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Contact [7]
2 years ago
8

Plane traveled 1120 miles each way to Munich and back. The trip there was with the wind. It took 10 hours. The trip back was int

o the wind. The trip back took 20 hours. What is the speed of the plane in still air? What is the speed of the wind?
ANSWER IT ASAP IT DUE TMRW
Mathematics
1 answer:
kotegsom [21]2 years ago
6 0

Answer:

  • 84 mph and 28 mph

Step-by-step explanation:

Let the speed of plane is p and speed of the wind is w.

<u>Then we have:</u>

  • 10*(p + w) = 1120 ⇒ p + w = 112
  • 20*(p - w) = 1120 ⇒ p - w = 56

<u>Sum the two equations and solve for p:</u>

  • p + w + p - w = 112 + 56
  • 2p = 168
  • p = 84

<u>Find w:</u>

  • 84 + w = 112
  • w = 112 - 84
  • w = 28
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Answer:

Partial fraction = 1/(x-2) - x/(x^2+1)

Step-by-step explanation:

Question:

Express 2x+1/(x-2)(x²+1) as a partial fraction.

Note: it will be assumed that there was a typo in the interpretation of parentheses to mean

(2x+1) / ( (x-2)(x^2+1) )

Let

(2x+1) / ( (x-2)(x^2+1) ) = A/(x-2) + (Bx+C)/(x^2+1) .........................(0)

(2x+1) / ( (x-2)(x^2+1) ) = (A(x^2+1)+(Bx+C)(x-2)) / ( (x-2)(B/(x^2+1) )

(2x+1) / ( (x-2)(x^2+1) ) = (Ax^2+A+Bx^2+(C-2B)x-2C) / ( (x-2)(B/(x^2+1) )

(2x+1) / ( (x-2)(x^2+1) ) = ( (A+B)x^2+(C-2B)x+A-2C ) / ( (x-2)(B/(x^2+1) )

Match numerators

2x+1 = (A+B)x^2+(C-2B)x+A-2C

Match coefficients,

A+B = 0 ..................(1)

-2B+C = 2 .................(2)

A-2C = 1 ...................(3)

Solve for A, B and C

Substitute A from (1) in (3)

-B - 2C =1  

transpose and solve for B

B = -2C-1  ....................(4)

Substitue B from (4) in (2)

-2(-2C-1) + C = 2  

simplify

5C = 2-2 = 0

C=0  ..........................(5)

substitute (5)  in (4)

B = -2C-1 = -1  ...............(6)

Substitue (6) in (1)

A+(-1) = 0

A=1 .............................(7)

Using values from (7), (6) and (5) to substitute in (0)

we get

(2x+1) / ( (x-2)(x^2+1) ) = 1/(x-2) - x/(x^2+1)

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Step-by-step explanation:

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Answer:

Two imaginary solutions:

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Step-by-step explanation:

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The discriminant gives us information on how the solutions of the equations will be.

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So:

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The second solution x₂ = (-b-√b²-4ac)/2a

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