Answer:
work is shown and pictured
Write each set of numbers in set-builder and interval notation X>50
1 answer:
Answer:
---- Set Builder
(50, ∞) ---- Interval Notation
Step-by-step explanation:
Given
x > 50
Required
Write as a
- Set builder
- Interval notation
As Set Builder:
x > 50 means that x is an integer and x is greater than 50.
In set builder notation, integers are represented with z.
So, the above can be represented as:
This translates to:
x is a member of the set of integers such that x is greater than 50
As Interval Notation:
In interval notation, we make use of brackets to represent the intervals.
In this case > is represented by (a,b)
Where a and b are the intervals of the notation
Since x > 50, then a = 50 and b = ∞ because we only know the starting point and not the end point.
<em>Hence: x > 50 in interval notation is (50, ∞)</em>
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Answer:
a) Hence the equation of the sinusoidal function that describes the height of the shorts in terms of time is
b) Hence the height of the shorts at exactly t = 10 minutes, to
the nearest tenth of a meter is 5.5 meters
Step-by-step explanation:
a) The wind turbine blade traverses a circular path as it rotates with time (t), whose time variation is given by the following trajectory equation :
,
where
R = (16 m - 2 m)/2 (since diameter = maximum height - minimum height of the pink short)
= 14 m / 2
= 7 m (radius of the circle)
Also, center of the circle will be at (0, 2 + R) i.e (0,9)
So, is the trajectory path equation to the circle
Let be the parametric form of the above circle equation which represent the position of the pink shorts at the tip of the blade at time t
At t= 10s, y = 16 m so we have,
---------------(1)
Also, at t= 25s, y =2 m so we have,
--------------(2)
Solving we have,
Therefore is the instantaneous height of the pink short at time t ( in seconds)
b) At t= 10minutes = 10 * 60 s = 600s, we have,
= 5.5 meters (pink short will be at 5.5 meters above ground level at t= 10 minutes)