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Alex_Xolod [135]
4 years ago
9

Find the distance between each pair of points.

Mathematics
1 answer:
BigorU [14]4 years ago
8 0

Answer:

Distance between the points (-3,1) and (1, -2),

\sqrt{ {(1 + 3)}^{2} +  {( - 2 - 1)}^{2}  }

=  \sqrt{ {(4)}^{2} +  {( - 3)}^{2}  }

=  \sqrt{16 + 9}  =  \sqrt{25}  = 5

Option C

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Step-by-step explanation:

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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
In one area, the lowest angle of elevation of the sun in winter is 24degrees Find the distance x that a plant needing full sun c
sweet [91]

Answer:

round answer is : 10 ft

Step-by-step explanation:

The explanation is in the picture!

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Answer:

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Step-by-step explanation:

c^2=a^2+b^2

c^2-a^2=b^2

Substitute

18^2-4^2=b^2

324-16=b^2

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Norma-Jean [14]

Answer:

-1/2

Step-by-step explanation:

using the slope formula 3-(-2)/-4-6=-1/2

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3 years ago
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