Answer:
-i.
Step-by-step explanation:
Applying DeMoivre' s theorem:
(sin 30 + i cos 30)^18
= sin(18*30) + i cos(18*30)
= sin 540 + i cos 540
= sin (3*180) + i cos (3*180)
= 0 + -1 * i
= -i.
Answer:
C
Step-by-step explanation:
A triangle always consists of it being 180 degrees. The box on the triangle on angle A depicts that it is a right angle, 90 degrees. And since Angle B is given at 45, angle C must be 45 degrees as well, since 180-45-90 (triangle angles=given angles for A and B) equal up to 45. When the angles beside the right angle is both identical and the same, the sides that correspond with that triangle is also the same. AC is given at 9 feet, and since Angle C and B both have the same angles, AB must ALSO be a 9ft.
Now, since we know the two sides, it is very easy to find BC, or the hypotenuse of the triangle, using the Pythagorean Theorem:
, where a and b are sides, and c is the hypotenuse (or the long end) of a right triangle.
We can plug both 9s in for a and b since they're both the same, and it should equal to
9^2+9^2=c^2.
9^2 is 9*9, and that is 81. We have two of these so add them together to find 162. Since c^2 is equal to 162, we would need to square root both sides so we can find a number that equals c.

We can either plug this into a calculator, and we should get something around 12.72, and that would be the same as C if you plug that value into a calculator.
You can also simplify the radical if you know how to. 162 is 81 times 2 (example) and 81 is 9*9, so we can add that to the outside and 2 is still under the radical. But this would only make sense if you know how to do that.
Answer:
The original price is $650
Step-by-step explanation:
There's an actual algebra method for this, but this is my method because I find it way easier to remember.
Since the most you can discount out of an item is 100% (well, it's considered free then) let's subtract 100 - 34, which is 66.
Now, turn it into a decimal because it makes the numbers easier- 0.66.
Since when you're finding the discount of an original price, you multiply the original price by the discount- instead for finding the original price for a discounted item we divide $429 by 0.66 instead, since when you divide a number by another number that's under 1 the quotient is a larger number.
So, 429 ÷ 0.66 = 650.
Therefore, the original price of the $429 sale price for a 34% discount is $650.