# Hard maths question need helpWatch

#1
part c) is what im having issue with, i have found k < 37/4, but have no clue how to find the other value, which is meant to be k=7?
Last edited by ccc8; 1 week ago
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#2
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1 week ago
#3
(Original post by ccc8)
part c) is what im having issue with, i have found k < 37/4, but have no clue how to find the other value, which is meant to be k=7?
If you managed to draw the sketch in (b)(i), you'll know that you have a portion of a parabola. Now consider the line x + y = k drawn on the same graph. You should be able to see that there are only certain positions where the line intersects the parabola in two places. You have found one condition on k for this to happen - that's the condition for the line not to be too "far up". But you should also be able to see that if the line moves too "far down", it will only intersect the parabola at one point.

The limiting case is where the line passes through the right-hand endpoint of the parabola. Take the coordinates of this point, plug them into the equation of the line, and see what you get.
1
#4
oh i completely understand now thank you
(Original post by Pangol)
If you managed to draw the sketch in (b)(i), you'll know that you have a portion of a parabola. Now consider the line x + y = k drawn on the same graph. You should be able to see that there are only certain positions where the line intersects the parabola in two places. You have found one condition on k for this to happen - that's the condition for the line not to be too "far up". But you should also be able to see that if the line moves too "far down", it will only intersect the parabola at one point.

The limiting case is where the line passes through the right-hand endpoint of the parabola. Take the coordinates of this point, plug them into the equation of the line, and see what you get.
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