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kicyunya [14]
3 years ago
6

Solve 6 sin((π/5)x)=5 for the four smallest positive solutions

Mathematics
1 answer:
cupoosta [38]3 years ago
3 0

Answer:

1.568, 3.432, 11.568, 13.432

Step-by-step explanation:

Divide equation 6\sin\left(\dfrac{\pi }{5}x\right)=5 by 6:

\sin\left(\dfrac{\pi }{5}x\right)=\dfrac{5}{6}.

Then

\dfrac{\pi }{5}x=(-1)^k\arcsin\left(\dfrac{5}{6}\right)+\pi k,\ k\in Z,

x=(-1)^k\dfrac{5}{\pi }\arcsin\left(\dfrac{5}{6}\right)+5k,\ k\in Z.

Since \arcsin\left(\dfrac{5}{6}\right)\approx 56^{\circ}\approx \dfrac{\pi }{3.2},

four smallest positive solutions are

1. \dfrac{5}{3.2}\approx 1.568,\ k=0;

2. \dfrac{-5}{3.2}+5\approx 3.432,\ k=1;

3. \dfrac{5}{3.2}+10\approx 11.568,\ k=2;

4. \dfrac{-5}{3.2}+15\approx 13.432,\ k=3.

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Mnenie [13.5K]

Least value is too vague.

You can have least positive then answer is A.

You can have most negative then C.

Hope this helps.

6 0
2 years ago
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SOMEONE HELP ????<br><br> Select steps that could be used to solve the equation 1+ 3x = -x+4
Alex

Answer:

a) add x , subtract 1 and divide by 4

The solution of given equation x = \frac{3}{4}

<u>Step-by-step explanation:</u>

Given equation  1+3 x  = -x +4

                <em>  Add 'x' on both sides , we get</em>

                     1 + 3 x + x = - x + x +4

                     1 + 4 x  = 4

      <em>  Subtract '1' on both sides , we get</em>

<em>                     1+4 x -1 = 4 -1</em>

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<em>       Dividing '4' on both sides, we get</em>

                          \frac{4x}{4} = \frac{3}{4}

                          x = \frac{3}{4}

<u><em>Final answer</em></u>:-

<em>The solution of given equation </em>x = \frac{3}{4}<em></em>

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Answer:

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Step-by-step explanation:

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hypotenuse = 13/sin 64

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