Which set of ordered pairs represents a function?
1 answer:
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Answer:
Step-by-step explanation:
<u><em>The correct question is</em></u>
what is the equation for a line passing through (-2,3) and perpendicular to y= -1/2<em>x</em>+1 ?
Remember
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes are equal to -1)
The slope of the given line is m=-1/2
so
the opposite reciprocal is m=2
<em>Find the equation of the line in point slope form</em>
we have
substitute
<em>Convert to slope intercept form</em>
isolate the variable y
25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path. This can be obtained by considering this as a right angled triangle.
<h3>How fast is the tip of his shadow moving?</h3>Let x be the length between man and the pole, y be the distance between the tip of the shadow and the pole.
Then y - x will be the length between the man and the tip of the shadow.
Since two triangles are similar, we can write
⇒15(y-x) = 6y
15 y - 15 x = 6y
9y = 15x
y = 15/9 x
y = 5/3 x
Differentiate both sides
dy/dt = 5/3 dx/dt
dy/dt is the speed of the tip of the shadow, dx/dt is the speed of the man.
Given that dx/dt = 5 ft/s
Thus dy/dt = (5/3)×5 ft/s
dy/dt = 25/3 ft/s
Hence 25/3 ft/s is speed of the tip of his shadow moving when a man is 40 ft from the pole given that a street light is mounted at the top of a 15-ft-tall pole and the man is 6 ft tall who is walking away from the pole with a speed of 5 ft/s along a straight path.
Learn more about similar triangles here:
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