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kozerog [31]
3 years ago
12

I need help getting the answer

Mathematics
1 answer:
valentina_108 [34]3 years ago
3 0

Answer:

Step-by-step explanation:

The center is at (2,-7). The radius is 2.

(x-2)² + (y+7)² = 2²

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A small plane took 3 hours to fly 960 km from Ottawa to Halifax with a tail wind. On the return trip, flying into the wind, the
Rina8888 [55]

Answer:

  • Wind speed: \rm 40\; km \cdot h^{-1}.
  • Speed of the plane in still air: \rm 320\; km \cdot h^{-1}.

Step-by-step explanation:

This problem involves two unknowns:

  • wind speed, and
  • speed of the plane in still air.

Let the speed of the wind be x \rm \; km \cdot h^{-1}, and the speed of the plane in still air be y\rm \; km \cdot h^{-1}. It takes at least two equations to find the exact solutions to a system of two variables.

Information in this question gives two equations:

  • It takes the plane three hours to travel \rm 960\; km from Ottawa to with a tail wind (that is: at a ground speed of x + y.)
  • It takes the plane four hours to travel \rm 960\; km from Halifax back to Ottawa while flying into the wind (that is: at a ground speed of -x + y.)

Create a two-by-two system out of these two equations:

\left\{ \begin{aligned}&3(x + y) = 960 && (1) \\ &4(-x + y) = 960 && (2) \end{aligned}\right..

There can be many ways to solve this system. The approach below avoids multiplying large numbers as much as possible.

Note that this system is equivalent to

\left\{ \begin{aligned}&4 \times 3 (x + y) = 4\times960 && 4 \times (1) \\ &3\times 4(-x + y) = 3\times 960 && 3 \times (2) \end{aligned}\right..

\left\{ \begin{aligned}&12 x + 12y = 4\times960 && 4 \times (1) \\ &- 12x + 12y = 3\times 960 && 3 \times (2) \end{aligned}\right..

Either adding or subtracting the two equations will eliminate one of the variables. However, subtracting them gives only 1 \times 960 on the right-hand side. In comparison, adding them will give 7 \times 960, which is much more complex to evaluate. Subtracting the second equation (3 \times (2)) from the first (4 \times (1)) will give the equation

(12 - (-12) x = 1 \times 960.

24 x = 960.

x = 40.

Substitute x back into either equation (1) or (2) of the original system. Solve for y to obtain y = 320.

In other words,

  • Wind speed: \rm 40\; km \cdot h^{-1}.
  • Speed of the plane in still air: \rm 320\; km \cdot h^{-1}.
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