auxiarc

_{12√2 (cos (7pi/6) + i sin (7pi/6)} 

3√3 (cos (pi/4) + i sin (pi/4)                      ⁼

_12√2     

 3√3     ^{[ cos ((7pi/6) - (pi/4)) + i sin ((7pi/6) - (pi/4)) ]              =}

_4√6

3                ^{[ cos (11pi/12) + i sin (11pi/12) ]           =}

   _4√6

    3          cis     (11pi/12)

For #3, write out the equation C = m / V, where m is the moles of NaCl and V is the total volume of the solution.
 

To find the number of moles, we'd need to refer back to question 2, which states that 1 gram of H2O is equal to 0.055508435061792 mole.

Because the question states there is 2 grams of sodium chloride, we'd multipy 2 and 0.055508435061792 to get the number of moles used.

2 x 0.055508435061792 = 0.11101687012

To get the volume of the water, you would divide the 500 mL by 1,000, to convert it to liters.

500 / 1,000 = 0.5

Your liters is 0.5.

Now, you can use c = 0.1 / 0.5 

Plug in the values you found, and divide them to find the concentration of your solution.

0.1 / 0.5 = 0.25

Your concentration can either be written as 0.25 M OR 0.25 mol/L.

I tried explaining a bit more so you can understand! Hopefully that helps:) You're very welcome!

1)

  a) This is gonna be carbon. The compound for carbon is covalent, because carbon forms covalent bonds.

  b) The compound for sulfer dioxide is covalent, because it also forms covalent bonds.

  c) The compound for iron oxide is covalent. The bond character is polar covalent although the difference is very close to that of ionic bonds. So iron oxide is a polar covalent compound with ionic character.

  d) Dinitrogen trioxide type of compound is also covalent, because it has two nonmetals.

2) 1 grams H2O is equal to 0.055508435061792 mole.

The interval [0,50] would mean that we use numbers (t) between 0 and 50 to replace with x and y. This would be rather difficult to solve since it would involve a lot of work. 

So, to make this easier, I used the numbers given in the multiple choices, 3.2, 4.8, and 2.4. Because t is measured in tenths of seconds, you'd multiply the numbers by ten, making the numbers 32, 48, and 24. (This will make more sense at the end.)

Using these numbers, make a chart representing Ari's and Matthew's path.

Ari's Path

Matthew's Path

Next, you would identify if Ari and Matthew collide by looking at the end results of the x and y. If NONE of the results match, then do NOT collide. If they do collide, you can determine the answer by simply dividing (t) by ten to get your final answer. (t) is the number in red.

The end results show that Ari and Mattew do collide at (44, 30). (t) is 48. 

Because t is measured in tenths of seconds, you would divide 48 by 10.

48 / 10 = 4.8

Your answer for when they would collide would then be 4.8. 

Ari and Matthew collide at 4.8 seconds.

I'm not sure if I'm understanding your question correctly. From my understanding, it's asking what same numbers add to 6. I don't know if that's right, but I came up with 3. I don't think there's a 4th one unless it's a decimal.

2+2+2

3+3

1+1+1+1+1+1

If you plot the points (7, 4) and (6, 3), you can gather information about the slope of the line. From point (7, 4) you would go down two, and go to the left two to get (6, 3).

For the next point, you would do the same. From point (6, 3) you would go down two, and go the left two. You would then get (5, 2).

Because it asks for the x-intercept, you would use the slope to plot points on the line until you reach the x-axis.

The points on the line would then include:

(7, 4) 

(6, 3)

(5, 2)

(4, 1)

(3, 0)

(3, 0) is the point at which the x-intercept lies. Therefore, your answer is (3, 0).

Thank you so much! I see what I did wrong. I got the 37.5 part, but after that, I was beyond confused! I understand a lot better:)

So, would that mean the ship was 31 miles to the south and 21 miles to the west of where the ship left port? 
I graphed the point, and that's what my conclusion was, I just want to be sure! 
Thank you again xx 

Nevermind, I got it!!

Thank you so much! I also tried seeing if there were other answers, and there weren't. You had all of the solutions correct. I appreciate it, and I know how to solve these type of problems now. Thank you. :)