A bird is flying along the straight line 2𝑦−6𝑥=42y−6x=4. In the same plane, an aeroplane starts to fly in a straight line and passes through the point (4,12)(4,12). Consider the point where aeroplane starts to fly as origin. If the bird and plane collides then enter the answer as 1 and if not then 0. Note: Bird and aeroplane can be considered to be of negligible size.
Question
A bird is flying along the straight line 2𝑦−6𝑥=42y−6x=4. In the same plane, an aeroplane starts to fly in a straight line and passes through the point (4,12)(4,12). Consider the point where aeroplane starts to fly as origin. If the bird and plane collides then enter the answer as 1 and if not then 0. Note: Bird and aeroplane can be considered to be of negligible size.
Solution
To solve this problem, we need to determine if the line of the bird's flight intersects with the line of the plane's flight.
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First, let's rewrite the equation of the bird's flight line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. The given equation is 2y - 6x = 4, which simplifies to y = 3x + 2.
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The plane's flight line passes through the point (4,12). Since we're considering this point as the origin, the equation of the plane's flight line is simply y = mx, where m is the slope. However, we don't know the slope of the plane's flight line.
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If the bird and the plane are to collide, their flight lines must intersect. In other words, there must be a point (x, y) that satisfies both y = 3x + 2 (the bird's flight line) and y = mx (the plane's flight line).
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Since we don't know the slope of the plane's flight line, we can't determine if there's such a point. Therefore, we can't definitively say whether the bird and the plane will collide or not.
So, without additional information, the answer is 0 (the bird and the plane will not necessarily collide).
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