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borishaifa [10]
1 year ago
6

Suppose you are given a parabola with two points that have the same y-value, such as (-7, 11) and (3, 11). Explain how to find t

he equation of the axis of symmetry for this parabola, and then determine that equation.
Mathematics
1 answer:
Hoochie [10]1 year ago
3 0

By using the midpoint formula and the equation of the line, the equation of the line of symmetry is x = - 2.

<h3>How to derive the equation of the axis of symmetry </h3>

In this question we know the locations of two points with the same y-value, which means that the axis of symmetry is parallel to the y-axis and that both points are equidistant. Thus, the axis of symmetry passes through the midpoint of the line segment whose ends are those points.

First, calculate the coordinates of the midpoint by the midpoint formula:

M(x, y) = 0.5 · (- 7, 11) + 0.5 · (3, 11)

M(x, y) = (- 2, 11)

Second, look for the first coordinate of the midpoint and derive the equation of the line associated with the axis of symmetry:

x = - 2

By using the midpoint formula and the equation of the line, the equation of the line of symmetry is x = - 2.

To learn more on axes of symmetry: brainly.com/question/11957987

#SPJ1

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An aircraft manufacturer wants to determine the best selling price for a new airplane. The company estimates that the initial co
Blizzard [7]

Answer:

(a) C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2

    p(x)=320-7.7p

    R(x)=(320-7.7p)p=320p-7.7p^2

(b) x=82 \text{planes}

(c) p=\$30.91 M\;\; \text{per plane}

(d) maximum profit =\$ 15.90M

Step-by-step explanation:

Given that,

The company estimates that the initial cost of designing the aeroplane and setting up the factories in which to build it will be 500 million dollars.

The additional cost of manufacturing each plane can be modelled by the function.

m(x)=20x-5x^{\frac{3}{4}}+0.01x^2

(a)  Find the cost, demand (or price), and revenue functions.

   C(x)=500+20x-5x^{\frac{3}{4}}+0.01x^2

   p(x)=320-7.7p

   R(x)=(320-7.7p)p=320p-7.7p^2

(b)  Find the production level that maximizes profit.

    f=R(x)-C(x)

 \Rightarrow f=320p-7.7p^2-(500+20x-5x^{\frac{3}{4}}+0.01x^2)

\Rightarrow df=320dp-15.4pdp-20dx+5(\frac{3}{4} )x^{\frac{-1}{4} }dx-0.02xdx

     x=320-7.7p

     p=\frac{320-x}{7.7}

    \frac{dp}{dx} = \frac{-1}{7.7}

\frac{df}{dx}=\frac{320}{-7.7} -\frac{15.4(320-x) }{7.7(\frac{-1}{7.7} )}-20+5\frac{3}{4} x^{\frac{-1}{4}} -0.02x=0

    \Rightarrow -41.5584+83.1169-0.2597x-20+3.75x^{\frac{-1}{4} }-0.02x=0

   \Rightarrow 21.5585+3.75x^{\frac{-1}{4} }-0.279x=0

   \Rightarrow x=82 \text{planes}

(c)  Find the associated selling price of the aircraft that maximizes profit.

  p=\frac{320-82}{7.7}

\Rightarrow p=\$30.91 M\;\; \text{per plane}

(d)  Find the maximum profit.

Manufacturing cost of one plane is:

m(1)=20-5+0.01

         =\$15.01 M

maximum profit =\$(30.91-15.01)M

                           =\$15.90M

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Answer:

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Step-by-step explanation:

The best way to isolate x is to add 5 to both sides first:

21 = 7x

Then to isolate x by itself divide both sides by 7

x = 3

That would be the value of x and your final answer.

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