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valkas [14]
2 years ago
13

How many gallons of a 90% antifreeze solution must be mixed with 90 gallons of 20% antifreeze to get a mixture that is 80% antif

reeze?
Mathematics
1 answer:
lozanna [386]2 years ago
7 0

Answer:

540

Step-by-step explanation:

Amount of antifreeze in the 90% solution + amount of antifreeze in the 20% solution = amount of antifreeze in the 80% solution

0.90 x + 0.20 (90) = 0.80 (x + 90)

0.90 x + 18 = 0.80 x + 72

0.10 x = 54

x = 540

You need 540 gallons of 90% antifreeze solution.

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Solve: 2cos(x)-square root 3=0 for 0 less than x less than 2 pi
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Answer:

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                                                x = 2nπ±\frac{\pi }{6}

The general solution values  

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Step-by-step explanation:

Explanation:-

Given equation is  

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Dividing '2' on both sides, we get

                             cos x =\frac{\sqrt{3} }{2}

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<em>General solution of cos θ = cos ∝ is θ = 2nπ±∝</em>

<em>Now The general solution of   </em>cos x = cos(\frac{\pi }{6})<em>   is  </em>

<em>                                                 x = 2nπ±</em>\frac{\pi }{6}<em></em>

put n=0

x = - \frac{\pi }{6}  and x = \frac{\pi }{6}

Put n=1  

x = 2\pi +\frac{\pi }{6} = \frac{13\pi }{6}

x = 2\pi -\frac{\pi }{6} = \frac{11\pi }{6}

put n=2

x = 4\pi +\frac{\pi }{6} = \frac{25\pi }{6}

x = 4\pi -\frac{\pi }{6} = \frac{23\pi }{6}

And so on

But given 0 < x< 2π

The general solution values  

                                 x = - \frac{\pi }{6}  and x = \frac{\pi }{6}

                               

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