Answer:
hope it helps...
Step-by-step explanation:
The value of the constant of proportionality is k=5k=5
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=ky/x=k or y=kxy=kx
The value of the constant k is equal to the value of the slope
In this problem we have
y=5xy=5x ------> is a linear direct variation
The slope is m=5m=5
therefore
The value of the constant of proportionality is k=5k=5
Answer:
y=1x-5
Step-by-step explanation:
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.
