Answer:
=ei x
Step-by-step explanation:
Consider the function on the right hand side (RHS)
f(x) = cos( x ) + i sin( x )
Differentiate this function
f ' (x) = -sin( x ) + i cos( x) = i f(x)
So, this function has the property that its derivative is i times the original function.
What other type of function has this property?
A function g(x) will have this property if
dg / dx = i g
This is a differential equation that can be solved with seperation of variables
(1/g) dg = i dx
integral (1/g) dg = integral i dx
ln| g | = i x + C
| g | = ei x + C = eC ei x
| g | = C2 ei x
g = C3 ei x
So we need to determine what value (if any) of the constant C3 makes g(x) = f(x).
If we set x=0 and evaluate f(x) and g(x), we get
f(x) = cos( 0 ) + i sin( 0 ) = 1
g(x) = C3 ei 0 = C3
These functions are equal when C3 = 1.
Therefore,
cos( x ) + i sin( x ) = ei x
Answer:
116°
Step-by-step explanation:
together both angles equal 180 because they are on a straight line and are opposite of each other.
180 - 64 = 116
I hope this helps!!
Answer: 9
Step-by-step explanation:
12 insulators = 183/4 hours
x = 281/8
x × 183/4 = 12 ×281/ 8
183x/4 = 6 × 281/4
183x / 4 = 1686 / 4
4 cancel out 4
183x = 1686
Divide bothside by 183
x = 1686/183
x= 9.21311
x = 9 approximately.
Combine place value strategy is useful if you try to subtract a number with bigger digits from a number with a smaller digit in the same place... such as now, where 3 is smaller than 9 in the ones place.
Then we can combine two place values: 23 and 19 and subtruct those. 23-19 is 4 (you can just count up from 19 to 23), so you know that the two will give the result of 04, and then you can proceed to the left: 2-1=1.
so the final result will 104.
Answer:
Step-by-step explanation:
5