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ikadub [295]
2 years ago
5

Given tan theta = -2 and pi/2 < theta < pi; find cos2theta.

Mathematics
1 answer:
Kay [80]2 years ago
8 0

Answer:

Cos 2theta = -3/5

Step-by-step explanation:

Given that;

tan theta = -2

tan theta = -2/1 = opp/adj

hyp^2 = (-2)^2+1^2

hyp = √4+1

hyp = √5

sin theta = opp/hyp

sin theta = -2/√5

Cos theta = adj/hyp

Cos theta = -2/√5

Cos 2theta = 1-2sin^2 theta

Cos 2theta = 1- 2(-2/√5)^2

Cos 2theta = 1- 2(4/5)

Cos 2theta = 1- 8/5

Cos 2theta = (5-8)/5

Cos 2theta = -3/5

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at maximum speed, an airplane travels 1720 miles against th wind in 5 hours. Flying with the wind, the plane can travel the same
iragen [17]

Answer:

x = 387

Step-by-step explanation:

The wind acts in the opposite direction to the plane when the time is longer.

The wind acts in the same direction as the plane when the time is shorter.

Equation

d = r*t

Givens

  • d = 1720
  • x = plane's speed
  • y = wind speed
  • t1 = 5 hours
  • t2 = 4 hours.

Substitution

  • d = (x + y) * t
  • 1720 = (x + y) * 4
  • 1720 = (x - y) * 5

Since the two distances are the same, you can equate the right hand sides.

  • (x + y) * 4 = (x - y)*5              Remove the brackets.
  • 4x + 4y = 5x - 5y                  Add 5y to both sides
  • 4x + 4y + 5y = 5x - 5y + 5y  Combine all the terms.
  • 4x + 9y = 5x                          Subtract 4x from both sides
  • 9y + 4x - 4x = 5x - 4x           Combine
  • 9y = x

Now use one of the given equations with the distance

  • 1720 = (x + y)*4           Substitute 9y for x
  • 1720 = (9y + y) *  4      Combine
  • 1720 = 10y * 4             Multiply the right
  • 1720 = 40y                  Divide by 40
  • 1720/40 = 40y/40      Do the division
  • 43 = y                          y = wind speek
  • 9y = x                          x = 9*y  
  • 9*43 = x
  • x = 387 miles per hour.
4 0
3 years ago
You pay $22 to rent 6 video games. The store charges $4 for a new game and $2 for older games. How many new games did you rent?
AlexFokin [52]
You rented 5 new games
6 0
3 years ago
Read 2 more answers
How can you use the graph to f he amount of distilled water to use for 4.5 milliliters of ammonia?
Elden [556K]

Answer:

The graph can show you how much distilled water for 4 milliliters of ammonia and 5 milliliters of ammonia. You can use the graph to find 4.5 by find the midpoint of two amounts of distilled water. Such as, say that 4 milliliters of ammonia = 200 distilled water and 5 milliliters of ammonia=  250 distilled water. Then the answer to 4.5 milliliters of ammonia is 225 distilled water.

Step-by-step explanation:


6 0
3 years ago
the managers of a corporation were surveyed to determine the background that leads to a successful manager. each manager was rat
lubasha [3.4K]

The probability that the selected manager has no college background and only have a fair look is 0.05625

Table is missing. Attached below.

Given,

We have to find the probability that the selected manager has no college background and only have a fair look;

From the table;

The total number of managers surveyed = 160

Number of managers surveyed are fair = 9

Probability;-

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The probability = Number of managers surveyed are fair / The total number of managers surveyed

The probability = 9/160 = 0.05625

That is,

The probability that the selected manager has no college background and only have a fair look is 0.05625

Learn more about probability here;

brainly.com/question/11234923

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8 0
1 year ago
For f(x) = 5x-2 and g(x) = 4x4 - 3 find the following.
Allisa [31]
Correct answer is B
6 0
2 years ago
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