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
lozanna [386]
3 years ago
14

The number of salmon swimming upstream to spawn is approximated by the following function:

Mathematics
1 answer:
umka2103 [35]3 years ago
5 0

Answer:

The water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

Step-by-step explanation:

Let S(x) = -x^{3}+2\cdot x^{2}+405\cdot x +4965, for 6 \leq x \leq 20. x represents the temperature of the water, measured in degrees Celsius, and S is the number of salmon swimming upstream to spawn, dimensionless.

We compute the first and second derivatives of the function:

S'(x) = -3\cdot x^{2}+4\cdot x +405 (Eq. 1)

S''(x) = -6\cdot x +4 (Eq. 2)

Then we equalize (Eq. 1) to zero and solve for x:

-3\cdot x^{2}+4\cdot x +405 = 0

And all roots are found by Quadratic Formula:

x_{1} \approx 12.305\,^{\circ}C, x_{2}\approx -10.971\,^{\circ}C

Only the first root is inside the given interval of the function. Hence, the correct answer is:

x \approx 12.305\,^{\circ}C

Now we evaluate the second derivative at given result. That is:

S''(12.305) = -6\cdot (12.305)+4

S''(12.305) = -69.83

According to the Second Derivative Test, a negative value means that critical value leads to a maximum. In consequence, the water temperature that produces the maximum number of salmon swimming upstream is approximately 12.305 degrees Celsius.

You might be interested in
. Write the missing base. 9 16​
chubhunter [2.5K]

Answer:

c

Step-by-step explanation:

ur welcome

7 0
2 years ago
Aubrey went shopping at her favorite store target she bought three shirts and a pair of jeans that cost $28 she spent a total of
aliya0001 [1]

Answer:

Each shirt cost $20

Step-by-step explanation:

88- $28= 60

60/3= $20

8 0
2 years ago
the coordinates of one point of a line segment are (-2,-7). The line segment is 12 units long. Give three possible coordinates o
valentinak56 [21]

(-2,-19) , (-2, 5), ( 2,10)

4 0
3 years ago
Suppose a study estimated that 62% of the residents of a community (with an
kati45 [8]

Answer:

D. 55%

Step-by-step explanation:

The error range ± 9% means that the range is 9% below 62% or 9% above 62%.

The range is:

(62% - 9%) to (62% + 9%)

53% to 71%.

The only answer between 53% and 71% is 55%.

Answers A, B, C are all greater than 71%.

5 0
3 years ago
HELP ILL AWARD BRAINLIEST
inna [77]

Answer:

Think about it

Step-by-step explanation:

If you made $20 in 2 hrs you made $10 per hour

To find out how much you make per certain number of hrs multiply $10 by the number of hours

The equation is y = 10x + 0 <-- this is also answer to number 4

10x is the constant of proportionality I think.

5 0
3 years ago
Read 2 more answers
Other questions:
  • What is 2/3 divided by 5/6
    7·1 answer
  • Ariel has already spent 79 minutes on the phone and she expects to spend 4 more minutes with every phone call she routed. In all
    7·1 answer
  • Find the length of the missing side of the right triangle below.
    11·1 answer
  • What is the result of subtracting the second equation from the first?
    7·2 answers
  • Muffins 61 20 32 58 62 61 56
    6·1 answer
  • A quarter is one fourth of a dollarHugo has 24 quarters how much does he have show your work
    11·1 answer
  • What would be a method
    10·2 answers
  • 1/2 (3x + 5) = 7 <br> anyone can someone explain this problem to me so I can understand it better.
    6·1 answer
  • Square of 2x+3y.Please help me​
    11·2 answers
  • Is -4 greater than or less than -1?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!