Answer:
5.54 miles
Step-by-step explanation:
1. Assume she runs up to a point that is x miles to the east of the coral reef:
distance running =
distance swimming =
2. Times:
time= distance / speed
time running =
time swimming =
3. Total time
time running + time swimming:
4. Minimize time
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:
Solve for x:
5. Distance the visitor should run to minimize the time
Hence, the visitor should run 5.54 miles.
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Answer:
OPTION C
Step-by-step explanation:
We have the following rules:
![$ \sqrt[a]{x} = x^{\frac{1}{a} $](https://tex.z-dn.net/?f=%24%20%5Csqrt%5Ba%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7Ba%7D%20%24)
and
OPTION A: ![$ x \sqrt[7]{x} $](https://tex.z-dn.net/?f=%24%20x%20%5Csqrt%5B7%5D%7Bx%7D%20%24)
= 
= 
So, it can be eliminated.
OPTION B: ![$ \bigg ( \frac{1}{\sqrt[7]{x}} \bigg )^9 $](https://tex.z-dn.net/?f=%24%20%5Cbigg%20%28%20%5Cfrac%7B1%7D%7B%5Csqrt%5B7%5D%7Bx%7D%7D%20%5Cbigg%20%29%5E9%20%24)
= 
= 
= 
So, this option is also eliminated.
OPTION C: ![$ x . \sqrt[7]{x} $](https://tex.z-dn.net/?f=%24%20x%20.%20%5Csqrt%5B7%5D%7Bx%7D%20%24)
= 
= 
= 
So, OPTION C is the answer.
Current volume = 10 glns
Miles he can drive currently = 28miles/ gln * 10= 280miles
Cost of gas= 1.40/gln
Function= s /1.40 *28 +280= 28s/1.40 +280=20s + 280
Final answer would be 20s + 280
The number of the adult leaders will be 4
<h3>What will be the number of adult leaders?</h3>
A Number of cub scouts in troop 584 is = 25 .As per the statement given in the question "The number of scouts is 5 more than five times the number of adult leaders"
Number of scouts = 5(Number of adults) + 5
Here number of scouts = 25
Therefore, the equation will become as
25 = 5(Number of adults) + 5
5(Number of adults) = 25 - 5
5(Number of adults) = 20
(Number of adults) = 20/5=4
Hence the number of the adult leaders will be 4
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