De Moivre's theorem uses this general formula z = r(cos α + i<span> sin α) that is where we can have the form a + bi. If the given is raised to a certain number, then the r is raised to the same number while the angles are being multiplied by that number.
For 1) </span>[3cos(27))+isin(27)]^5 we first apply the concept I mentioned above where it becomes
[3^5cos(27*5))+isin(27*5)] and then after simplifying we get, [243 (cos (135) + isin (135))]
it is then further simplified to 243 (-1/ √2) + 243i (1/√2) = -243/√2 + 243/<span>√2 i
and that is the answer.
For 2) </span>[2(cos(40))+isin(40)]^6, we apply the same steps in 1)
[2^6(cos(40*6))+isin(40*6)],
[64(cos(240))+isin(240)] = 64 (-1/2) + 64i (-√3 /2)
And the answer is -32 -32 √3 i
Summary:
1) -243/√2 + 243/√2 i
2)-32 -32 √3 i
M = -8
-15 minus -7 equals -8
This would be point-slope form.
Slope-intercept form is in the form: y = mx + b
Standard is in the form ax + by = c
Point-slope form is in the form y - y.1 =m(x - x.1)
The form this most closely resembles is point-slope.
The inequality that correctly represents this scenario is given as follows:
The graph is given at the end of the question.
<h3>What is a system of inequalities?</h3>
A system of inequalities is when two or more variables are related, and inequalities are built to find the values of each variable.
In this problem, the variables are given as follows:
- Variable x: number of chocolate chips purchased.
- Variable y: number of pecans sold.
Chocolate chips are $2 per pound and pecans are $5 per pound. She wants to spend at most $25, hence:
More can be learned about a system of inequalities at brainly.com/question/3656398
#SPJ1
Answer:
15
Step-by-step explanation:
First we need to remove the parenthesis
4 + 37 + 8 - (34)
4 + 37 + 8 -34
Add 4 and 37
41 + 8 - 34
Add 41 and 8
49 - 34
Subtract
15
