Melody

a*10=8090045757667635534544660

a=809004575766763553454466

I just took the zero off the end.  :)

Alan's answer

Hi 

These questions are not difficult.  It is just the wording that you have to get your head around.

You do not need to use most of the information that you are given you just need to spot which bits are relevant.

The first one gives you a speed and a distance and you just need to work out how long it will take.

you can use the formula     speed=distance / time

Question 2 is even easier.  I do not want to give you the answer.  Think about it.  Ignore the irrelevant info and hone in on the little bit of info that you actually need to use.  It will be so much better if you work it out for yourself.   

A great answer anon.  

Alan, I also answered this question a little while ago.  My answer is a bit simpler.   

Annual compounding

$$FV=PV(1+i)^n$$

$$\\1500=1000(1+0.05)^n\\
3=2(1.05)^n\\
1.5=1.05^n\\
log1.5=log1.05^n\\
log1.5=nlog1.05\\
n=\frac{log1.5}{log1.05}\\$$

$${\frac{{log}_{10}\left({\mathtt{1.5}}\right)}{{log}_{10}\left({\mathtt{1.05}}\right)}} = {\mathtt{8.310\: \!386\: \!222\: \!520\: \!560\: \!2}}$$    

8.31 years

Daily compounding

$$\\1500=1000(1+0.05/365)^{365n}\\
1.5=(1+0.05/365)^{365n}\\
log1.5=log(1+0.05/365)^{365n}\\
log1.5=365n*log(1+0.05/365)\\
365n=\frac{log1.5}{log(1+0.05/365)}\\
n=\frac{log1.5}{365log(1+0.05/365)}\\$$

$${\frac{{log}_{10}\left({\mathtt{1.5}}\right)}{\left({\mathtt{365}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{0.05}}}{{\mathtt{365}}}}\right)\right)}} = {\mathtt{8.109\: \!857\: \!581\: \!140\: \!344\: \!3}}$$

8.11 years  (2dp)

The difference if 0.2 of a year = 2.4 months

Well if you look around for more than 2.4 months you will start losong money.

BUT If the interest is only added yearly with the first one then you might have to wait for the full year 9 years before you can withdraw the $1500.

With the daily one I would assume that the interest is added to the account daily and you can withdraw the $1500 in 8.11 years.

Now  the daily one is looking quite a lot better.  

What graph?

Here is a diagram

$$\\sin23=\frac{F_x}{64N}\\\\
F_x=64sin23\;\;\;\;N\\\\\\
cos23=\frac{F_y}{64N}\\\\
F_y=64cos23\;\;\;\;N\\\\\\$$

$$\\T=x^2+y^2-4x+2y\\\\
T+4+1=(x^2-4x+4)+(y^2+2y+1)\\\\
T+5=(x-2)^2+(y+1)^2\\\\
T=(x-2)^2+(y+1)^2\;-5\\\\$$

Now anything squared has to be  greater or equal to zero so T has to be greater to or equal to -5 degrees. 

This will occur when x=2 and y=-1

Do it on the calculator on the home page