Answer:t=2.11 hr
Step-by-step explanation:
Given
Aydlett is 2 miles offshore and village is 6 miles down a straight line from the Point on the shore nearest the island
Person can row boat at 2 mph in water and can walk 5 mph in land
Let us suppose Person land the boat at a x miles from Point on the shore
thus time taken by him to reach
![t_1=\frac{\sqrt{x^2+2^2}}{2}](https://tex.z-dn.net/?f=t_1%3D%5Cfrac%7B%5Csqrt%7Bx%5E2%2B2%5E2%7D%7D%7B2%7D)
Time taken person to reach village by land is
![t_2=\frac{6-x}{5}](https://tex.z-dn.net/?f=t_2%3D%5Cfrac%7B6-x%7D%7B5%7D)
total time![=\frac{\sqrt{x^2+2^2}}{2}+\frac{6-x}{5}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Csqrt%7Bx%5E2%2B2%5E2%7D%7D%7B2%7D%2B%5Cfrac%7B6-x%7D%7B5%7D)
we need the time to be least so differentiate t w.r.t to x
![\frac{\mathrm{d} t}{\mathrm{d} x}=\frac{2x}{2\cdot 2\cdot \sqrt{4+x^2}}-\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cmathrm%7Bd%7D%20t%7D%7B%5Cmathrm%7Bd%7D%20x%7D%3D%5Cfrac%7B2x%7D%7B2%5Ccdot%202%5Ccdot%20%5Csqrt%7B4%2Bx%5E2%7D%7D-%5Cfrac%7B1%7D%7B5%7D)
Equating Above term to zero to get minimum time
![\frac{x}{2\sqrt{4+x^2}}=\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%5Csqrt%7B4%2Bx%5E2%7D%7D%3D%5Cfrac%7B1%7D%7B5%7D)
![25x^2=16+4x^2](https://tex.z-dn.net/?f=25x%5E2%3D16%2B4x%5E2)
![x=\frac{4}{\sqrt{21}}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%7D%7B%5Csqrt%7B21%7D%7D)
Substituting x in time equation
![t=\frac{\sqrt{4+0.761}}{2}+\frac{6-0.872}{5}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B%5Csqrt%7B4%2B0.761%7D%7D%7B2%7D%2B%5Cfrac%7B6-0.872%7D%7B5%7D)
![t=2.116 hr](https://tex.z-dn.net/?f=t%3D2.116%20hr)
Sirrrr do u mean equivalent???
To find equivalent inequalities you have to work the inequality given.
The first step is transpose on of sides to have an expression in one side and zero in the other side:
x - 6 x + 7
--------- ≥ --------
x + 5 x + 3
=>
x - 6 x + 7
--------- - -------- ≥ 0
x + 5 x + 3
=>
(x - 6) (x + 3) - (x + 7) (x + 5)
--------------------------------------- ≥ 0
(x + 5) (x + 3)
=>
x^2 - 3x - 18 - x^2 - 12x - 35
--------------------------------------- ≥ 0
(x + 5) (x + 3)
15x + 53
- ------------------- ≥ 0
(x + 5) (x + 3)
That is an equivalent inequality. Sure you can arrange it to find many other equivalent inequalities. That is why you should include the list of choices. Anyway from this point it should be pretty straigth to arrange the terms until making the equivalent as per the options.
Since the vertex is located outside of the triangle, refer to the formula
Angle = Ba - Sa
———
2
(Ba = Big Arc, Sa = Small arc)
So just fill in the missing pieces
22=125-x
———
2
X=81