First list all the terms out.
e^ix = 1 + ix/1! + (ix)^2/2! + (ix)^3/3! ...
Then, we can expand them.
e^ix = 1 + ix/1! + i^2x^2/2! + i^3x^3/3!...
Then, we can use the rules of raising i to a power.
e^ix = 1 + ix - x^2/2! - ix^3/3!...
Then, we can sort all the real and imaginary terms.
e^ix = (1 - x^2/2!...) + i(x - x^3/3!...)
We can simplify this.
e^ix = cos x + i sin x
This is Euler's Formula.
What happens if we put in pi?
x = pi
e^i*pi = cos(pi) + i sin(pi)
cos(pi) = -1
i sin(pi) = 0
e^i*pi = -1 OR e^i*pi + 1 = 0
That is Euler's identity.
Answer: B: n^2+6n+1
Step-by-step explanation:
A=n
B=2n+6
C=n^2-1
AB-C
n(2n+6)-n^2-1
2n^2+6n-n^2+1
n^2+6n+1
Average rate of change: r=[f(b)-f(a)]/(b-a)
r=-60→[f(b)-f(a)]/(b-a)=-60
b=5; f(b)=-213; a=1; f(a)=27
(-213-27)/(5-1)=(-240)/4=-60
Answer: The <span>two points in the table which create an interval with an average rate of change of -60 are:
x f(x)
1 27
5 -213</span>
Answer:
a=35 given
b=40
c=110
I couldn't complete see c. Please look at the picture to see what I assumed it to be.
Step-by-step explanation:
Hmmm... I guess a and b are not vertical.
We are given b=180-4a and a=35 so b=180-4(35)=180-140=40.
So b=40.
Isosceles triangles always have congruent base angles. So let's call both of the base angles in the bottom triangle x.
That means x+x+40=180.
We need to solve this for x.
Combine like terms:
2x+40=180
Subtract 40 on both sides:
2x=140
Divide both sides by 2:
x=140/2
Simplify:
x=70
So I'm assuming that c and it's adjacent angle are sitting on a straightedge together which means 70+c=180.
70+c=180
Subtract 70 on both sides:
c=180-70
Simplify:
c=110
Answer:
6
Step-by-step explanation:
