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bekas [8.4K]
2 years ago
5

In your own words explain how to evaluate a function using function notation. ​

Mathematics
1 answer:
Gala2k [10]2 years ago
8 0

Answer:

In order to evaluate a function, replace the input variable (the number or expression given) (place holder, x). Replace the x by the number or word.

Step-by-step explanation:

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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

3 0
2 years ago
PLSSS HURRY ILL GIVE YOU A BRAINLYEST
8090 [49]

Answer:

36 inches

Step-by-step explanation:

lets think of it as a ratio,

80:w

20:9

so we want 20 to get to 80

and 9 to get to w right?

so if we just move the smaller rectangle to the corner, then 20*4=80 right?

and if we do that, we do it to 9 as well, 9*4=36

w=36

6 0
2 years ago
3A(48+C)<br> What is the answer
Roman55 [17]

Answer:

144A+3AC

Step-by-step explanation:

I think you provided half of the problem. Because this does not make sense to any problem I can think of.

3 0
3 years ago
8/9 + 4/7 =<br> Can you get the Anwar for this sum
attashe74 [19]

here. I don't know if its right but i hope it is.

7 0
3 years ago
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Which of the following are one dimensional and have infinite length
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I got the one that truck was coming up and
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3 years ago
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