Line L has an undefined slope. Line M is perpendicular to line L. Which of the following could be the equation of line M?

1 answer:

6 0

"Line L has an undefined slope" so line L is any vertical line.

Anything perpendicular to this vertical line will be horizontal. So line M is horizontal.

Horizontal lines are of the form y = k for some fixed number k. The only thing that fits is choice B) y = 7 where k = 7 in this case.

Choice A graphs out a diagonal line, choice C graphs a vertical line, while choice D graphs out a hyperbola. These facts are why we can eliminate these non-answers.

Answer: Choice B) y = 7

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Step-by-step explanation:

[using calculus] When the function h(t) reaches its maximum value, its first derivative will be equal to zero (the first derivative represents velocity of the ball, which is instantaneously zero). We have $h'(t) = -32t + 48$ , which equals zero when $t = 3/2 = 1.5$ . The ball therefore reaches its maximum height when t = 1.5. To find the maximum height, we need to find h(1.5), which is 64 feet.

[without calculus] This is a quadratic function, so its maximum value will occur at its vertex. The formula for the x-coordinate of the vertex is -b/2a, so the maximum value occurs when t = -48/(2*16), which is 1.5. The maximum height is h(1.5), which is 64 feet.