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Leni [432]
3 years ago
9

write a system of equations for the problem, and then solve the system. if a plane can travel 340 miles per hour with the wind o

nly 260 miles per hour against the wind, find the speed of the wind and the speed of the plane in still air. please show step by step
Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
7 0

Answer:

w = 40 miles per hour

r = 300 miles per hour

Step-by-step explanation:

We add w with the wind and subtract w against the wind

r+w = 340 miles per hour

r - w = 260 miles per hour

Add the two equations together to eliminate w

r+w = 340 miles per hour

r - w = 260 miles per hour

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

2r = 600

Divide by 2

r = 300 miles per hour without the wind

Now find w

r+w = 340

300 + w = 340

Subtract 300

w = 340-300

w = 40 miles per hour

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The standard form of a parabola with points through (2, 0) (3, 2) (4, 6)

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Step-by-step explanation:

The standard form of a parabola is y = ax² + bx + c, where a, b , c are constant

To find a , b , c

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  • Substitute the coordinates of each point in the equation to make system of equations of a , b and c
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∵ The standard form of a parabola is y = ax² + bx + c

∵ The parabola passes through points (2 , 0) , (3 , 2) , (4 , 6)

- Substitute the coordinates of each point in the equation

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∵ x = 2 and y = 0

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- Switch the two sides

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Point (3 , 2)

∵ x = 3 and 2 = 0

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- Switch the two sides

∴ 9a + 3b + c = 2 ⇒ (2)

Point (4 , 6)

∵ x = 4 and y = 6

∴ 6 = a(4)² + b(4) + c

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- Switch the two sides

∴ 16a + 4b + c = 6 ⇒ (3)

Subtract equation (1) from equations (2) and (3)

∴ 5a + b = 2 ⇒ (4)

∴ 12a + 2b = 6 ⇒ (5)

- Multiply equation (4) by -2 to eliminate b

∴ -10a - 2b = -4 ⇒ (6)

- Add equations (5) and (6)

∴ 2a = 2

- Divide both sides by 2

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Substitute the value of a in equation (4) to find b

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∴ 5 + b = 2

- Subtract 5 from both sides

∴ b = -3

Substitute the value of a and b in equation (1) to find c

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∴ y = (1)x² + (-3)x + (2)

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There is another solution you can substitute the x-coordinate of each point in each answer to find the corresponding value of y, if the value of y gives the same value of the y-coordinate of the point for the three points then this answer is the standard form of the parabola

Learn more:

You can learn more about the parabola in brainly.com/question/8054589

#LearnwithBrainly

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