maths question help (1 Viewer)

chrstinee

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A satellite dish is in the shape of a parabola
with equation y = −3x^2 + 6, and all dimensions are in metres.

Find w, the width of the dish, to 1 decimal
place.

answer is 2.8
 

jimmysmith560

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1616235175023.png

You need to find the roots by making y = 0

-3x^2 + 6 = 0
3x^2 - 6 = 0
x^2 - 2 = 0
x^2 = 2
x = +/- sqrt 2 (approximately -1.4 and 1.4).

The width of the satellite dish would then be the distance between the roots

w = 1.4 + 1.4 = 2.8 metres (1 decimal place)
 
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CM_Tutor

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@jimmysmith560's answer is correct and the question is badly written. For a start, a satellite dish is a three-dimensional object, and further it is finite, so saying it has an equation like the one given is problematic. The question should be re-written as something like:

A satellite dish is in the shape of a parabola rotated about its axis. With all distances in metres, a cross-section
of the dish through its vertex matches that part of that is on or above the y-axis.
Find w, the width of the dish at its widest point, in exact form and to 1 decimal place.​

The answer would be
 

jimmysmith560

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@jimmysmith560's answer is correct and the question is badly written. For a start, a satellite dish is a three-dimensional object, and further it is finite, so saying it has an equation like the one given is problematic. The question should be re-written as something like:

A satellite dish is in the shape of a parabola rotated about its axis. With all distances in metres, a cross-section
of the dish through its vertex matches that part of that is on or above the y-axis.
Find w, the width of the dish at its widest point, in exact form and to 1 decimal place.​

The answer would be
Thank you!
 

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