If Hank shoots from inside the three point line, what can be said about his distance from the center of the basket?

Mathematics

1 answer:

Pie3 years ago

4 0

Answer:

Distance between centre of basket and point at which shot is taken will be less than 246 inches

Step-by-step explanation:

From the figure Given, the distance between the three line mark and the center of the basket is 246 inches. This means that, if a shot is taken from inside the 3 point line, then the distance from the point within the 3 point mark and the centre of the basket will be less than 246 inches. As the shooter moves towards the basket, past the 3 point arc and is positioned inside the line, then the distance between the line and the centre of the basket has been shortened and hence, the shooters horizontal Distance to the centre of the basket on the ground is less than 246 inches.

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Click here to see ALL problems on Geometry Word ProblemsQuestion 503498: a community flower garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What ill be the width of the pathway?

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Borders are interesting because you have to remember that you have to pave the 4 corners.
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Then you add the border with width 'x'.
So,
Length is now L + 2x
Width is now W + 2x
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We are told:
(L+2x)(W+2x) = 285
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(12+2x)(16+2x) = 285
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192 +24x +32x +4x^2 = 285
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4x^2 + 56x + 192 = 285
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4x^2 + 56x - 93 = 0
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Solved by pluggable solver: SOLVE quadratic equation with variableQuadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=4624 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

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You cannot have a negative width, so the border is 1.5 m.
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Always check your work.
L = 12 + 2(1.5) = 15
W = 16 + 2(1.5) = 19
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Correct.
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Answer: The border is 1.5 meters wide.
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