\right]\\ P_1=100+\left[1\times 19.60044135\right]\\ P_1=119.60044135\\ P_1=\$119.60\)

So, if you bought the bonds on 1st june 15 you would have paid $119.60

But you didn't.  You bought them later so you will get some ' free' interest period.

So you will be prepared to pay a little more.

So you need to work out how many free interest days that there are.

From the 1st of June to the 2nd Nov = 30+31+31+30+31+1 = 154 days

And how long it will be till the next cycle begins

And from 1st June to 1st December = 30+31+31+30+31+30=183 days

So the free portion is   154/183 of a cycle.

\(S=P_1(1+i)^{154/183}\\ S=119.60\times(1.03)^{154/183}\\ S=$122.61 \)

So you should pay a maximum of $122.61 per $100 Coupon.

Mmm,

Well I might think about it but you can google haow far it is from Cuba to Key West first!    

Australians do not have shrimps.  We have prawns and we rarely BBQ them.  

You have been watching too much of Paul Hogan's silly ads!!   Shame on you!!

Anyway, as much as La-TeX may like prawns, they are not good for him.

If we allow him to eat rubbish he will get sick and then we will not get our peanuts and bananas worth out of him.

NO La-TeX will not be fed prawns on my watch!