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@@ End of Day Wrap   Thurs 19/3/15   Sydney, Australia Time   12:50 am   (really Friday)  ♪ ♫

Hi all,

Answer credits:  Heureka, Yoepic123, Geno3141, Will85237, Samgelinas, CPhill, TayJay, ThisGur, TheJonyMyster, Civonamzuk and Rosala.  Thank you.  You are all wonderful.

great thanks :) 

Fri 20/3/15

X/2-3(x+9)=X/5

I am going to assume this is

(1/2)x - 3(x + 9)  = (1/5)x    rearrange as

(1/2)x - (1/5)x  = 3(x + 9)     get a common denominator on the left and simplify the right

([5 - 2]/10)x  = 3x + 27

(3/10)x = 3x + 27    multiply both sides by 10

3x = 30x + 270     subtract 30x from both sides

-27x = 270     divide both sides by -27

x = -10

Well it is not in the OEIS so I do not like your chances of getting an answer :)

Thanks Chris,

I really need practice at these so it is great when they come onto the forum.

I even got the same answer as you - isn't that great :)

Thanks anon for giving us this question :)

The number of stairs doesn't matter......the angle of elevation is given by

tan^-1(17/32)  = about 27.98°

To start with you should learn how to spell mathematician :)

you need to study really hard at school and then go to university (or maybe college in your country) and study mathematics there as well. :)

Let A = {-.67 ≤ Z ≤ .67} and B = {.26 ≤ Z ≤ 1.30}. Find A ∩ B complement (i.e. the union of "A and the complement of B").

This notation looks really weird to me but I shall following on the same path.

$$\cap$$   means intersection - not union!

Find A ∩ B complement

$${-.67\le Z \le .26}$$

well it might have been if there was an x next to the 12. :/

I think that a square is a special type of rhombus.

I think this might be

³√(x⁹)   ....if so.....we have

(x⁹) ^(1/3) = x³

I do not understand the question but

$$\sqrt3=3^{1/2}$$

Hit the "pi" key on the on-site calculator

Hit the square root key 

Hit the = key

$$\\FV=PV(1+r)^n\\
$rearranging we get$\\
PV=\frac{FV}{(1+r)^n}\\\\
FV=2860\\\\
r=\frac{8.5\%}{2 }= 0.0425\\\\
n=3\frac{7}{12}*2 =7 \frac{1}{6}$$

Now just plug the number in :)

Very nice, rosala....!!!

e^xy  = x + y    

Using implicit differentiation, we have

ye^xy + xy'e^xy  = 1 + y'

y' ( xe^xy - 1) = 1 - ye^xy

y' = [ 1 - ye^xy  ] / [ xe^xy - 1]  

You have both assumed that these are combinations - and you are most likely correct BUT

Couldn't those be vectors?

$$\begin{pmatrix}
16 \\
4
\end{pmatrix}
&-
\begin{pmatrix}
16 \\
12
\end{pmatrix}&=
\begin{pmatrix}
0 \\
-8
\end{pmatrix}$$

{The volume has to be in cubic, not square, inches }

So we have

45 pi = pi (5)(r^2)  divide both sides by pi

45 = 5 r^2     divide by 5

9= r^2       take the square root of both sides

3 = r

The volume of the bottom tier is

5in x 9in x 2 in  = 90 in^3

And the volume of the top tier is

5in x 5in x 2in  =  50 in^3

So the total volume is (90 + 50) in^3 = 140 in^3

to find anything to any power we just have to multiply it the same number of times for example to find 4 to the 16th power we'll multiply it 16 times by itself...

so....

4^16 =  4294967296

I purposely did not go further with my calculatations.

I wanted to show how i would do it without using any high level calculators.    

yes the quesiton is correct

The term "tonnage" doesn't make sense here.....I assume you want to know the "volume"

We just need to convert the inches to meters

We have

3in x 1m/39.37in = (3/39.37)m 

So the total volume is given by

330m x 3m x (3/39.37)m = 68.58m^3