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Answer:
We kindly invite you to see the result in the image attached below.
The number in polar form is .
Step-by-step explanation:
A complex number is represented by elements of the form , for all
,
. The first part of the sum is the real component of the complex number, whereas the second part of the sum is the imaginary component of the complex number. The real component is located on the horizontal axis and the imaginary component on the vertical axis.
Now we proceed to present the point on the graph: (,
) We kindly invite you to see the result in the image attached below.
The polar form of the complex number is defined by:
(1)
Where:
- Magnitude of the complex number, dimensionless.
- Direction of the complex number, measured in radians.
The magnitude and the direction of the complex number are defined by the following formulas:
Magnitude
(2)
Direction
(3)
If we know that and
, then the polar form of the number is:
The number in polar form is .
The 210 feet diameter of the ferris wheel rotated 45° gives;
The amount by which the height of the seat changes is the option;
- startfraction 210 startroot 2 endroot over 2 endfraction ft.
Given parameters;
Diameter of the wheel, <em>D </em>= 210 feet
Angle of rotation of the wheel = 45°
Required;
The measure by which the height changes.
Solution;
The equation of a Ferris wheel can be represented as follows;
y = A•sin(B•(x - c)) + D
Change in height, ∆y, is found as follows;
∆y = A•sin(t1) + D - A•sin(t2) + D
∆y = A•(sin(t1) - sin(t2))
Where;
t1 = 0
t2 = 45°
A = The radius = 210 feet
Therefore;
∆y = 210×2×(sin((45+0)/2)° × cos((45-0)/2)°)
∆y = 210×2×(sin(22.5)° × cos(22.5)°)
∆y = 210×sin(2×22.5)° = 210×sin(45)°
- ∆y = 210×(√2)/2
The amount by which the height of the seat changes is therefore;
The correct option is therefore;
startfraction 210 startroot 2 endroot over 2 endfraction ft.
Learn more about the equation of a Ferris wheel here:
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