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Burka [1]
3 years ago
6

The stream of water from a fountain follows a parabolic path. The stream reaches a maximum height of 7 feet, represented by a ve

rtex of (4,7)
, and lands 8 feet from the water jet, represented by (8,0)
. Write a function in vertex form that models the path of the stream.

Mathematics
1 answer:
xenn [34]3 years ago
3 0

First of all, I'm going to assume that we have a concave down parabola, because the stream of water is subjected to gravity.

If we need the vertex to be at x=4, the equation will contain a (x-4)^2 term.

If we start with y=-(x-4)^2 we have a parabola, concave down, with vertex at x=4 and a maximum of 0.

So, if we add 7, we will translate the function vertically up 7 units, so that the new maximum will be (4, 7)

We have

y = -(x-4)+7

Now we only have to fix the fact that this parabola doesn't land at (8,0), because our parabola is too "narrow". We can work on that by multiplying the squared parenthesis by a certain coefficient: we want

y = a(x-4)^2+7

such that:

  • a
  • when we plug x=8, we have y=0

Plugging these values gets us

0 = a(8-4)^2+7 \iff 16a+7=0 \iff a = -\dfrac{7}{16}

As you can see in the attached figure, the parabola we get satisfies all the requests.

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Step-by-step explanation:

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3 years ago
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Solve 15 ≥ -3x or 2/3 x ≥ -2.
hjlf
Solve each of the equations independently, then determine if the are continuous or discontinuous. 
15≥-3x [start here]
-5≤x    [divide both sides by (-3). *Dividing by a negative number means the direction of the sign changes!]
x≥-5  [just turned around for analysis]

Next equation:
2/3x≥-2    [start here]
x≥-2(3/2)  [multiply both sides of the equation by the reciprocal, 3/2)
x≥-3

So, (according to the first equation) all values of x must be greater than, or equal to -5.

(According to the second equation) all values of x must be greater than, or equal to -3. 
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in a small town 68% of the people own television 78% own radio and 12% neither own television nor radio question 1 represent the
Oksana_A [137]

Answer:

The answer is attached as an image.

Step-by-step explanation:

- If we assume that the space is 100% of the population then:

88% have something and 12% have nothing.

So within the 88% there are 10% who have TV, 20% who have Radio and 58% who have both TV and Radio.

8 0
3 years ago
The volume of the pyramid shown in the figure is cubic centimeters. If the slant height of the pyramid increases by 4 centimeter
Nostrana [21]

Answer:

Part a) The volume of the original pyramid is 15\ cm^{3}

Part b) The volume of the pyramid increases by  6\ cm^{3}

Step-by-step explanation:

<u><em>The complete question is</em></u>

Part 1) The volume of the pyramid shown in the figure is 9,15,21, or 63 cubic centimeters?. Part 2) If the slant height of the pyramid increases by 4 centimeters and its height increases by 2 centimeters, the volume of the pyramid increases by 6,9,12 or 21 cubic centimeters?

we know that

The volume of the pyramid is equal to

V=\frac{1}{3}Bh

where

B is the area of the base

h is the height of pyramid

see the attached figure to better understand the problem

Step 1

Find the volume of the original pyramid

the area of the base B is equal to

B=3^{2}=9\ cm^{2}\\h=5\ cm

substitute

V=\frac{1}{3}(9)(5)=15\ cm^{3}

Step 2

Find the volume of the new pyramid

B=9\ cm^{2} -------> the area of the base is the same

h=5+2=7\ cm ------> the height increase by

substitute

V=\frac{1}{3}(9)(7)=21\ cm^{3}

Subtract the original volume from the new volume

21\ cm^{3}-15\ cm^{3}=6\ cm^{3}

5 0
3 years ago
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