Consecutie odd integers are 2 apart
odd integers are represented by 2n+1 where n is a whole number
so the numbers are
2n+1 and 2n+1+2
(2n+3)²-(2n+1)²=24
4n²+12n+9-(4n²+4n+1)=24
4n²+12n+9-4n²-4n-1=24
8n+8=24
minus 8 both sides
8n=16
divide by 8
n=2
2n+1 is first one
2(2)+1=4+1=5
5+2=7
the numbers are 5 and 7
Answer:
The trigonometric form of the complex number is 12(cos 120° + i sin 120°)
Step-by-step explanation:
* Lets revise the complex number in Cartesian form and polar form
- The complex number in the Cartesian form is a + bi
-The complex number in the polar form is r(cosФ + i sinФ)
* Lets revise how we can find one from the other
- r² = a² + b²
- tanФ = b/a
* Now lets solve the problem
∵ z = -6 + i 6√3
∴ a = -6 and b = 6√3
∵ r² = a² + b²
∴ r² = (-6)² + (6√3)² = 36 + 108 = 144
∴ r = √144 = 12
∵ tan Ф° = b/a
∴ tan Ф = 6√3/-6 = -√3
∵ The x-coordinate of the point is negative
∵ The y-coordinate of the point is positive
∴ The point lies on the 2nd quadrant
* The measure of the angle in the 2nd quadrant is 180 - α, where
α is an acute angle
∵ tan α = √3
∴ α = tan^-1 √3 = 60°
∴ Ф = 180° - 60° = 120°
∴ z = 12(cos 120° + i sin 120°)
* The trigonometric form of the complex number is
12(cos 120° + i sin 120°)
The answer is A because if you graph 2x from the origin you will get the blue line perfectly whereas y=-4x plotted will come up with your red line and walla. :)
Answer:
D is the answer
Step-by-step explanation:
