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3 years ago

Darwin's best time for running 5000 metres is 16 minutes. He wants to run it in 15 minutes and 30 seconds.

Mathematics

2 answers:

Rudik [331]3 years ago

6 0

Answer:

3 percent

Step-by-step explanation:

convert to seconds

960 seconds to 930 seconds

30 seconds ÷ 960=3 per cent

marshall27 [118]3 years ago

4 0

Answer:

-3.125%

Step-by-step explanation:

Percentage change = new-original/original x 100

15.5-16= -0.5

-0.5/ 16 x100 = -3.125%

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

umka2103 [35]

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.

5 0

3 years ago

PLEASE I NEED HELP QUICKLY!!! Find the solution for the given system of equations in the form (x,y).

goblinko [34]

Answer: