Melody

This one is for you MathsGod1

I am not sure about the 'best, way to do this but

$$\\r=\sqrt{4+9}=\sqrt{13}\\
tan\theta=3/2\\$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{1.5}}\right)} = {\mathtt{56.309\: \!932\: \!474\: \!02^{\circ}}}$$

$$(2,3)\approx(\sqrt{13}, 56.3^0)$$

I think that is correct :)

Because this is a commercial site.

No one inside this forum gets paid a cent (nor does anyone get charged anything)  but the owner of the site has spent an enormous amount of time creating the calulator and the site in general.  Plus he has a lot of running costs.  All this must be paid for.  The advertising recovers some of these costs for him.  He has kept the advertising quite unobtrusive which is very nice of him.    

You have made a bit of a mess of the multiplication.

$$1\frac{1}{14}\times 2\frac{2}{20}$$

You changed them inot improper fractions well, although it would have been good if you had noticed that 2/20=1/10 right at the ver beginning.

When you are cancelling.

You must cancel something on the top with something on the bottom.  I don't know what you did!

I'll show you the best way to handle this one, I have put in extra steps that will hwelp you understand.

$$\\1\frac{1}{14}\times 2\frac{2}{20}\\\\
1\frac{1}{14}\times 2\frac{2\div 2}{20\div 2}\\\\
=1\frac{1}{14}\times 2\frac{1}{10}\\\\
=\frac{1*14+1}{14}\times \frac{2*10+1}{10}\\\\
=\frac{15}{14}\times \frac{21}{10}\\\\
=\frac{15\div 5}{14}\times \frac{21}{10\div 5}\\\\
=\frac{3}{14}\times \frac{21}{2}\\\\
=\frac{3}{14\div 7}\times \frac{21\div 7}{2}\\\\
=\frac{3}{2}\times \frac{3}{2}\\\\$$

$$\\=\frac{3*3}{2*2}}\\\\
=\frac{9}{4}}\\\\
=2\frac{1}{4}}\\\\$$

When you finish check with a calculator that your answer is corrrect

$$\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{14}}}}\right){\mathtt{\,\times\,}}\left({\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}}{{\mathtt{20}}}}\right) = {\frac{{\mathtt{9}}}{{\mathtt{4}}}} = {\mathtt{2.25}}$$             that is good

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

Have you gone through those fraction videos that I told you to look at ?

You have a very good memory MG.  

In many ways this is great     BUT     

it can lead you to think that you understand things that you really do not understand.

You may have copied and learned a method and you may not even realize that you don't understand what you are doing.

Eventually this catches up with you and you cannot advance further.

You will always need to be very aware of this!

There is a lot of briliant videos out there where you can learn a lot.

This video was good but certainly not one of the very best one.

BUT

Be very careful MG.  You must get a  really good grounding or it WILL catch up with you.

Do fractions decimals and percents (with ordinary numbers) until you can do EVERY question in your sleep.

THEN you will have a good grounding for everything else!

Try this one

$$1\frac{1}{14}\times 2\frac{2}{20}$$

Try and do it the easiest way.  Make the best use of cancelling  

Good but I want you to cancel BEFORE you multiple.  That way you do not need to worry about such big numbers.

Also when you cancel you can also do it sideways so long as it is multiply and you cancel something on the top with something on the bottom.

eg

$$\\\frac{5}{3}\times \frac{9}{10}\\\\
=\frac{\not{5}^1}{3}\times \frac{9}{\not{10}^2}\\\\
=\frac{1}{3}\times \frac{9}{2}\\\\
=\frac{1}{\not{3}^1}\times \frac{\not{9}^3}{2}\\\\
=\frac{1}{1}\times \frac{3}{2}\\\\
=1\times \frac{3}{2}\\\\
=\frac{3}{2}\\\\
=1\frac{1}{2}\\\\$$

When you get good at it you can do all of this in 1 step :)

Thanks for sharing Dbg, I like listening to your clips.

Since you are onto movie themes tonight I will add another :)

This is music from an old movie, Coccoon, it was made in 1985, the music was written by James Horner :)

Mmm the horizonal speed will stay 25m/s

$$\\\ddot y=-9.8\\
\ddot y=-9.8t+0\\
y=-4.9t^2+5.5
\\\\
\ddot x=0\\
\dot x=25\\
x=25t$$

The ball will hit the ground when y=0

$$\\-4.9t^2=-5.5\\
t^2=5.5\div 4.9\\
t=\sqrt{5.5\div 4.9}\\$$

$${\sqrt{{\frac{{\mathtt{5.5}}}{{\mathtt{4.9}}}}}} = {\mathtt{1.059\: \!456\: \!926\: \!727\: \!951\: \!9}}$$

1.059 seconds  approx

Horizontal distance = 25t = $${\mathtt{25}}{\mathtt{\,\times\,}}{\mathtt{1.059\: \!456\: \!9}} = {\mathtt{26.486\: \!422\: \!5}}$$      about 26.5 metres

Angle

x velocity = 25m/sec              

 y velocity = $${\mathtt{\,-\,}}\left({\mathtt{9.8}}{\mathtt{\,\times\,}}{\mathtt{1.059\: \!456\: \!9}}\right) = -{\mathtt{10.382\: \!677\: \!62}}$$  = about 10.4m/s

$$tan\theta = 10.4/25$$

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{10.4}}}{{\mathtt{25}}}}\right)} = {\mathtt{22.587\: \!310\: \!531\: \!366^{\circ}}}$$

angle is about 22.6 degrees 

The ticket (original) price was $7.00

the discount is 20%  that is  20/100*7 =1.4 =  $1.40    (from a calc)

selling price = old price - discount    

you can finish it Eloise :)