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makkiz [27]
3 years ago
11

A water balloon is tossed into the air. The function h(x)=-0.5(x-4)squared +9 gives the height, in the feet, of the balloon from

the surface of a pool as a function of the balloons horizontal distance from where it was first tossed. Will the balloon hit the ceiling 12 ft above the pool? Explain
Mathematics
1 answer:
NNADVOKAT [17]3 years ago
8 0

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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3 years ago
If f(1) = 160 and f(n+ 1) = -2f(n), what is f(4)?
sertanlavr [38]
F(1) = 160 is given to us. We'll use it to find f(2)
f(n+1) = -2*f(n)
f(1+1) = -2*f(1) ... replace every n with 1
f(1+1) = -2*160 ... replace f(1) with 160
f(2) = -320

Now use f(2) to find f(3)
f(n+1) = -2*f(n)
f(2+1) = -2*f(2) ... replace every n with 2
f(3) = -2*(-320) ... replace f(2) with -320
f(3) = 640

Finally, use f(3) to find f(4)
f(n+1) = -2*f(n)
f(3+1) = -2*f(3) ... replace every n with 3
f(4) = -2*640 ... replace f(3) with 640
f(4) = -1280

Final Answer: -1280

7 0
3 years ago
Read 2 more answers
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