Answer:
NB: There are two possible answer to this question, depending on the correctness of the question asked.
<em>In the case where the question 'who was measured ?' is the correct question</em>, then the the <em>correct answer will be D</em>, since <em>the word 'who' is an interrogative pronoun and a relative pronoun, used chiefly to refer to </em><u><em>humans</em></u><em>. </em>In that case, no one was actually measure or <em>we simply state that the 'information is not given'.</em>
<em>But if assume that the question to the answer is 'what was measured ?' and not 'who was measured ?',</em> In this case, <em>only the data gotten from the measurement of properties of the fillings in the sandwiches served by the restaurant chain was given</em>, and option B is the correct answer.
<em></em>
Answer:
![A\approx 0.55](https://tex.z-dn.net/?f=A%5Capprox%200.55)
Step-by-step explanation:
<u>Optimizing With Derivatives
</u>
One of the most-used applications of derivatives is to maximize or minimize functions. We need to recall that if f(x) is a real function and f'(x) is the derivative of f, then we can find the critical points of f by setting
![f'(x)=0](https://tex.z-dn.net/?f=f%27%28x%29%3D0)
Then we must test the critical points in the second derivative f''(x) and if
f''(x) is positive, then x is a minimum
f''(x) is negative, then x is a maximum
The problem requires us to find the maximum area of the rectangle which base is x and height is f(x), where
![f(x)=e^{-x^2}](https://tex.z-dn.net/?f=f%28x%29%3De%5E%7B-x%5E2%7D)
The area of the rectangle is the product of the base by the height, so
![A=xe^{-x^2}](https://tex.z-dn.net/?f=A%3Dxe%5E%7B-x%5E2%7D)
Let's find the first derivative
![A'=e^{-x^2}-2x^2e^{-x^2}](https://tex.z-dn.net/?f=A%27%3De%5E%7B-x%5E2%7D-2x%5E2e%5E%7B-x%5E2%7D)
![A'=e^{-x^2}(1-2x^2)](https://tex.z-dn.net/?f=A%27%3De%5E%7B-x%5E2%7D%281-2x%5E2%29)
Setting A'=0
![e^{-x^2}(1-2x^2)=0](https://tex.z-dn.net/?f=e%5E%7B-x%5E2%7D%281-2x%5E2%29%3D0)
![(1-2x^2)=0](https://tex.z-dn.net/?f=%281-2x%5E2%29%3D0)
Solving for x
![\displaystyle x=\sqrt{\frac{1}{2}}=\frac{\sqrt{2}}{2}=0.707](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Csqrt%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%3D0.707)
Let's compute the second derivative
![A''=-2xe^{-x^2}(1-2x^2)+e^{-x^2}(-4x)](https://tex.z-dn.net/?f=A%27%27%3D-2xe%5E%7B-x%5E2%7D%281-2x%5E2%29%2Be%5E%7B-x%5E2%7D%28-4x%29)
![A''=e^{-x^2}(4x^3-6x)](https://tex.z-dn.net/?f=A%27%27%3De%5E%7B-x%5E2%7D%284x%5E3-6x%29)
Factoring
![A''=2xe^{-x^2}(2x^2-3)](https://tex.z-dn.net/?f=A%27%27%3D2xe%5E%7B-x%5E2%7D%282x%5E2-3%29)
Evaluating for the critical point we can see the first factor (2x) is positive. The exponential is always positive, we only need to find the sign of
![2x^2-3](https://tex.z-dn.net/?f=2x%5E2-3)
Since
the expression is negative, thus
A''(x)<0 and the critical point is a maximum
The maximum area is
![A=\frac{\sqrt{2}}{2}e^{-(\frac{\sqrt{2}}{2})^2}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7De%5E%7B-%28%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%29%5E2%7D)
![\boxed{A\approx 0.55}](https://tex.z-dn.net/?f=%5Cboxed%7BA%5Capprox%200.55%7D)
Answer:
1.4
Step-by-step explanation:
We need to convert 103/7497 into a percentage.
All we have to do is multiply the fraction by 100:
103/7497 * 100 = 1.37
To one decimal place, the equivalent fraction is 1.4
No because when you plug 5 into x and 6 into y it does not equal 10
According to irrational numbers the answer is c