All Answers 358087 Answers

You have lots of options.

You will see them all if you look at this thread.  

Im happy Melody you liked them!im sure your gonna laugh when every you open your computer!

Have a nice weekend!

u get green and white heart from anonomous. ewe

I'm giving you a blue too!

I'm sorry you have been ill and I am very glad that you are back!

There are lots of good ones in there but 'Good Night is definitely my favourite! 

I just set it as my desktop background lol.

I like the moose one 2nd best.     

Thank you CPhill!blue from me as well for u all!

And even some teachers in my school also are like that , if a lesson reading or dictating or copying from the board is going on then the first sentence of the teacher is after the lunch bell " Just sit down , no one will move"!and once we had to miss half of our lunch time becoz of this!

everyone was really mad at the teacher but as we all know....................their is an automatic zip in the mouth that just zips itself on seeing the teacher!

Anyways im happy you liked the pic!

have a nice weekend CPhill!

We all give you "blue,"  rosala.......glad you feel better...nothing worse than being in bed and feeling bad!!

I love the last picure... I had a Chemistry teacher like that, once.....a really nice lady, but "lunch" time didn't mean a thing to her. She even used to keep talking after the bell to change classes rang!!!

I assume you are talking about on a right angled triangle and it sounds like you are having problems labeling the sides

The Hypotenuse is the longest side and it is opposite the right angle.

The opposite side is opposite the angle that you are dealing with.

The adjacent is the other one (it is one of the arms of the angle - adjacent means touching)

So the first thing you must do is put these labels on your triangle.

Now, which ratio do you choose???

Just remember this

Some Old Hags           Sin=Opp/Hyp

Can't Always Hide       Cos=adj/hyp

Their Old Age              Tan = opp/Adj

You usually have two sides OR one and an unknown one so you choose the ratio that uses these sides. 

I really hope that this helps  

159= -x -4(-7x -6)   distribute the -4 across both terms in the parentheses..we have

159 =-x +28x +24   subtract 24 from both sides and simplify

135 = 27x    divide by 27 on both sides

5 = x

Aziz has found that there ARE NO REAL SOLUTIONS (ROOTS)!

Since most school students have not ever experienced imaginary numbers it is okay to say there are no solutions. 

Thanks Alan but now I cannot understand why 

$$\dfrac{1}{p}\; \dfrac{d}{dt}\;p=\dfrac{d}{dt}ln(p)$$

You can put this one straight into the on-site calculator....

Here's the proof of this using the "Squeeze Theorem".....it's somewhat complicated, but if you have some patience, I think you will appreciate the geometry involved. The proof is the first one on the page.

Yes much better!

Ok  I hope that you are feeling all better now. 

No MElody that me !soo scared!lol!just kidding!(but yes its me only)

and i'm sorry for making Zegroes feel bad!you know Zegroes has many colours so i just thought he was joking!Sorry Zegroes!i didnt do it purposely!

from now on i'll take care of what he really means!

anyways, i was just unable to come here becoz i was quiet ill and u know bed has been my best friend the past days!

It is good to see you back Rosala,

Is that a picture of me? Blue always was my colour  

Yes you got just a little scolding.  Not enough of a one to stay away for days though.

Zegroes was feeling bad.  I was saying things that he didn't want to hear.  I didn't want you to say anything to make him him feel even worse.  That is all.

You over reacted.  But I am really glad that you are back.  I like having you here.  You are fun.   

Zegroes this is for you!

And Melody this ones for you!

Am i getting a scolding!

Ok Alan, I just worked out your answer.   

I didn't know I could do this

$$\begin{array}{rll}
\frac{}{}dp&=&-2dt\\\\
\int \frac{1}{p}dp&=&\int-2 dt
\end{array}$$

You are integrating both sides but one is being integrated with respect to p and the other with respect to t.

I didn't know you could do this.  Can you try to think of a simple explanation of why this is allowed?

Thank you.  

Alan's understanding of calculus is much better than mine.  I am sure his method is the best one, however

I am having trouble following his logic.    I will come back to that.

This is how I would do it:

$$\begin{array}{rlll}
\frac{dp}{dt}&=&-2p\qquad \qquad &p(0)=20\\\\
\frac{dt}{dp}&=&\frac{1}{-2p}\qquad \qquad &p(0)=20\\\\
\int{\frac{dt}{dp}}dp&=&\int \frac{1}{-2p}dp\\\\
t&=&\frac{1}{-2}ln(p)+c &when\; t=0\;p=20\;\;substitute\; to\; find\; c
\\\\
0&=&\frac{1}{-2}ln(20)+c\\\\
c&=&\frac{ln(20)}{2}\\\\
t&=&\frac{-ln(p)}{2}+\frac{ln(20)}{2}\\\\
2t&=&-ln(p)+ln(20)\\\\
2t&=&ln(\frac{20}{p})\\\\
e^{2t}&=&e^{ln(\frac{20}{p})}\\\\
p&=&\frac{20}{e^{2t}}\\\\

\end{array}$$

You really don't need algebra for this.

$5 is spent on to toys that are equal in price so each toy must be $5/2 = $2.50

I'll take your word for it Aziz. lol 

Why would you ever want to do this?  The units in Aziz's answer would be Kg².  What would that be good for?

I'd like to take Alan's explanation and expand upon it a little.

NOTE: THIS IS ONLY TRUE AS THE ANGLE TENDS TO 0

   $$The circumference of a circle is $2\pi r$\\
If the radius is 1 unit then the circumference is $2\pi$\\
So if the angle is measured in radians then the arc length will be equal to the angle that it is subtended from. This is for a unit circle.\\\\$$

You can do this by a normal expansion if you want but it is a difference of 2 squares and you should commit this to memory.

$$\boxed{(a+b)(a-b)=a^2-b^2}$$

So for your question the simplification will be 

$$\\(3 \sqrt2 + \sqrt5) (3 \sqrt2 - \sqrt5)\\\\
=(3 \sqrt2)^2-(\sqrt5)^2\\\\
=3^2 (\sqrt2)^2-(\sqrt5)^2\\\\
=9*2-5\\\\
=18-5\\\\
=13$$