If this means find the coordinates of the midpoint of A and B then you just average the two x-coordinates and average the two y-coordinates.

((8-12)/2, (20+4)/2)  =  (-2, 12)

For this u can also use the on-site calculator that's on the home page. You just have to click on "sqrt" , then type the number and then hit enter and here u get your answer!

These are just two ways of saying that y = -x.  That's all!

If d is the distance of the boat from the lighthouse then

tan(13.4°) = 239/d  or  d = 239/tan(13.4°) so the boat is d - 655 ft from the shallow reef:

$${\frac{{\mathtt{239}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{13.4}}^\circ\right)}}}{\mathtt{\,-\,}}{\mathtt{655}} = {\mathtt{348.216\: \!993\: \!063\: \!345\: \!862\: \!1}}$$

The boat is approximately 348 ft from the reef.

Thank you so much , Anonymous! That gave me a big help! I would like to give u some points for that, I know they r of not much use to u but though you deserve them! Thank you once again!

5/6 is the answer

With 10% increase, the new salary will be 110% of his old salary. 

Original salary*110=New salary*100

Original salary = New salary*100/110

Half of a quater of a billion to the nearst  ten thousand

Half of a quater of a billion to the nearst  ten thousand

Thanks Melody.

For a change, I was confident I was right even though I had a different answer to their solution.

I am not sure what you mean BUT

(2a+8b) + (3a+5b) 

=2a+8b+3a+5b

=2a+3a+8b+5b

=5a+13b

$$3x^2-2x$$

This cannot be simplfied.

It can however be factorised to     $$x(3x-2)$$

There is nothing to solve, but we can simplify it:

$$(\frac{81x^{-4}}{16y^4})^{-\frac{3}{4}}\\\\
(\frac{81}{16x^4y^4})^{-\frac{3}{4}}\\\\
(\frac{81^{\frac{1}{4}}}{16^{\frac{1}{4}}x^{4\frac{1}{4}}y^{4\frac{1}{4}}})^{-3}\\\\
(\frac{3}{2xy})^{-3}\\\\
\frac{2^3x^3y^3}{3^3}\\\\
\frac{8x^3y^3}{27}$$

Yes!

Micrometer (one millionth of a meter) is often shortened to "micron".

Just like a flagpole can be a few meters long, some small structures can be a few "microns" long. 

Maclaurin series of f(x) says:

f(x) = f(0) + f`(0)x + f``(0)x²/2! + f```(0)x³/3! + ...

If

f(x) = (1 + x)^1/2 then  f(0) = 1

f`(x) = (1/2)(1+x)<sup>-1/2</sup> and f`(0) = 1/2

f``(x) = -(1/4)(1+x)<sup>-3/2</sup> and f``(0) = -1/4

... etc.

So f(x) = 1 + x/2 - x²/8 + ...

To first order this is f(x) ≈ 1 + x/2

3(3-3)(3+9) 3-3

Do you mean: 3(3-3)(3+9)*3-3 ?

You must always calculate what's in the paranthesis first. Remember the order  in arithmetics: 

1. Calculate the things in the paranthesis. 

2. multiply and divide  (* and :)

3. Add and subtract     (+ and -)

Ok we see that there are four factors: 3, 3, (3-3) and (3+9). We observe that 3-3 = 0. Therefore the product (answer in a multiplication) is 0:

3(3-3)(3+9)*3-3 = 0*3-3 = 0-3 = -3

@@ End of Day Wrap       Tues 30/9/14        Sydney, Australia      Time 9:35 pm      ♬  

Good evening all,

Great answers today for aoanewbie, MexicanWave6, Geno3141, Rosala, CPhill, DragonSlayer554, AngelicaMarrufo, Bugzy28871, NinjaDevo, Unknown and Alan and Stu.   Thanks all.

I was busy today and did not answer many questions.  I really  want to give a very big thankyou to CPhill, Alan and Geno3141.  Without you, very few questions would get answered.   I am very grateful to each of you for your great contributions to this forum.   

I do not have many interest posts because I have not looked at many questions or answers well.  Please, if you answer or see a really good question or answer send the address to me in a private message and I will include it in the wrap.   

1) Finding last digit

1/10/14

1) MacLaurin Series Expansion  (Thanks Alan)

Thanks alan, I think that is all a bit too much for me.

 Never mind, maybe I will work it out some time in the future.   

Thank you Alan.   

if 7x=35 then x=5 

Your answer is correct.

theirs is wrong.    

It is just

$$\frac{-x}{2}$$

thanks Chris,

One day I will get the time to 'study' your vector answers.