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
finlep [7]
2 years ago
15

For the cost function c equals 0.1 q squared plus 2.1 q plus 8​, how fast does c change with respect to q when q equals 11​? Det

ermine the percentage rate of change of c with respect to q when q equals 11.
Mathematics
1 answer:
Soloha48 [4]2 years ago
7 0

Answer:

Rate of change of c with respect to q is 4.3

Percentage rate of change c with respect to q is  9.95%

Step-by-step explanation:

Cost function is given as,  c=0.1\:q^{2}+2.1\:q+8

Given that c changes with respect to q that is, \dfrac{dc}{dq}. So differentiating given function,  

\dfrac{dc}{dq}=\dfrac{d}{dq}\left (0.1\:q^{2}+2.1\:q+8 \right)

Applying sum rule of derivative,

\dfrac{dc}{dq}=\dfrac{d}{dq}\left(0.1\:q^{2}\right)+\dfrac{d}{dq}\left(2.1\:q\right)+\dfrac{d}{dq}\left(8\right)

Applying power rule and constant rule of derivative,

\dfrac{dc}{dt}=0.1\left(2\:q^{2-1}\right)+2.1\left(1\right)+0

\dfrac{dc}{dt}=0.1\left(2\:q\right)+2.1

\dfrac{dc}{dt}=0.2\left(q\right)+2.1

Substituting the value of q=11,

\dfrac{dc}{dt}=0.2\left(11\right)+21.

\dfrac{dc}{dt}=2.2+2.1

\dfrac{dc}{dt}=4.3

Rate of change of c with respect to q is 4.3

Formula for percentage rate of change is given as,  

Percentage\:rate\:of\:change=\dfrac{Q'\left(x\right)}{Q\left(x\right)}\times 100

Rewriting in terms of cost C,

Percentage\:rate\:of\:change=\dfrac{C'\left(q\right)}{C\left(q\right)}\times 100

Calculating value of C\left(q \right)

C\left(q\right)=0.1\:q^{2}+2.1\:q+8

Substituting the value of q=11,

C\left(q\right)=0.1\left(11\right)^{2}+2.1\left(11\right)+8

C\left(q\right)=0.1\left(121\right)+23.1+8

C\left(q\right)=12.1+23.1+8

C\left(q\right)=43.2

Now using the formula for percentage,  

Percentage\:rate\:of\:change=\dfrac{4.3}{43.2}\times 100

Percentage\:rate\:of\:change=0.0995\times 100

Percentage\:rate\:of\:change=9.95%

Percentage rate of change of c with respect to q is 9.95%

You might be interested in
How can a sequence of transformations be used to justify whether two figures are congruent or similar?
Lena [83]

Answer:

A sequence of transformation can move two congruent figures to the same place (vertical / horizontal shifts). This causes them to perfectly overlap, proving their congruency.

A sequence of transformations can be used to show that something is similar, because if one were to transform a figure with only shrinks / stretches, one can shrink / stretch them to make them congruent. If only shrinks or stretches were done, and if the result of the transformation is congruent to the other figure, then the figures are similar (sides are proportional and shrinking/stretching them proves proportionality to other figure).

3 0
3 years ago
During the summer, Shane earns $450 every two weeks from being a lifeguard. He saves $125 from each paycheck. According to the t
DanielleElmas [232]

Answer:

5 to 18 ; 1 to 225

Step-by-step explanation:

BEACAUSE IT WAS FROM USA TEST PREP AND GOT IT RIGHT

4 0
3 years ago
Read 2 more answers
Probability PLZ HELP
Y_Kistochka [10]

Answer:

I cant see the picture srry

Step-by-step explanation:

8 0
2 years ago
Eurostar is a high-speed railway service connecting
erma4kov [3.2K]

Answer:

Step-by-step explanation:

This is simply a units conversion problem.  It gives us for the number of passengers, the number of seats per carriage and the number of carriages per train.  To change the units from passengers to trains without changing the value, we use the multiplicative identity (that is, 1).

350000 passengers

(350000 passengers) * 1

(350000 passengers) * ((1 carriage)/(32 passengers)) * ((1 train)/(15 carriages)

   [note:  passengers and carriages cancel. Leaving only trains]

(350000)*(1/32)*(1/15) trains       [note: I write this way to paste into MS Excel]

729.1667  trains                 [oh, but don’t just round this number either up or down]

   729 full trains can carry 729*32*15 = 349920 passengers

   730 full trains can carry 730*32*15 = 350400 passengers

Now, we can say that 730 trains are adequate to carry 350000 passengers.

6 0
2 years ago
What types of activities would you incorporate into your marathon training and why
Luda [366]
Running so you can build up both endurance and stamina. It’ll keep you in shape so you can last longer in a marathon. Constant conditioning will do the trick.
3 0
3 years ago
Read 2 more answers
Other questions:
  • Please answer now correct answer fast
    9·1 answer
  • The sum of a number v and 18 what is the algebraic expression?
    15·1 answer
  • Help me please please
    6·1 answer
  • (1) A manufacturer of tires believes that their mean time to failure (MTTF) is 20 613 km. They also believe that time to failure
    8·1 answer
  • How do you find the surface area of a pyramid
    11·1 answer
  • Profit or loss. Jim bought 30 roses for $3 each. He sold the roses for $4 each. did Jim have a profit or a loss? How much is his
    14·1 answer
  • A rectangle is graphed on the coordinate grid.
    15·1 answer
  • Express each percent as a fraction: <br><br><br> 86 2/3%
    9·1 answer
  • What are the solutions to the equation: (x - 6)(x + 5) = 0?
    15·2 answers
  • Hpw does the graph of the function g (x) =5x +1 differ from the graph of f(x) = 5x
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!