Answer: the speed of the current is 9 mph.
Step-by-step explanation:
Let x represent the speed of the current.
A boat can travel 21 mph in still water. If it travels 270 miles with the current. It means that the total speed with which the boat travelled with the current is (21 + x) mph.
Time = distance/speed
Time spent by the boat in travelling 270 miles is
270/(21 + x)
In the same length of time, it travels 108 miles against the current. It means that the total speed with which the boat travelled against the current is (21 - x) mph.
Time = distance/speed
Time spent by the boat in travelling 108 miles is
108/(21 - x)
Since the time is the same, then
270/(21 + x) = 108/(21 - x)
270(21 - x) = 108(21 + x)
5670 - 270x = 2268 - 108x
108x + 270x = 5670 - 2268
378x = 3402
x = 3402/378
x = 9
I'll try it.
I just went through this twice on scratch paper. The first time was to
see if I could do it, and the second time was because the first result
I got was ridiculous. But I think I got it.
You said <span><u>3sin²(x) = cos²(x)</u>
Use this trig identity: sin²(x) = 1 - cos²(x)
Plug it into the original equation for (x).
3(1 - cos²(x) ) = cos²(x)
Remove parentheses on the left: 3 - 3cos²(x) = cos²(x)
Add 3cos²(x) to each side: 3 = 4cos²(x)
Divide each side by 4 : 3/4 = cos²(x)
Take the square root of each side: <em>cos(x) = (√3) / 2</em> .
There it is ... the cosine of the unknown angle.
Now you just go look it up in a book with a table cosines,
or else pinch it through your computer or your calculator,
or else just remember that you've learned that
cos( <em><u>30°</u></em> ) = </span><span><span>(√3) / 2 </span>.
</span>
Answer: PiN, Pi/3+2PiN, 5Pi/3+2PiN
Step-by-step explanation: Use formula sheet
