P.S: This last answer, the one including vector notation, was posted by me, Dragontmaer (I still haven't got an account here, so this is my name from other forums)

weight = mass * gravity 

is that what you mean?

@@ End of Day Wrap    Fri 14/11/14      Sydney,   Australia       Time 10:10 pm             ♬

Hi everybody and thanks to Happy7 and the others who have given points for my wrap.  I appreciate it and i am glad that you find the wrap worth while.    

If anyone would like to recommend any threads for the wrap please let me know.  The most obvious way is to send me the address by private message.  These days the forum is very busy.  I do not read all the questions and answers.  I expect that I miss many good ones.  So please let me know if any draw your attention.  More people than just me would really appreciate it.   

It was very busy today.  I am very glad that so many people get in and help answer questions.  Today these people were Lanayia, haimaithproblems, BrittanyJ, Alan, CPhill, Heureka, Relic, Happy7, Tiddle, geno3141, Anonymous4338, Mathematician and SevenUp.  There were some good answers from anonymous people too.  Thank you for all these great answers.   

Now for some interesting posts:

1) The children have been very acive today :)  A toungue twister from Jillybean   

a+b=2 b-a=4

$$\begin{array}{ccc|c|c|}
& & & I.& II.\\
b+a & = & 2 \ & &\\
& & & + & -\\
b-a & = & 4 \ & &
\end{array}$$

I.

 $$\small{\text{
$
\begin{array}{rcl}
2b + a + (-a) & = & 2 +4 \\
2b +0 & = &6 \\
2b & = &6 \quad | \quad : 2\\
b & = & \frac{6}{2} \\
b &=& 3
\end{array}
$
}}$$

II.

$$\small{\text{
$
\begin{array}{rcl}
b - b + a - (-a) & = & 2 - 4 \\
0+2a & = &-2 \\
2a & = &-2 \quad | \quad : 2\\
a & = & \frac{-2}{2}\\
a &=& -1
\end{array}
$
}}$$

Sat 15/11/14

1) More Physics for me to learn.  Thanks Alan.

None that I can see.  Thanks Alan :))

-1/2=sin((pi*x)/(11));

1. Isolate x:  arcsin(-1/2) = pi*x/11;

All answered  Thank you   :)))

Once again I am not 100% comfortable with the terminology BUT

I assume 4.8% is the nominal rate and you want the effective rate.

1+effective rate = (1+0.048/365)^365

effective rate = (1+0.048/365)^365 -1

$${\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{0.048}}}{{\mathtt{365}}}}\right)}^{{\mathtt{365}}}{\mathtt{\,-\,}}{\mathtt{1}} = {\mathtt{0.049\: \!167\: \!344\: \!264\: \!922\: \!5}}$$

the effective interest rate is 4.9167%

The  fundamental distance formula for any problem involving speed and time is:

1. d = s*t (rearranged from s = d/t) and

eg:

speed = 50 kphtime = 2.5 hours

d = 50*2.5 = 125 kilometres.

Here, your distance is 125 kilometres.

2. r - r1 = + v*t (where r is the position vector of an object at a certain point and r1 is the position vector of the same object at t = 0). This method is to be employed when using i and j vector notation.

eg:

velocity = 2i + 3j

t = 5s

r - r1 = 5*(2i + 3j) = 10i + 15j

Then, to find the distance, you must find the modulus* of (r - r1), as you have calculated THE DISPLACEMENT OF THE OBJECT (distance is a scalar quantity, displacement is a vector).

|r - r1| = (10^2 + 15^2)^1/2 = (100 + 225)^1/2 = 325^2 = 18.03 (rounded to 4 significant figures).

So, your distance here is 18.03 units.

*The modulus is to find the magnitude of a vector; you take the value of the vector, square them, add them together, and get their square root. It is the inverse of Pythagoras' theorem.

Hope this was helpful.

Charlie Company is expected to grow at an annual rate of 6% indefinitely. The return on similar stocks is currently 11%. Charlie's board of directors declared a dividend of $1.85 yesterday. What should a share of Charlie Company sell for?

This one I am totally guessing BUT

if the return is 11% and the growth is 6% then the dividend must be 11-6=5%

You question does not say how often the dividend is paid but I will assume it is yearly.

5%X=1.85

X=1.85 / 0.05

X= $37

that might be the answer  LOL 

A $1,000 corporate bond with 20 years to maturity pays a coupon of 7% (semi-annual) and the market required rate of return is a) 6.6% b) 13%. What is the current selling price for a) and b)?

I just answered one almost identical to this so you can copy the technique of that one.  :)

a + b = 2

   (Step 1) b = 2 - a → (Step 3) b = 2 - (-1) → b = 3

b - a = 4 

   (Step 2) 2 - a - a = 4 → 2 - 2a = 4 → -2a = 2 → a = -1 

a = -1; b = 3

I do not know how US govt bonds work.

I assume the redepmtion value is the same as the face value.

Don't they pay any interest.  That doesn't sound  right.     

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

I can see what you have done SevenUp.

You have simply found the present value of  $10000 given that the annual value is 3.5%.

Mmm okay.

Now that I have done the first one you can copy the technique and do the second one yourself.   

A $1,000 corporate bond with 10 years to maturity pays a coupon of 8% (semi-annual) and the market required rate of return is a) 7.2% 

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

First lets think about this a bit.

You will be happy with at return of 7.2%.  This is less than the coupon rate of 8% so that means you will be prepared to pay more than $1000 for the bond.  You will use this logic when you check the reasonableness of the answer that we will get.  

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

r=0.08/2=0.04 every 6 months

i=0.072/2=0.036 every 6 months

C=1000

$$P=C+[(I-Ci)a_{n|i}]$$

Where 

n=20 (lots fo 6 months) and

$$a_{n|i}\\\\
=\frac{1-(1+i)^{-n}}{i}\\
=\frac{1-(1+0.036)^{-20}}{0.036}\\
=\frac{1-(1.036)^{-20}}{0.036}\\$$

$$\left({\frac{\left({\mathtt{1}}{\mathtt{\,-\,}}{{\mathtt{1.036}}}^{\left(-{\mathtt{20}}\right)}\right)}{{\mathtt{0.036}}}}\right) = {\mathtt{14.084\: \!658\: \!505\: \!338\: \!905\: \!8}}$$

near enough to 14.08466

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

$$\\P=C+[(I-Ci)a_{n|i}]\\\\
P=1000+[(40-1000*0.036)*14.08466]\\
P=1000+[(40-36)*14.08466]\\
P=1000+[4*14.08466]\\$$

$${\mathtt{1\,000}}{\mathtt{\,\small\textbf+\,}}\left[{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{14.084\: \!66}}\right] = {\mathtt{1\,056.338\: \!64}}$$

The price you wil pay to get a return of 7.2% is   $1056.34

this is more than $1000 so it fits with the reasonableness check   

Any reason why x should be restricted to integers?

.

U.S. Government bonds are sold at a discount and redeemed at maturity.

Par value * (1+APR)^-Y Y = years to maturity

Present value = 10000 * (1.0350)^-8

Present value = $7594.12

_7UP_

Here's a way of tackling the problem (approximately):

You could always improve on this by using the exact expression for small values of n, and switching to Stirlings approximation when you can no longer evaluate the exact expression.

.

I thought you needed another interest rate.  A desired return.  

It seems to me that the price should still be $10000.

Let us know when you get your answer.  

I am not at all sure that any one here can answer this question any better.

You say it is yeilding 3.5% is that per annum?  When are the payments made?

Let us know when you find out the answer.  

You need to put the question that you are answering as there are a lot of different questions on this thread 

Brittany you should finish it as  $$w\le19$$

okay Heureka so you did it the long way.  I thought there might have been a short cut.

Thank you :)

Do you mean this (if you do then then it should  have been written like this)

28xy^2/(14xz^3)

$$\\\frac{28xy^2}{14xz^3}\\\\
=\frac{2y^2}{z^3}\\\\$$

I have not answered the question that you asked but I have probably answered the question that you intended. :)

How can I do a calculation of genu: radical 2225 over 10000

Do you mean

$$\\\sqrt{\frac{2225}{10000}}\\\\
=\sqrt{\frac{89*25}{10000}}\\\\
=\frac{\sqrt{89*25}}{100}\\\\
=\frac{5\sqrt{89}}{100}\\\\$$