Translation (from Dutch)

what is the highest common factor of 400 and 1080? i got 40 is it right?

I like the fact that you have offered a possible solution so lets take a look

400=40*10

1080=40*27

10 and 27 have no common factors (except 1)

therefore 40 is the highest common factor - You were correct  

I'm going to assume that observer B is at the bottom of the chasm, on the same side as observer A.

In this case:

The height of the chasm is given by 81*tan(51°)

The height of the climber is given by 81*tan(θ)  where θ is the as yet unknown angle of elevation of the climber as seen by observer B.

The distance of the climber below the top of the chasm is given by 81*tan(20°).

Since the last two added together must equal the height of the chasm we have:

 81*tan(θ) + 81*tan(20°) = 81*tan(51°)

tan(θ) + tan(20°) = tan(51°)

tan(θ)  = tan(51°) - tan(20°)

θ = tan^-1(tan(51°) - tan(20°))

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left(\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{51}}^\circ\right)}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}{\left({\mathtt{20}}^\circ\right)}\right)} = {\mathtt{41.053\: \!483\: \!814\: \!122^{\circ}}}$$

so θ ≈ 41°

.

20 out of 30 is

66.7% of 100%

( 2a²b³ )² = ( 2a²b³ )( 2a²b³ )

= 4 a⁴ b⁶

If you were not sure of your working, in an exam you could check by giving a and b some numerical values, and using your calculator to see whether the answer gives the same result as the expression you started with.

e.g., set a=3, b=10

(2 x 9 x 1000) x (2 x 9 x 1000) = 324 000 000

4 x 81 x 1000000 = 324 000 000

                        ☑

1.99 * 3.01

5.9899

Thurs 5/2/15

@@ End of Day Wrap          Wed 4/2/15 Sydney,        Australia Time      5:15 pm          ♪ ♫

Hi everyone,

I have been raced off my feet today ( which was difficult because I have been sitting at my computer almost all day.)  Oh well, it has been very busy anyway.

I fabulous answerers today were Heureka, CPhill, Mikado, Tetration, Hellokittygirl5b, Trincent, YocenatheRipper, NotTheBestMathMaster, BrittanyJ, Kitty<3, Dragonslay3rl, Mathematician, sasini, Anima and Saseflower.

A big thank you to each of you.

Interest Posts:

23degrees

v

This was a really good question to make a person sort out the relevant info from the irrelevant info.

I liked it.   

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

You need the speed of sound to work out how long it took for the lighthouse to hear the horn

the speed of sound is 340.29m/sec  

You need the speed of light to work our how long it takes for the return the flash of light.

Speed of light is 299797458m/s        This is so fast that I am going to ignore it and say that it is instantaneous.

in 8 sconds  the sound will travel    8*340.29 metres          $${\mathtt{340.29}}{\mathtt{\,\times\,}}{\mathtt{8}} = {\mathtt{2\,722.32}}$$

so the boat is 2.722 km from Sleepyton.

in 6 seconds it will travel              6*340.29 metres          $${\mathtt{340.29}}{\mathtt{\,\times\,}}{\mathtt{6}} = {\mathtt{2\,041.74}}$$

so the boat is 2.041 km from Lazyville. 

Well then do not bother answering!

william earns $13 an hour working at a movie theater. last week he worked h hours at the concession stand and three times as many hours at the ticket counter. write and simplify an expression for the amount of money william earned last week.

(h+3h)*13 = 4h*13 = 52h      dollars

This is a better answer dragon1

In the stricky topics on the bottom right of your page is a thread called "how do I type in fractions"  look there.

Mmm

$$\\\pi-A=B+C\;\rightarrow\;A=\pi-(B+C)\\
or\\
A=B+C$$

But I can add 2pi*n to these answers where n is an integer

$$\\A=\pi-(B+C)+2n\pi=(2n+1)\pi-(B+C)\\
or\\
A=B+C +2n\pi$$

Mmm

$$\\A=(2n+1)\pi-(B+C)\\
or\\
A=2n\pi+(B+C)\\\\\\\\
$I think the general formula for this would be$\\
A=(-1)^n(B+C)+n\pi$$

I think that is right but I really need another mathematician to check my working.  :))

17.34  * 13

225.42

 4 + (-6) + 1 - 5

4 - 6 + 1 -5

5 - 6 - 5

-6//

A+B+C = Pi

B + C    =  Pi - A

cos(B +C)= cos (Pi -A)

cos (B+C) = -(cos A)

-(cos A) = cos(-A)

so that,

cos(B +C)   = cos(-A)

now we cut cos

B+C    = -A//

Yes i believe it does.  I had to think about that for a moment . :))

$${\frac{\left({\mathtt{16}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}}{{\mathtt{3}}}}\right)}{{\mathtt{100}}}}{\mathtt{\,\times\,}}{\mathtt{15}} = {\frac{{\mathtt{5}}}{{\mathtt{2}}}} = {\mathtt{2.5}}$$

I am going to interprete this differently Chris.         [ Plus 2*8=16 LOL ]

we count in base 10  so we use 10 digits that is 0,1,2,3,4,5,6,7,8,9    the next on is 10 etc

if we were counting in base 4 the numbers would be 0,1,2,3,10,11,12,13,20,21,22,23,30,31,32,33,100, etc

$$\\16^8=(4^2)^8=4^{16}\\\\$$

If we write this base 10 number as a base 4 number then the answer is

10,000,000,000,000,000      that is a 1 followed by 16 zeros - base 4

3 x 3/2

Turn 3 into a fraction

3/1 x 3/2

Multiply across

9/2

Simplify

4 1/2

[2nd]  [asin]

(3/5)y =57

3y      =5 * 57

y        =(5* 57) /3

y        = 19 * 5

y        = 95//

So the measures of supplementary angles add up to 180 degrees. Knowing this, we can set up a system of equations:

First, let:

m∠T = t

m∠S = s

t = 3s

t + s = 180

Substitute 3s for t in the second equation:

3s + s = 180

4s = 180

s = 45

So m∠S = 45 degrees.

Now, plug 45 back into the first equation:

t = 3s

t = 3(45)

t = 135

So m∠T = 135 degrees. :)

Hi Dragon1 wait till you are a little older and you will find out that geometry can be very difficult   :)))