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3 years ago

Logarithm help needed

Mathematics

1 answer:

sashaice [31]3 years ago

4 0

Answer:

See below.

Step-by-step explanation:

Helen made a mistake in the last step.

2^(4/3) / e = (∛(2^4) / e = ∛(16) / e .

It is the cube root of 2^4 not the 4th root of 2^3.

Stephen made a mistake in the first step.

He replaced ln2 by 2 which is evidently wrong (e^ln2 = 2 NOT ln 2).

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X-6/2=2x/7 solve the equation

Triss [41]

Answer:

x-6/2=2x/7

7x-42=4x

7x-4x=42

3x= 42

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3 years ago

PLEASE HELP TIMED. Verify which of the following are identities.

Scrat [10]

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2 years ago

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.

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3 years ago

1/(cot^2 (x)) - 1/(cos^2 (x))

Airida [17]

Step-by-step explanation:

1 is your answer its law of trig identises