E maths graph
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A tower with vertical walls stands on horizontal ground. A stone is thrown from a window of the tower. At any instant, the horizontal distance of the stone from the building is x metres and the height of the stone above the ground is y metres, given by the formula
y = 18 + 3x - x^2
The table below shows some values of x and the corresponding values of y:
x 0 1 2 3 4 5 6
y 18 20 20 p 14 q 0
By drawing a suitable straight line on the graph, find the range of values of x for which the horizontal distance of the stone from the building is greater than the height of the stone above the ground.
I analyzed the question for some time but then, is there anyway i can draw a straight line? No gradient, nothing... the previous parts of the question also did not ask me to draw any tangent, etc.
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Originally posted by anpanman:
A tower with vertical walls stands on horizontal ground. A stone is thrown from a window of the tower. At any instant, the horizontal distance of the stone from the building is x metres and the height of the stone above the ground is y metres, given by the formula
y = 18 + 3x - x^2
The table below shows some values of x and the corresponding values of y:
x 0 1 2 3 4 5 6
y 18 20 20 p 14 q 0
By drawing a suitable straight line on the graph, find the range of values of x for which the horizontal distance of the stone from the building is greater than the height of the stone above the ground.
I analyzed the question for some time but then, is there anyway i can draw a straight line? No gradient, nothing... the previous parts of the question also did not ask me to draw any tangent, etc.
Hi,
The first thing which you should do is to draw out y=18+3x-x^2. After that sub in y = x into the equation and find the values of x. Reject the negative value, and use the positive value ( let us take it to be a ) to draw a line ( x=a ).
Hence, for all values of 6 >/= x > a, the horizontal distance of the stone from the building is greater than the height of the stone above the ground.
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Just for u to check, ur graph should look something like the one shown below if the both of us are correct
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Originally posted by TrueHeart:
Hi,
The first thing which you should do is to draw out y=18+3x-x^2. After that sub in y = x into the equation and find the values of x. Reject the negative value, and use the positive value ( let us take it to be a ) to draw a line ( x=a ).
Hence, for all values of 6 >/= x > a, the horizontal distance of the stone from the building is greater than the height of the stone above the ground.
Yes,. I can understand from your explanation how i am supposed to go about finding the answer. But may I know why the steps are taken to find the ans? why must we draw y=x?Thank you very much!
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Originally posted by anpanman:
Yes,. I can understand from your explanation how i am supposed to go about finding the answer. But may I know why the steps are taken to find the ans? why must we draw y=x?Thank you very much!
Hi,
the point on the graph where y=x intersects with y=18+3x-x^2 is the point where the horizontal distance of the stone from the building is the same as the height of the stone above the ground. This is because as mentioned previously, x represents the horizontal distance of the stone from the building and y represents the height of the stone above the ground.