Answer:
$2.96
Step-by-step explanation:
Answer:
(I am assuming that you don't need the answer, but just an explanation of what to do.) Let's take the first problem for an example the first thing you are going to do is subtract 12 on both sides and you will get n> -1 so then you will put a open circle on -1 going to the right.
Hope this helps :)
Answer:
Explanation:
<u>1. Assume she runs up to a point that is x miles to the east of the coral reef:</u>
- distance running =
![9-x\text{ }miles](https://tex.z-dn.net/?f=9-x%5Ctext%7B%20%7Dmiles)
- distance swimming =
![\sqrt{x^2+6^2}=\sqrt{x^2+36}\text{ }miles](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%2B6%5E2%7D%3D%5Csqrt%7Bx%5E2%2B36%7D%5Ctext%7B%20%7Dmiles)
<u>2. Times:</u>
time= distance / speed
- time running =
![\dfrac{9-x}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7B9-x%7D%7B4%7D)
- time swimming =
![\dfrac{\sqrt{x^2+36} }{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%7Bx%5E2%2B36%7D%20%7D%7B2%7D)
<u>3. Total time</u>
- time running + time swimming:
![T=\dfrac{9-x}{4}+\dfrac{\sqrt{x^2+36} }{2}](https://tex.z-dn.net/?f=T%3D%5Cdfrac%7B9-x%7D%7B4%7D%2B%5Cdfrac%7B%5Csqrt%7Bx%5E2%2B36%7D%20%7D%7B2%7D)
<u>4. Minimize time</u>
The minimum time is when the derivative of the function of time is zero.
Find the derivative of T(x), using rule of the sum, the derivative of the sum is the sum of the derivatives, and the chain rule:
![\dfrac{dT}{dx}=\dfrac{-1}{4}+\dfrac{1}{2}\cdot \dfrac{1}{2}\dfrac{2x}{\sqrt{x^2+36}}=0](https://tex.z-dn.net/?f=%5Cdfrac%7BdT%7D%7Bdx%7D%3D%5Cdfrac%7B-1%7D%7B4%7D%2B%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B1%7D%7B2%7D%5Cdfrac%7B2x%7D%7B%5Csqrt%7Bx%5E2%2B36%7D%7D%3D0)
Solve for x:
![\dfrac{2x}{\sqrt{x^2+36}}=1\\ \\ \\ 2x=\sqrt{x^2+36\\ } \\ \\ (2x)^2=x^2+36\\ \\ \\ 4x^2=x^2+36\\ \\ \\ 3x^2=36\\ \\ \\ x^2=12\\ \\ \\ x=2\sqrt{3}](https://tex.z-dn.net/?f=%5Cdfrac%7B2x%7D%7B%5Csqrt%7Bx%5E2%2B36%7D%7D%3D1%5C%5C%20%5C%5C%20%5C%5C%202x%3D%5Csqrt%7Bx%5E2%2B36%5C%5C%20%7D%20%5C%5C%20%5C%5C%20%282x%29%5E2%3Dx%5E2%2B36%5C%5C%20%5C%5C%20%5C%5C%204x%5E2%3Dx%5E2%2B36%5C%5C%20%5C%5C%20%5C%5C%203x%5E2%3D36%5C%5C%20%5C%5C%20%5C%5C%20x%5E2%3D12%5C%5C%20%5C%5C%20%5C%5C%20x%3D2%5Csqrt%7B3%7D)
<u>5. Distance the visitor should run to minimize the time</u>
Hence, the visitor should run
miles.
The answer for this question is letter c