All Answers 358098 Answers

Very nice, Melody.......

A test is like 2 quizzes Test = Q+Q =2Q

so

$$\begin{array}{rll}
\frac{62+75+77+2Q}{5} &\ge& 70\\\\
\frac{214+2Q}{5} &\ge& 70\\\\
214+2Q &\ge& 350\\\\
214-214+2Q &\ge& 350-214\\\\
2Q &\ge& 136\\\\
Q &\ge& 68\\\\

\end{array}$$

The student needs to get at least 68 in the next test  

Mon 25/8/14

* 1) Using the web 2 calc for unit conversions. MAYBE this could go in reference material.  What do you think Ninja. 

@@ End of Day Wrap :     Sun 24/8/14    Sydney, Australia      Time 1:25am     (Really monday morning)   ♬  

Hello all,

Great weekend answers from xvxvxv, CPhill, AzizHusain, Alan, BlinxD, NinjaDevo and Will85237.  A big thank you to each of you.      

Edit: note to DS.  A bit thank you is a bit of a thankyou because each answerer gets a part of it.  Of course the thank you is infinite so the 'bit' is infinite as well.  Does that answer your question DS?

Now for some interest threads:

* 1) Why is  $$-3^2=-9\;\; not\;\; +9?$$       (Great answer from Ninja)

ok which one really is your question.

Technically irt should  be the first one but I suspect it was supposed to be the last one. I doubt that it is the middle one.  You needed more backets to make the meaning clear.  Which would our like solved?

$$\\\frac{5(2x+1)^{2}}{4}\times x+5 = 5x-1\\\\
\\\frac{5(2x+1)^{2}}{4}\times (x+5) = 5x-1\\\\
\frac{5(2x+1)^{2}}{4x+5} = 5x-1$$

When traveling downstream speed = boat + current = 20miles in 2 hours = 10miles/hour

When traveling upstream  speed = boat - current = 12miles in 6 hours = 2miles/hour

so we have 2 equations which must be solved simultaneously.

B+C=10

B-C=2

add and we get

2B=12

B=6

subtract and we get

2C=8

c=4

So the boat is traveling at 6 miles per hour and the current is traveling at 4 miles/hour.

$$$64x-\frac{4x}{3}$\\\\
$=\frac{64*3x}{3}-\frac{4x}{3}$\\\\
$=\frac{192x}{3}-\frac{4x}{3}$\\\\
$=\frac{188x}{3}$\\\\$$

This is not a question.

dOn't forget to reverse the sign because you divide on negative number 

Thanks for the help 

100*10^6 + 0.3*10^k = 1.3*10^8

$$\begin{array}{rll}
100*10^6 + 0.3*10^k &=& 1.3*10^8\\
10^8 + 0.3*10^k &=& 1.3*10^8\\
10^8-10^8 + 0.3*10^k &=& 1.3*10^8-10^8\\
0.3*10^k &=& 0.3*10^8\\
k &=& 8\\
\end{array}$$

Thanks for the question Takahiro 

I cheated (or used the resources available to me)

The 'x' besides the 4 refers to an expression like 

64x-4y/3

Thanks,

Flattery goes a long way with me  

$$\left( \frac{e^x-e^{-x}}{2}\right)^2-1\\\\
= \frac{(e^x-e^{-x})^2}{2^2}-1\\\\
= \frac{e^{2x}-2e^xe^{-x}+e^{-2x}}{4}-\frac{4}{4}\\\\
= \frac{e^{2x}-2+e^{-2x}}{4}-\frac{4}{4}\\\\
= \frac{e^{2x}+e^{-2x}-6}{4}\\\\
\mbox{Do you want me to keep going? It is probably finish now:)}\\\\
= \frac{e^{2x}+\frac{1}{e^{2x}}-6}{4}\\\\
= \frac{\frac{e^{4x}+1-6e^{2x}}{e^{2x}}}{4}\\\\
= \frac{e^{4x}+1-6e^{2x}}{4e^{2x}}\\\\
= \frac{e^{4x}-6e^{2x}+1}{4e^{2x}}\\\\$$

melody !! You are gorgeous 

$$\frac{1}{\sqrt2}\\\\
=\frac{1\times \sqrt2}{\sqrt2\times \sqrt2}\\\\
=\frac{\sqrt2}{2}\\\\\\
or\;alternatively\\\\
\frac{\sqrt2}{2}\\\\
=\frac{\sqrt2\div \sqrt2}{2\div \sqrt2}\\\\
=\frac{1}{2^1\div 2^{1/2}}\\\\
=\frac{1}{2^{1-(1/2)}}\\\\
=\frac{1}{2^{(1/2)}}\\\\
=\frac{1}{\sqrt2 }\\\\$$

$$If f(x) =4x-7\\
then\\
$f(9)=4*9-7=36-7=29$\\
$f(a)=4a-7$\\
$f(-3)=4*-3-7=-12-7=-19$\\
$f(0)=4*0-7=0-7=-7$\\\\
See, each time the x that was in the function bracket to start with is \\replaced with the new thing in the function bracket.\\
Does that help?$$

I don't see any question here!  

for 1800$ you can buy 3 computers and 1 printer. if the price of a computer will go down by 500$, then for 1300$ you can buy 2 computers and 2 printers. what is the cost of a computer?

3C+1P=1800  (eqn 1a)  $$\rightarrow$$   P=1800-3C   (eqn 1b)

2(C-500)+2P=1300  (eqn 2a)

2C-1000+2P=1300   (eqn 2b)

2C+2P = 2300    (eqn 2c)

C+P=1150  (eqn 2d)

sub P=1800-3C into equation (eqn 2d)

C+1800-3C=1150

-2C=-650

C=$325

The original cost of the computer is $325

This doesn look right because it means that the price fell ot a negative number which is pretty silly.

But I will keep thinking about it anyway.

Check

1P=1800-3*625 = $825

3c+1P=3*325+825=$1800 correct

If the price of the computers fell by 500 then they fell to 325-500=-$175

Now 2 computers and 2 printers cost -175*2+2*825 = $1300  correct

Okay, the answer is correct.  The only way this works is if the computers have become so obsolete that the company will PAY $175 to have them taken away.

No CPhill!i didnt check for the answer there!actually , i had over reacted on giving the answer becoz it was just a guess but i was confident as well cuz i knew theres only one word with X thats X-ray! anyways i just won though!

i see i have been missing a lot of riddles!but nevermind now IM BACK!

it mean 4 

hi anonymous,

Why don't you join up.  It is very easy to do.  Much easier than posting anonymously every time.  

I liked you proof.  I just wrote it in LaTex as I worked through it.  

$$\begin{array}{rll}
e^{\pi i}&=&cos\pi+isin\pi\\
e^{\pi i}&=&-1+0\\
e^{\pi i}&=&-1\qquad \\
ln(e^{\pi i})&=&ln(-1)\qquad \\
ln(-1)&=&\pi i\qquad \\
now&&\\
x&=&i^i\\
lnx&=&lni^i\\
lnx&=&ilni\\
lnx&=&iln(-1)^{1/2}\\
lnx&=&\frac{i}{2}ln(-1)\\
lnx&=&\frac{i}{2}\times \pi i\\
lnx&=&\frac{\pi\times i^2}{2}\\
lnx&=&\frac{\pi\times -1}{2}\\
lnx&=&\frac{-\pi}{2}\\
e^{lnx}&=&e^{\frac{-\pi}{2}}\\
x&=&e^{\frac{-\pi}{2}}\\
x&\in&Z\\
therefore&&\\
i^i&\in&Z\\


\end{array}$$