All Answers 358129 Answers

You missed the & in front of \frac.

How much do you lose if there are 2 zeros?

x=c    {c: r1 < c < r2 }

maybe?

where c is a given constant.

I'll answerthe question asked but you do need to use brackets AllSmilesAlways to make your meaning clear.

$$\begin{array}{rll}
12^x-2&=&20\\\\
12^x&=&22\\\\
log(12^x)&=&log22\\\\
xlog12&=&log22\\\\
x&=\frac{log22}{log12}\\\\
x&\approx &1.244 \mbox{ correct to 3 decimal places}
\end{array}$$

Can someone please tell me why this did not align properly?

\begin{array}{rll}

12^x-2&=&20\\\\

12^x&=&22\\\\

log(12^x)&=&log22\\\\

xlog12&=&log22\\\\

x&=&\frac{log22}{log12}\\\\

x&\approx &1.244 \mbox{ correct to 3 decimal places}

\end{array}

First do tan^-1(2.64) (use 2nd atan on the calculator)

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{2.64}}\right)} = {\mathtt{69.253\: \!919\: \!724\: \!317^{\circ}}}$$

This is 69° plus a fraction of a degree.  Multiply the fraction by 60 to get minutes.

$${\mathtt{0.253\: \!919\: \!724\: \!317}}{\mathtt{\,\times\,}}{\mathtt{60}} = {\mathtt{15.235\: \!183\: \!459\: \!02}}$$

This gives 15' plus a fraction of a minute. Multiply the fraction by 60 to get seconds.

$${\mathtt{0.235\: \!183\: \!459\: \!02}}{\mathtt{\,\times\,}}{\mathtt{60}} = {\mathtt{14.111\: \!007\: \!541\: \!2}}$$ 

This is 14'' to the nearest second.  So the result is 69°15'14''

Tan is also positive in the 3rd quadrant, so you could add this angle to 180° to get the 3rd quadrant solution.

Your question does not make any sense!

Great picture reinout!  Thumbs up from me.

Hi Rosala,

Let the time travelled be T hours

Plane:  3500km in T hours so      $$speed=\frac{3500}{T}\:km/hour$$

Train:  600km in T hours so   $$speed=\frac{600}{T}\:km/hour$$

5 times speed of train =  $$\frac{5*600}{T}=\frac{3000}{T}\:km/hour$$ 

Speed of plane = $$\left(\frac{3000}{T}+50\right)km/hour$$

so      $$speed=\frac{3500}{T}\:km/hour$$   =  $$\left(\frac{3000}{T}+50\right)km/hour$$

$$\begin{array}{rll}
\frac{3500}{T}&=&\left(\frac{3000}{T}+50\right)\\\\
T\times\frac{3500}{T}&=&T\times\left(\frac{3000}{T}+50\right)\\\\
3500&=&3000+50T\\\\
500&=&50T\\\\
T&=&10
\end{array}$$

Plane speed = 3500/10 = 350km/hour

Train speed = 600/10 = 60 km/hour

 You should check that these answers make the word problem correct!

It's just the scale factor squared.

To see this, note that one square foot = 1 ft X 1ft

Now, let us suppose that we increased or decreased every side of the square foot by some scale factor, "p."  So now, the "new" area is just (1p) X (1p) = 1p^2 sq ft.

And every square foot of the object would behave in the very same way.......

I don't think so !!!

2014-1998=16

Which means you will turn 16 this year. 

But you haven't had your birthday yet (it is only may) so you are only 15 years old

Alan has done some mind reading and answered what he assume the question was.

Thanks Alan.

If you are clever enough to do maths at this level then you are clever enough to ask your question properly!

-9+12i/1+2i

This the question Alan has answered

Simplify the following complex expression and make the denominator real. 

(-9+12i)/(1+2i)    

I stand corrected - Thanks Chris

Thank you rosala,

No zegroes this is not the hacker.  Just a random user.

Sat 24-5-14

Speed questions.  Good (High level) junior high problems.  Also rosala says she doesn't understand.

I'll take a run at the pearl problem......although I kind of like the idea that Anonymous had...snatching the bag and running!!!

I also believe that drawing all the pearls out of the bag, except one, is the correct strategy. Since, after any number of "even" draws, we never know how many white or black ones we have, we can never be sure that their totals are equal...if we could, "fabulous" Steve would soon be "broke" Steve.

Notice that after just 2 draws, there are 3 possibilities.....0W 2B, 1W 1B, 2W 0B  ........Thus only one thing out of 3 wins for us.

Notice that after just 4 draws, there are 5 possibilities.....0W 4B, 1W 3B , 2W 2B, 3W 1B, 4W 0B........Thus only one thing out of 5 wins for us

And after 100 draws, again, only one thing out of 101 wins for us - 50W 50B, and 100 other combinations lose for us.

But, consider the scenario in which two pearls remain in the bag......If we draw either a white or black one on the next draw and a white one remains, we win. Thus, (draw white)(white remains) or (draw black)(white remains) are two winning scenarios.

But, if we draw either a black or white one and a black remains, we lose no matter what. Thus, out of the four remaining scenarios, 2 win for us and 2 lose, so we have a 50% chance of winning. And drawing all but one pearl out of the bag results in a greater chance of winning than stopping at any other point of even draws. Also note, that when we draw 2 pearls out ot the bag at first, we have a 33% chance of winning, but when two pearls remain, we are even money to win !!!

One final note....you could turn the tables on "fabulous" Steve and tell him that you will take one pearl out of the bag, and whatever remains in the bag is your "draw." Thus, if you draw a white one out, you win......otherwise, no.

That's my story, and I'm sticking to it!! (But, it might be incorrect, too......)

The enclosed region shows where they are all true at the same time.

This is the INTERSECTION of the regions.

3x+21 cannot be simplified!

Antilog(x)=10^x     

60 minutes in an hour

60 seconds in every one of those minutes

so

60*60= 3600 seconds in an hour.

Thank you Maddie that was a really good answer.

Welcome to Web2.0calc forum!

Just remember to give the units.  

There were no units given in the question so the best you can do is unit^2.

okay,

Thank you for telling us that you didn't understand - We need your honest feed  back.  Just make sure you think really hard first.  But if you still don't understand - Always say so.

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

CPhill's answer is very good but I will try and break it down further.

First look at the whole trip.

6 hours at 116km/hr   will take the car 6*116 = 696km

So the whole trip is 696km and will take 6 hours.

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

Now I am going to look at the first part of the trip.

You travel 262km at a speed of 131km/hour

It will help if you understand that 131km/1hour is the same as 1hour/131km

That is if you go 131km in an hour then you must take 1 hour to travel 131km.

I want to know how long this part of the journey took.

$$\frac{1hour}{131km}\times\frac{262km}{1}$$

the km cancel out and you are left with     $$\frac{262}{131}hours=2 hours$$

So for this first stretch you travel 262km in 2 hours

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

Now you need to know the average speed for the second part of the trip.

speed = distance/time

So you need  distance and time taken.

The whole trip took 6 hours.  The first part took 2 hours.  So the second part must have taketn 6-2=4 ours

I worked out that the whole distance was 696km.  The first part was 262km.  So the second part has to be 696-262=434km

Speed for the second part is 434km/4hours = 108.5Km/hour

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

I hope that that helps.

Can you explain a little better.  I don't understand.

I think you might be talking about finding some angle, given a ratio.....use the tangent inverse for this.......hit the "2nd" button on the calculator, and then "atan" and key in your value.......then hit enter or the "=" key

$$a=\frac{k}{t^2}\\\\
\mbox{ When } t=20\quad a=5m/s^2\quad \mbox{ Find k}\\\\
5=\frac{k}{400}\\\\
k=2000\\\\
so\\\\
a=\frac{2000}{t^2}\\\\
When\quad t=25\\\\
a=\frac{2000}{25^2}\\\\
a=\frac{2000}{625}\\\\
accel=3.2m/s^2$$

Look in the Sticky Topics at the bottom right of your page.

There is one there called "Hoe do I type in fractions"

Look there