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]
3 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]3 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
Ken makes a salad for 20 people. The salad dressing contains olive oil and 1/8 cup lemon juice per person. If there are 3 and 3/
sineoko [7]
I have no clue what the answer is to this
3 0
3 years ago
A pet store donated a percent to very sale to hospitals. The total sales were $9,925 so the store donated $397. WHat percent of
const2013 [10]

Answer:

4%

Step-by-step explanation:

\frac{part}{entirety} *100

\frac{397}{9925} *100 =4

4 0
2 years ago
1. - 4 + (-8) =
lara [203]
1)4-8=-4
2)3+4-5=2
3) -13
4)8+12=20
5) -14
4 0
3 years ago
Read 2 more answers
mai and priya were on scooters. mai traveled 15 meters in 6 seconds priya traveled 22 meters in 10 seconds. who was moving faste
Eduardwww [97]

Answer:

Its Mai

Step-by-step explanation:

I promise I know why

7 0
3 years ago
Caleb is making a drawing of a window that is 9 inches high. However, his ruler that he’s using only measures in centimeters. If
puteri [66]

Answer:

22.5 cm

Step-by-step explanation:

9 inches=9×2.5 cm =22.5 cm

5 0
3 years ago
Other questions:
  • Q #15 Graph ARTS With vertices R(6, 6), S(3, -6),and T(0, 3) and its image. over the Y -axis
    9·1 answer
  • Which translation maps the vertex of the graph of the function f(x) = x2 onto the vertex of the function g(x) = x2 + 2x +1?
    10·2 answers
  • Let event Aequalssubject is telling the truth and event Bequalspolygraph test indicates that the subject is lying. Use your own
    15·1 answer
  • Is this an arthimatic sequence ? 10,20,40,80
    9·1 answer
  • Find each absolute value | 2+3i |
    14·2 answers
  • Eighth grade
    12·1 answer
  • On the coordinate plane below, quadrilaterals TRAP and HELP are similar to each other.
    7·2 answers
  • A local fair has an entrance fee of $10. Each ride costs $1.25.
    7·1 answer
  • A 16-ft steel beam is to be cut into two pieces so
    6·1 answer
  • How is solving for a variable similar to solving an equation? How is it different
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!