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
Alenkasestr [34]
2 years ago
11

The publisher of a recently released nonfiction book expects that over the first 20 months after its release, the monthly profit

can be approximated with the model P(t) 240t - 40t t2 +20 where P is in thousands of dollars and t is in months from the time of release. a. Derive a model that gives the marginal profit of the book. P'(t) Preview b. Specify the expected marginal profit 5 months after release. Round to 2 decimal places thousands of dollars per month c. Specify the expected marginal profit 11 months after release. Round to 2 decimal places. thousands of dollars per month d. After which month is the monthly profit start to decrease steadily?
Mathematics
1 answer:
wolverine [178]2 years ago
6 0

Answer:

(a)\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}

(b)P'(5)=-($4.54) Thousand

(c)P'(11)=-($2.10) Thousand

(d)The fifth Month

Step-by-step explanation:

Given the monthly profit model:

P(t)=\frac{240t-40t^2}{t^2+20}

(a)We want to derive a model that gives the Marginal Profit, P' of the book.

We differentiate

P(t)=\frac{240t-40t^2}{t^2+20} using quotient rule.

\frac{dP}{dt}=\frac{(t^2+20)(240-80t)-(240t-40t^2)(2t)}{(t^2+20)^2}

Simplifying

\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}

We have derived a model for the marginal profit.

(b) After 5 months, at t=5

Marginal Profit=P'(5)

\frac{dP}{dt}=\frac{4800-1600t-240t^2}{(t^2+20)^2}

P^{'}(5)=\frac{4800-1600(5)-240(5)^2}{(5^2+20)^2}

=-($4.54) Thousand of dollars

(c)Marginal Profit 11 Months after book release

P^{'}(11)=\frac{4800-1600(11)-240(11)^2}{(11^2+20)^2}

=-($2.10) Thousand of dollars

(d) Since the marginal profit at t=5 is negative, after the 5th Month, the profit starts to experience a steady decrease.

You might be interested in
What is the midpoint of a line segment with the endpoints (-4, -3) and (7, -5)
Katyanochek1 [597]
Midpoint Formula: (\frac{x+x}{2},\frac{y+y}{2})
Midpoint = (\frac {-4+7}{2},\frac {-3-5}{2})
Midpoint = (\frac {3}{2},\frac {-8}{2})
Midpoint = (\frac {3}{2}, -4)
So, the midpoint of the endpoints (-4,-3) and (7,-5) is (\frac {3}{2}, -4).
Have a nice day! ♪
4 0
3 years ago
Read 2 more answers
What is the value of X?<br> Help please!
anastassius [24]

Answer:

(11√3)/3

Step-by-step explanation:

In order to solve for the variable, you will need to use a trig function. In this case, you will need to use the trig function tangent.

Tan = opposite/adjacent

⇒ Tan 30° = x/11

⇒ 11 · Tan 30° = x

⇒ (11√3)/3 = x

4 0
3 years ago
What does SATT stand for in geometry
Kitty [74]
SUM OF ANGLES IN A TRIANGLE THEOREM (SATT)
6 0
3 years ago
Give an example of a unit rate used in a real-world situation
Kaylis [27]
-- 30 miles per hour

-- $6.50 per hour

-- 365 days per year

-- 60 seconds per minute

-- $2.49 per pound

-- 3.47⁹ per gallon

-- 1800 calories per day

-- 360 degrees per revolution
7 0
3 years ago
In a game, the probability that a spinner will land on blue is 1/4. How many times would you expect to land on blue if you spin
JulijaS [17]

Answer:

2 times

Step-by-step explanation:

8 0
2 years ago
Other questions:
  • Determine the constant of variation for the direct variation given . (0,0) (3,12) (9,36). Answer choices A. 3 B. 4 C. 12
    6·1 answer
  • How do you solve x-6&gt;7=
    9·1 answer
  • For a project, Gabrielle made a model of an Egyptian pyramid. The square base has a side length measuring 10 inches. The pyramid
    14·2 answers
  • I need help _______________________________________________________________________
    7·1 answer
  • Find the greatest common factor of the following monomials:<br><br> 20m<br><br> 8m5
    15·1 answer
  • Semester I review <br> -15+n=-9
    10·1 answer
  • Find x AND the length of each side if ABC is an isosceles triangle with AB = BC . (Answers Rouen to the nearest tenth if needed)
    8·1 answer
  • Helpppppppppppppopppppp
    12·1 answer
  • Whats a integer ,can someone answer this a short explanation ?
    12·2 answers
  • A figure is located at (2,0), (2,-2) and (6,0)
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!