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.
We have 11 as our base value, meaning that we add 11 to something, so we have 11+<something>. To find that something, we want to know how long it takes to go 21.78 miles at 33 miles per hour. To get this, we want to turn miles per hour into minutes per mile and multiply that by 21.78 miles to get our answer. Therefore, we cross them out as shown in the equation to get
Answer:
x = 5
y = 1
Step-by-step explanation:
So move 2y from the second equation to the other side of the equals sign
2x +3y = 13
x = 3 + 2y
From here substitute X into the first equation
2(3 + 2y) + 3y = 13
Distribute
6 + 4y +3y = 13
Combine like terms and solve for y
7y = 7
y = 1
insert result into the original equation.
x-2(1) = 3
x - 2 = 3
x = 5
insert into other equation to check work
2(5) + 3(1) = 13
10 + 3 = 13 correct
The graph g(x) is the graph of f(x) translated (5,2,3) units (down,up,left,right) , and g(x) =(f(x-3),f(x)-5,f(x)+3,f(x-2),f(x)+
marusya05 [52]
Answer:
The graph g(x) is the graph of f(x) translated <u>2</u> units <u>right</u>, and g(x) = <u>f(x-2)</u>
Step-by-step explanation:
g(x) passes through points (0, -5) and (1, -2), then the slope of g(x) is the same as the slope of f(x), which is 3.
f(x) passes through (0, 1) and g(x) passes through (2, 1). Therefore, the graph g(x) is the graph of f(x) translated 2 units right.
f(x - c) translates f(x) c units to the right, therefore g(x) = f(x-2)
In order to check this result, we make:
f(x) = 3x + 1
f(x-2) = 3(x-2) + 1
f(x-2) = 3x - 6 + 1
f(x-2) = 3x - 5 = g(x)
Answer:
[ 
] where n is the number of hours.
Because the beginning will 10000/2 = 50000, then it keeps double the dividing the time.
