Answer:
See below.
Step-by-step explanation:
Fifth root of 243 = 3,
Suppose r( cos Ф + i sinФ) is the fifth root of 243(cos 240 + i sin 240),
then r^5( cos Ф + i sin Ф )^5 = 243(cos 240 + i sin 240).
Equating equal parts and using de Moivre's theorem:
r^5 =243 and cos 5Ф + i sin 5Ф = cos 240 + i sin 240
r = 3 and 5Ф = 240 +360p so Ф = 48 + 72p
So Ф = 48, 120, 192, 264, 336 for 48 ≤ Ф < 360
So there are 5 distinct solutions given by:
3(cos 48 + i sin 48),
3(cos 120 + i sin 120),
3(cos 192 + i sin 192),
3(cos 264 + i sin 264),
3(cos 336 + i sin 336).. (Answer).
<h2><u>In total, she will need $98.34 to pay all of the foods she plans to serve at the party.</u></h2>
All of the work:
<em>How to solve the amount of pizza she needs:</em>
20 x 3 = 60
60 divided by 10 = 6
<em>How to solve the amount of soda bottled needed:</em>
20 x 16 = 320
320 divided by 64 = 5
<em>How to solve the number of pans she needs:</em>
20(2 x 3) = 40 x 60
40 x 60 divided by 8 x 12 = 5
<h2>
THE COST CAN BE FOUND BY MULTIPLYING THE NUMBER OF THE ITEM NEEDED AND THE PRICE FOR EACH OF THE ITEM.</h2>
<em>Number of pizza she needs:6 pizza, costs $77.94</em>
<em>Number of soda bottles she needs:5 bottles, costs $8.45</em>
<em>Number of pans she needs:5 pans, costs $11.95</em>
<em>Add 77.94, 8.45, and 11.95 and get 98.34</em>
Answer:
5.2 x 10^-2
Step-by-step explanation:
Scientific notation is used to simplify very large or very small numbers.
The formula for scientific notation is (a x 10^ n)
(a) is a number that is both greater than 1 and less than 10
(n) is the number of places the decimal place moves. This number can be positive or negative depending on the number you are converting. If the original number is greater than 1 (n) will be positive, and if the number is less than 1 (n) will be negative.
First you should write out the number.
0.052
Then, you should determine the number places the decimal point must move, and create a number greater than 1 and less than 10. (You should also pay attention to the direction the decimal point moves)
For this problem you will move the decimal place 2 places to the right to create the number 5.2.
Last, substitute the values into the formula. For this problem (a)= 5.2 and (n)= -2. This gives us the expression 5.2 x 10^-2.
Answer:
i
Step-by-step explanation:
you need a teachers help
