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DochEvi [55]
3 years ago
14

A common equation used in business is a demand equation. It expresses the relationship between the unit price of some commodity

and the quantity demanded. In the​ equation, p represents the unit price and x represents the quantity demanded in thousands. A company sells desk lamps and has found that the demand equation for a certain style of desk lamp is given by the equation p equals negative x squared plus 23. Find the demand for the desk lamp if the price is ​$7 per lamp.
Mathematics
1 answer:
lianna [129]3 years ago
8 0

Answer:

The demand of the desk is 4000 units

Step-by-step explanation:

From the question we know that p is equals negative x squared plus 23, that can be written as:

p=-x^{2} +23

Where p is the unit price and x represent the quantity demanded in thousands. Replacing p by 7 and solving for x, we get:

7=-x^{2} +23\\x^{2} =23-7\\x^{2} =16\\x=\sqrt{16\\} \\x=4

Since x is given in thousands of units, if the price is $7, the demand of the desk is 4000 units.

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Tap for more steps...

x

y

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81

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Graph the parabola using its properties and the selected points.

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Vertex:  

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Focus:  

(

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Direction: Opens Down

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(

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(0,81)

Focus:  

(

0

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323

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)

(0,3234)

Axis of Symmetry:  

x

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Directrix:  

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4

y=3254

Select a few  

x

x

values, and plug them into the equation to find the corresponding  

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x

y

−

2

77

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80

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81

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xy-277-180081180277

Graph the parabola using its properties and the selected points.

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y=3254

x

y

−

2

77

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1

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xy-277-180081180277

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(

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=

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Direction: Opens Down

Vertex:  

(

0

,

81

)

(0,81)

Focus:  

(

0

,

323

4

)

(0,3234)

Axis of Symmetry:  

x

=

0

x=0

Directrix:  

y

=

325

4

y=3254

Select a few  

x

x

values, and plug them into the equation to find the corresponding  

y

y

values. The  

x

x

values should be selected around the vertex.

Tap for more steps...

x

y

−

2

77

−

1

80

0

81

1

80

2

77

xy-277-180081180277

Graph the parabola using its properties and the selected points.

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Focus:  

(

0

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323

4

)

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77

xy-277-180081180277

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x

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f(x)=81-x2??

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=

81

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