What is the domain of the function y = square root x+6 -7?
1 answer:
Answer:
-6 ≤ x < ∞
Step-by-step explanation:
You want the domain of the function y = √(x+6) -7.
<h3>Domain</h3>The domain of a function is the set of x-values for which the function is defined. On a graph, it is the horizontal extent of the graph.
The square root function is undefined for negative arguments, so that limits the domain of the given function:
x+6 ≥ 0
x ≥ -6 . . . . . domain of the given function
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<em>Additional comment</em>
When the domain is written in interval notation, both the left and right ends of the interval must be specified.
[-6, ∞)
The square bracket identifies -6 as being part of the domain. The parenthesis is used with ∞, because that number has no specific value.
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Answer:
(-2,21)
Step-by-step explanation:
2 days ago, Paulo's commute time was halfway between his commute times 8 and 9 days ago.
8 days ago means that x-coordinate -8 represents this day. Count 8 units to the left and find that when x = -8, y = 24 minutes.
9 days ago means that x-coordinate -9 represents this day. Count 9 units to the left and find that when x = -9, y = 18 minutes.
Find halfway commute time between points (-8,24) and (-9,18):
then coordinates that Paulo should graph are
(-2, 21)
(-2 means 2 days ago, 21 is the halfway)
The equation of the hyperbola is :
The center of a hyperbola is located at the origin that means at (0, 0) and one of the focus is at (-50, 0)
As both center and the focus are lying on the x-axis, so the hyperbola is a horizontal hyperbola and the standard equation of horizontal hyperbola when center is at origin:
The distance from center to focus is 'c' and here focus is at (-50,0)
So, c= 50
Now if the distance from center to the directrix line is 'd', then
Here the directrix line is given as : x= 2304/50
Thus,
⇒
⇒ a² = 2304
⇒ a = √2304 = 48
For hyperbola, b² = c² - a²
⇒ b² = 50² - 48² (By plugging c=50 and a = 48)
⇒ b² = 2500 - 2304
⇒ b² = 196
⇒ b = √196 = 14
So, the equation of the hyperbola is :