So, f[x] = 1/4x^2 - 1/2Ln(x)
<span>thus f'[x] = 1/4*2x - 1/2*(1/x) = x/2 - 1/2x </span>
<span>thus f'[x]^2 = (x^2)/4 - 2*(x/2)*(1/2x) + 1/(4x^2) = (x^2)/4 - 1/2 + 1/(4x^2) </span>
<span>thus f'[x]^2 + 1 = (x^2)/4 + 1/2 + 1/(4x^2) = (x/2 + 1/2x)^2 </span>
<span>thus Sqrt[...] = (x/2 + 1/2x) </span>
Answer:
42 - 6 - 6 - 6 - 6 - 6 - 6 - 6 = 0
or
42 - 7 - 7 - 7 - 7 - 7 - 7 = 0
Using proportions, it is found that Mason ran 620 meters.
<h3>What is a proportion?</h3>
A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the ratio, the <em>rule of three</em> is given as follows:
2 laps for Mason - 3 laps for Laney.
n meters for Mason - 930 meters for Mason.
Applying cross multiplication:
3n = 930 x 2
n = 930 x 2/3
n = 620
Mason ran 620 meters.
More can be learned about proportions at brainly.com/question/24372153
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Answer:
Step-by-step explanation:
Given
Required
Determine the formula
An exponential function is of the form:
For point
For point
Substitute 7 for a
Divide both sides by 7
Take 4th root of both sides
![\sqrt[4]{81} =\sqrt[4]{b^4}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B81%7D%20%3D%5Csqrt%5B4%5D%7Bb%5E4%7D)
![\sqrt[4]{81} =b](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B81%7D%20%3Db)
![b = \sqrt[4]{81}](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%5B4%5D%7B81%7D)
Substitute 7 for a and 3 for b in
Answer:
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Slope: 
Y-Intercept: 
