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Nastasia [14]
3 years ago
14

The straight line 2x + 3y = 7 meets the curve

Mathematics
1 answer:
NISA [10]3 years ago
5 0

Step-by-step explanation:

xy + 10 = 0. => y = -10/x.

2x + 3y = 7. => 3y = -2x + 7, y = -2/3 x + 7/3.

When -10/x = -2/3 x + 7/3,

-10 = -2/3 x² + 7/3 x, 2/3 x² - 7/3 x - 10 = 0.

=> 2x² - 7x - 30 = 0

=> (2x + 5)(x - 6) = 0

=> x = -2.5 or x = 6.

dy/dx = d/dx [-10/x] = 10/x².

When x = -2.5, dy/dx = 10 / (-2.5)² = 1.6.

When x = 6, dy/dx = 10 / (6)² = 5/18.

Hence the gradients at the points are 1.6 and 5/18.

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Answer:

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Step-by-step explanation:

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for instance on table one: I put y=4x into desmos then looked at graph one, I chose the point (2,8) I went to 2 on the x axis and moved my finger up 8 and that point was directly on the line meaning that table matches the equation. be sure to also do the same thing with the other points to double check!
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