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:
The correct answer is <em>b = 36</em>
Step-by-step explanation:
In order to find out what b is, you must find out what 9/10 is.
9/10 is 0.9. This will later be used to check our answer.
Now, solve by using cross-multiplication
b * 10 = 9 * 40.
Then use the commutative property to reorder the terms
10b = 9 * 40
Now Multiply 9 * 40 = 360
10b = 360
Now divide both sides of the equation by 10
<em>b = 36</em>
with a point given and the slope , you can find the the line, of this form, THE EQUATION POINT SLOPE IS
Y-Y1= M(X-X1) , Y-(-1) = -1/2( X- 10), Y+1 = -1/2X+ 5, Y = -1/2 X +5 -1, Y = -1/2X+ 4
Answer:
f(x) = -(x-4)^2 + 5
Step-by-step explanation:
The function 
is a quadratic function. Its graph looks like a parabola. The graph has a vertex of (4,5) and opens up downward.
Proving that 
for all x:
The prime factors of 63 in ascending order is 3,3,7
