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r-ruslan [8.4K]
1 year ago
5

Need help with courseReplace 250 with 575 and -3 with -5.

Mathematics
1 answer:
Svetlanka [38]1 year ago
8 0

Given

The demand function

p(x)=\frac{250}{\sqrt{x}}-5

To determine:

a) The revenue function.

b) The marginal revenue.

c) The marginal revenue when x=200.

d) The equation of tangent, and its derivation.

Explanation:

It is given that,

p(x)=\frac{250}{\sqrt{x}}-5

a) The revenue function is given by,

\begin{gathered} R(x)=x\cdot p(x) \\ R(x)=x\times(\frac{250}{\sqrt{x}}-5) \\ R(x)=250\sqrt{x}-5x \end{gathered}

b) The marginal revenue function is,

\begin{gathered} R^{\prime}(x)=\frac{d}{dx}(R(x)) \\ =\frac{d}{dx}(250\sqrt{x}-5x) \\ =250\times(\frac{1}{2}\times x^{-\frac{1}{2}})-5 \\ =\frac{125}{\sqrt{x}}-5 \end{gathered}

c) The marginal revenue when x=200 is,

\begin{gathered} R^{\prime}(200)=\frac{125}{\sqrt{200}}-5 \\ =\frac{125}{10\sqrt{2}}-5 \\ =8.8388-5 \\ =3.8388 \\ =3.84 \end{gathered}

Hence, the marginal revenue is 3.84.

d) Let y=mx+c is the tangent.

Then,

y=3.84x+c

That implies, for y=12.68, and x=200,

\begin{gathered} 12.68=3.84\times200+c \\ 12.68=768+c \\ c=12.68-768 \\ c=-755.32 \end{gathered}

Hence, the equation of tangent is,

y=3.84x-755.32

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Complete question:

Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby this mention is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect so the probability of a girl is 0.5. Assume that the group consists of 36 couples.

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Step-by-step explanation:

Given:

p = 0.5

n = 36

a) The mean is the product of n and p

Mean u = np

u = 36 * 0.5 = 18

The standard deviation is the square root of the product of n and p&q.

S.d ó = \sqrt{npq}

= \sqrt{np(1-p)}

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b) To find the range rule of thumb:

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= 12

• High range

= u + 2ó

= 18 + (2*3)

= 24

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A result of 33 girls would prove the method as effective.

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Have a great day!

Stay safe and healthy!

Happy holiday seasons!

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