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Volgvan
2 years ago
14

The speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to

Mathematics
1 answer:
Morgarella [4.7K]2 years ago
7 0

Answer:

  • 9 mph

Step-by-step explanation:

Let he speed of the boat on the lake is x.

<u>Considering the speed of the current it will take him:</u>

  • 22.5/(x + 6) + 22.5/(x - 6) = 9
  • 2.5 / (x  + 6) + 2.5 / (x - 6) = 1
  • 2.5(x - 6 + x + 6) = (x + 6)(x - 6)
  • 2.5*2x = x² - 36
  • x² - 5x - 36 = 0
  • x = (5 ± √(5² + 4*36))/2 = (5 ± 13) / 2
  • x = (5 + 13)/2 = 9 mph (negative root is discarded as the speed should be positive)
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\boxed{\boxed{\tt x=87^{\circ}}}

Step-by-step explanation:

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Find the measure of angle B using the law of sines
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Answer:  angle B = 15.04104216 degrees approximately

Round that however you need to.

============================================================

Explanation:

The lowercase letters a,b,c are used as side lengths while the uppercase letters A,B,C are the angles.

  • Side 'a' is opposite angle A
  • Side b is opposite angle B
  • Side c is opposite angle c

From the diagram, we have the following info:

  • side b = 22
  • side c = 63
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Use the law of sines to find B

sin(B)/b = sin(C)/c

sin(B)/22 = sin(48)/63

sin(B) = 22*sin(48)/63

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B = arcsin(0.25951089143656)

B = 15.04104216 which is approximate

------------------

Another possible value of B is

B = 180-arcsin(0.25951089143656) = 164.95896

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sin(15.04104216) = sin(164.95896) = 0.2595109

However, notice that this leads to

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But we cannot have a negative angle. Therefore only one triangle is possible here.

The only solution is approximately B = 15.04104216

5 0
2 years ago
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