Answer:
No, the maximum height that the balloon can reach is 9ft.
Step-by-step explanation:
Hi, to answer this question we have to analyze the information given:
The function h(x) =-0.5(x-4)² +9, is a Quadratic Function in the Vertex form.
Vertex form: f (x) = a(x - h) 2 + k
Where:
- (h, k) is the vertex of the parabola-
- h is the horizontal shift (how far left, or right, the graph has shifted from x = 0).
- k represents the vertical shift (how far up, or down, the graph has shifted from y = 0).
In this case a = -0.5, it means that the parabola opens downward and has a maximum point at the vertex.
So, the maximum height that the balloon can reach is k=9ft.
9 ∠ 12
The balloon will not hit the ceiling 12 ft above the pool.
Feel free to ask for more if needed or if you did not understand something.
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The limit does not exist. Why? Because the left hand limit DOES NOT equal the right hand limit. Let’s double check:
We could use -0.000001 to represent the left hand limit. This is less than 0. We plug in 5x - 8
5(-0.000001) - 8
-0.000005 - 8
-8.000005
If we would continue the limit (extend the zeros to infinity), we would get exactly
-8
That is our left hand limit.
Our right hand limit will be represented by 0.000001. This is greater than 0. We plug in abs(-4 - x)
abs(-4 - (0.000001))
abs(-4.000001)
4.000001
If we would continue the limit (extend the zeros to infinity), we would get exactly
4
4 does not equal -8, therefore
The limit does not exist
If you're just starting calculus, perhaps you're asking about using the definition of the derivative to differentiate 
.
We have
Expand the numerator using the binomial theorem, then simplify and compute the limit.
In general, the derivative of a power function 
is 
. (This is the aptly-named "power rule" for differentiation.)
7 because a(one side)= 1/sqrt2 * hypotenuse (7*sqrt2) THis equals 7
