1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
natulia [17]
3 years ago
10

Demand for Tablet Computers The quantity demanded per month, x, of a certain make of tablet computer is related to the average u

nit price, p (in dollars), of tablet computers by the equation x = f(p) = 100 9 810,000 − p2 It is estimated that t months from now, the average price of a tablet computer will be given by p(t) = 400 1 + 1 8 t + 200 (0 ≤ t ≤ 60) dollars. Find the rate at which the quantity demanded per month of the tablet computers will be changing 25 months from now. (Round your answer to one decimal place.) tablet computers/month
Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
8 0

x = f ( p ) = \frac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } } \\\\ \qquad { p ( t ) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \quad ( 0 \leq t \leq 60 ) }

Answer:

12.0 tablet computers/month

Step-by-step explanation:

The average price of the tablet 25 months from now will be:

p ( 25) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { 25 } } + 200 \\= \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \times 5 } + 200\\\\=\dfrac { 400 } { 1 + \dfrac { 5 } { 8 } } + 200\\p(25)=\dfrac { 5800 } {13}

Next, we determine the rate at which the quantity demanded changes with respect to time.

Using Chain Rule (and a calculator)

\dfrac{dx}{dt}= \dfrac{dx}{dp}\dfrac{dp}{dt}

\dfrac{dx}{dp}= \dfrac{d}{dp}\left[{ \dfrac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } }\right] =-\dfrac{100}{9}p(810,000-p^2)^{-1/2}

\dfrac{dp}{dt}=\dfrac{d}{dt}\left[\dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \right]=-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}

Therefore:

\dfrac{dx}{dt}= \left[-\dfrac{100}{9}p(810,000-p^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}\right]

Recall that at t=25, p(25)=\dfrac { 5800 } {13} \approx 446.15

Therefore:

\dfrac{dx}{dt}(25)= \left[-\dfrac{100}{9}\times 446.15(810,000-446.15^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt {25} \right]^{-2}25^{-1/2}\right]\\=12.009

The quantity demanded per month of the tablet computers will be changing at a rate of 12 tablet computers/month correct to 1 decimal place.

You might be interested in
Choose the correct solution and graph for the inequality.
kupik [55]

Answer:

The first one..

Step-by-step explanation:

4 0
3 years ago
Find each missing length to the nearest tenth.​
Llana [10]

Answer:

8.944

Step-by-step explanation:

To find the missing Length, Use Pythagorean Theorem!

a^2+b^2=c^2

4^2+8^2=c^2

16+64=c^2

80=c^2

\sqrt{80} =8.944

so it is approximately 10 but not quiet

hope this helps

6 0
3 years ago
Find the slope of the line passing through the points (-6,9) and (-6, -7).
jeyben [28]

Answer:

Slope is Zero 0

Step-by-step explanation:

this is because the line is horizontal and therefore has no slope

6 0
3 years ago
PLEASE HELP ASAP A glass stand to display a doll is in the shape of a right triangular pyramid. The area of the base is 40.5 squ
Effectus [21]

Answer: 202.5\ in.^3

Step-by-step explanation:

Given

The area of the base is A=40.5\ in.^2

height of the triangular prism is h=15\ in.

The volume of a triangular prism is  V=\dfrac{1}{3}Ah

The volume of given Prism is

V=\dfrac{1}{3}\times 40.5\times 15=202.5\ in.^3

The volume of the triangular prism is 202.5\ in.^3

8 0
3 years ago
The amounts of 8 charitable contributions are $100, $80, $250, $100, $500, $1000, $100, and $150.
cluponka [151]
Due to the fact that mode means most present number your answer would be mode or 100 dollars
5 0
3 years ago
Other questions:
  • Mr.Hollins determines that he gives away $800 each month. If he gives away 16% of his budget, how much is his overall budget?
    6·1 answer
  • at the end of the day vegetables at the farm market sell for $2 a pound and a basket cost $3.50 if Charlie wants to buy a basket
    14·1 answer
  • Answer quickly pls!!!! The two-way table below shows the number of students in a school who like hockey and/or football: (pic sh
    9·2 answers
  • What is one thousand less than 921,438​
    7·2 answers
  • Market so seven oranges for $2.45 how much would 8 oranges cost
    14·1 answer
  • How many times do 8 go into 5
    12·2 answers
  • You are renting a moving truck for a day. There is a daily fee of $30 and a charge of $0.65 per mile. Your budget allows a maxim
    5·2 answers
  • Find the area of the figure. please need help
    13·1 answer
  • Jerry runs up to a tank that holds up to 15 gallons of melted cheese When it is active it drains cheese onto crackers at a const
    8·1 answer
  • Rewrite the following in radical form <br> X^-11/3
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!