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these are also wrong

these were both wrong Aziz

       CONGRATULATIONS ON YOUR STAR DRAGONSLAYER554!!!       

It will make everybody smarter-er!

And we will advance as the human race!

Another person to the list !! 

Even I'm clever becoz I too know how to use google but wait a sec I'm super clever becoz I also know what is motion !!!( melody just told )

"i know how to use google arent i clever".No but with that answer you deserve the title of smart .......Yeah what you called me before

$${\mathtt{50}}{\mathtt{\,-\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{8.95}} = {\mathtt{\,-\,}}{\frac{{\mathtt{37}}}{{\mathtt{10}}}} = -{\mathtt{3.7}}$$

-3.70 pounds

$${\frac{{\mathtt{5\,664\,503}}}{{\mathtt{5}}}} = {\mathtt{1\,132\,900.6}}$$

That number does.

I know how to use Google.  Arn't I clever. 

Ok. Now I am going to give a much better more concise  answer.

The triangle on the top is similar to the full big triangle because they have two equal angles.  A common right angle and a common angle theta at the top.  Therefore their sides are in the same ratio therefore,

$$\begin{array}{rll}
\frac{y}{x}&=&\frac{6}{4.2}\\\\
y&=&\frac{6}{4.2}x\\\\
y&=&\frac{10}{7}x\\\\
\frac{dy}{dx}&=&\frac{10}{7}\\\\\\
\end{array}
\frac{dy}{dt}=\frac{dy}{dx}\times \frac{dx}{dt}\\\\
\frac{dy}{dt}=\frac{10}{7}\times 1 \qquad \mbox{We were given that }\frac{dx}{dt}=1\\\\
\frac{dy}{dt}=\frac{10}{7}$$

The end of the shadow is moving away from the light pole at a constant speed to 10/7 m/sec

The shadow is increasing in length at  constant rate of 3/7 m/s

I passed Physis 1, marginally. With a bad exam sit, tiredness including answering the hard question first, wrongly at that, and missing answering 2 or 3 questions leaves me pretty happy. Just thought I'd put it out there given the help recieved form a few of the regulars. 

Sat 2/8/13

A treason plot has been uncovered!     

@@ End of Day Wrap :    Fri 1/8/14     Sydney, Australia     Time 10:35am        ♬

Hello everyone,        ♫♪

Today our wonderful answerers were Alan, DragonSlayer554, NinjaDevo, Will8523, Rosala, CPhill, Sasini and AzizHusain.  Thank you.                         ♪ ♫ 

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 Some of these would make really nice additions to your 'Great questions to learn from' thread Ninja. 

I'll try and categorise them for you.   

 Working with logatithms. Hard one.                  ♪ ♫ 

What is the rule and ratios?

What does the C represent?

Deleted deleted.

You way will be nicest solve. No point dancing around the bush now. Getting to the neatest solution is always more benificial and makes life easier. I meant literally dancing around a bush wasting time going backwards to do that way. Should be bonus marks not less marks if solved with a 3x3 and in one go. lol. 

Thanks. Smart lady!

Yes I can do that Stu.  It is quite nifty and little used.

$$7^4 = 49^2=(50-1)^2=2500-100+1=2401$$

Thinks about perfect squares.

$$(a-b)^2=a^2-2ab+b^2$$

You can prove this easily enough by doing the expansion but you should just know it anyway.  So

$$7^4\\
=(7^2)^2\\
=49^2\\
=(50-1)^2\\
=50^2-2*1*50+1^2\\
=2500-100+1\\
=2401$$

When multiplying numbers with the same base, we can add the exponets.

For example, say we had

$$\begin{array}{}
5^2\times5^2\\
25\times25\\
625
\end{array}$$

and really, 625 is 5⁴, so we then come up with the rule

$$\begin{array}{}
5^2\times5^2=5^{2+2} = 2^4
\end{array}$$

Another thing to remember is that this adding exponets only works if the number have the same base. (here they do because they both have 5's. Your question works too because it's all the same base of 7)

Let's put this in your question.

$$\begin{array}{}
7^{765} \times 7^{450} \times 7^{-822} \times 7^{-389}\\
7^{(765)+(450)+(-822)+(-389)}\\
7^{(1215)+(-1211)}\\
7^{(1215)-(1211)}\\
7^{(4)}\\
(7)(7)(7)(7)\\
(49)(49)\\
2401
\end{array}$$

And we get 2401!

Can you explain the following further please? 

7^4 = 49^2=(50-1)^2=2500-100+1=2401

I know. It's there now for the search engine and for op to develop a desire to question. Unless it just makes the person confused, but in which case it will either be ignored or start a discussion in my opinion. As well, it is relevant to this part of learning in maths so when the op gets a negative inside a sqrt they know what they can and can't do with it. ;) 

There are no negative numbers here Stu. 

You cannot Sqrt a negative number if this comes up. It would become a complex number. Unless you take the absolute value in which case you can just Sqrt the positive I believe. Just for reference.