Feitan

Now we need to go backwards from atoms to grams. First, let's convert it into moles.

8.5*10^9 atoms Ne / 6.022*10^23 mol^-1 = 1.4114912*10^-14 mol Ne

Next, we multiply it by neon's molar mass, 20.180.

1.4114912*10^-14 mol Ne * 20.180 g/mol = 2.84838924*10^-13 g Ne

Now, all that's left is the significant figures. There were two at the start, so there need to be two in the answer.

2.8*10^-13 g Ne

Since we have the amount of moles, we really only have to multiply it by Avogadro's Number.

1.04 mol S * 6.022x10^23 = 6.26288x10^23 atoms S

And then the significant figures turns it into...

6.26x10^23 atoms S

Since this is a compound, we need to find the molar masses of each element and add them all together.

Fe = 55.845 x 3 = 167.535

P = 30.974 x 2 = 61.948

O = 15.999 x 8 = 127.992

And all of adds together to 357.475, which will be the molar mass for iron (II) phosphate (or Fe3(PO4)2). So now we just divide the mass by the molar mass.

130.17 g / 357.475 g/mol = 0.3641373523 mol Fe3(PO4)2

And then the significant figures come into play again. We have five figures this time.

0.36414 mol Fe3(PO4)2

First, we should simplify by distributing.

3x - 15 = 2x + 6

Next, it's just a matter of moving like terms together.

3x - 2x = 6 + 15

x = 21

I already answered this in a previous question, so I'll just copy paste my response.

It's basically the same thing, we just need to use sodium's molar mass instead of silicon's.

43.7 g / 22.990 g/mol = 1.900826446 mol Na

This time I'll be rounding it again, to 1.901 mol Na. We only need to round at the end, due to significant figures, but it's much easier than typing it all out unless you have a calculator that allows you to input the previous answer such as TI-89.

1.901 mol Na * 6.022x10^23 mol^-1 = 1.1447822x10^24 atoms Na

Because we have three figures in the starting measurement, we also need three figures in the answer. Make sure to round the last digit.

1.14x10^24 atoms Na

It's basically the same thing, we just need to use sodium's molar mass instead of silicon's.

43.7 g / 22.990 g/mol = 1.900826446 mol Na

This time I'll be rounding it again, to 1.901 mol Na. We only need to round at the end, due to significant figures, but it's much easier than typing it all out unless you have a calculator that allows you to input the previous answer such as TI-89.

1.901 mol Na * 6.022x10^23 mol^-1 = 1.1447822x10^24 atoms Na

Because we have three figures in the starting measurement, we also need three figures in the answer. Make sure to round the last digit.

1.14x10^24 atoms Na

First, simplify.

9x + 1 = 64

Then we combine the like terms, basically subtracting 1 from each side.

9x = 63

Then divide each side by 9.

x = 7

So technically, we can write the square root of 4/5 as...

sqrt(4) / sqrt(5)

And then simplify it as thus...

2 / sqrt(5)

Now we need to move the square root to the numerator. We can do it like this.

( 2 / sqrt (5) ) * ( sqrt(5) / sqrt (5) )

= 2 * sqrt(5) / 5

If you were asked for the exact answer, then leave it as is. If asked for a rounded answer, then find the square root of 5 using a calculator, and go on from there.

So first, we need to figure out how many moles there are.

7.55 g / 28.085 g/mol = 0.2688267758589995 mol

Rounding that to 0.269 mol for simplicity (it's better not to round it though, so avoid it if you can), let's multiply it by Avogadro's Number.

0.269 mol x 6.022x10^23 mol^-1 = 1.619918x10^23 atoms

Now we need to take significant figures into account. 7.55 has three figures, so the answer must have three figures. Round the third figure as well.

1.62x10^23 atoms

I hope that was useful. c:

You should be using sine, not cosine, since the adjacent "side" is her distance from the kite and the opposite "side" is the height of the kite.