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: B
Because...
3x + 2x < -2x + 2x + 7
5x < 7
So you have to do addition BEFORE division.
Answer:
30°
Step-by-step explanation:
the total angels of the triangle is 180
180-75-75=30
and since the Angle of 30 and x^0 are Head opposite angles , then x^0 = 30°
Answer:
![A=128\ cm^2](https://tex.z-dn.net/?f=A%3D128%5C%20cm%5E2)
Step-by-step explanation:
we know that
The area of the polygon is equal to the area of a square plus the area of four congruent triangles
so
![A=b^2+4[\frac{1}{2}(b)(h)]](https://tex.z-dn.net/?f=A%3Db%5E2%2B4%5B%5Cfrac%7B1%7D%7B2%7D%28b%29%28h%29%5D)
where
![b=8\ cm\\h=4\ cm](https://tex.z-dn.net/?f=b%3D8%5C%20cm%5C%5Ch%3D4%5C%20cm)
substitute
![A=8^2+4[\frac{1}{2}(8)(4)]](https://tex.z-dn.net/?f=A%3D8%5E2%2B4%5B%5Cfrac%7B1%7D%7B2%7D%288%29%284%29%5D)
![A=64+64=128\ cm^2](https://tex.z-dn.net/?f=A%3D64%2B64%3D128%5C%20cm%5E2)
Answer:
No. of x-intercepts is equal to the no. of distinct species factors of a polynomial
Since this curve has only one distinct factor i.e (x+7)
The only x-intercepts is -7
(-7,0)
Y intercept would be at (0+7)⁷
Which is (0,7⁷)
Or (0,823543)
Since it's an odd power, branch of the curve for x > 7 would approach positive infinity
Branch for x < 7 would approach negative infinity