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Oliga [24]
2 years ago
11

Melody can cycle for 30 miles against the wind in the same amount of time that it takes to cycle 56 miles with the wind. If the

speed of the wind is 3mph, what is Melody's speed when she cycles with the wind?
Answer with Solution:​
Mathematics
1 answer:
erma4kov [3.2K]2 years ago
3 0

Answer:

  • 12.92 mph

Step-by-step explanation:

<u>Given:</u>

  • Speed of the wind = 3 mph
  • Speed in calm weather = x
  • Speed with the wind = x + 3
  • Speed against the wind = x - 3

<u>We know that:</u>

  • distance = time*speed or
  • time = distance / speed

<u>We have equal time in both cases so comparing d/s ratios:</u>

  • 30/(x - 3) = 56/(x + 3)

<u>Solve for x:</u>

  • 56(x - 3) = 30(x + 3)
  • 56x - 168 = 30x + 90
  • 56x - 30x = 90 + 168
  • 26x = 258
  • x = 258/26
  • x ≈ 9.92

<u>The speed with the wind is:</u>

  • 9.92 + 3 = 12.92 mph
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6 0
3 years ago
Given cosα = −3/5, 180 &lt; α &lt; 270, and sinβ = 12/13, 90 &lt; β &lt; 180
torisob [31]

I got

-  \frac{6 3}{65}

What we know

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What we need to find

Cos(b)

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What we are going to apply

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Basics Sine and Cosines Identies.

1. Let write out the cos(a-b) formula.

\cos(a - b)  =  \cos(a)  \cos(b)  +  \sin(a)  \sin(b)

2. Use the interval it gave us.

According to the given, Angle B must between in second quadrant.

Since sin is opposite/hypotenuse and we are given a sin b=12/13. We. are going to set up an equation using the pythagorean theorem.

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{12}^{2}  +  {y}^{2}  =  {13}^{2}

144 +  {y}^{2}  = 169

25 =  {y}^{2}

y = 5

so our adjacent side is 5.

Cosine is adjacent/hypotenuse so our cos b=5/13.

Using the interval it gave us, Angle a must be in the third quadrant. Since cos is adjacent/hypotenuse and we are given cos a=-3/5. We are going to set up an equation using pythagorean theorem,

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( - 3) {}^{2}  +  {x}^{2}  =  {5}^{2}

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Now use cosine difference formula

-  \frac{3}{5}  \times  \frac{5}{13}  +   - \frac {4}{5}  \times  \frac{12}{13}

- \frac{15}{65} + (  - \frac{48}{65}  )

-  \frac{63}{65}

Hope this helps

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Answer:

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