9.write an any quality for the following situation mail truck makes at least 50 stops a day

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

soldier1979 [14.2K]

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

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.

8 0

3 years ago

What is the measure of major B 84° O 276° O252° O 84° O 168 arc AB? A

alekssr [168]

Answer:

A - 84°

Step-by-step explanation:

The measure of an arc is equal to the measure of the central angle that intersects it.

The central angle of this circle measures 84° and it intercepts arc AB, meaning arc AB measures 84°

4 0

2 years ago

Which table has a constant al proportionality between y and 1.57 Choose 1 answer

Blizzard [7]

Answer:

b

Step-by-step explanation:

I did this problem before

8 0

3 years ago

Suppose a city with population 800,000 has been growing at a rate of 5% per year. If this rate continues, find the population of

AleksandrR [38]

Answer:

2,340,208.5 or 2,340,209

Step-by-step explanation:

You could answer this by multiplying the current population of 800,000 by 1.05 (1.05 represents the annual growth rate of population) and do that 22 times. But that would take a while.

we got 1.05 because the formula says that y = a( 1 + r ) power t

for a we will give it 1

so y = 1 ( 1 + 0.05) power t

it will give us 1.05

to do this faster, you would first calculate (1.05)22and then multiply this by 800,000.

So, 800,000 x (1.05)22 = 2,340,208.5 or 2,340,209

5 0

2 years ago

15 points, solve the variables! Will give Brainliest!

Anon25 [30]