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2 years ago

1. What is the slope of the line tangent to the curve defined by y2 + xy - x2 = 11x at the point (2, 3)?

Mathematics

1 answer:

andreyandreev [35.5K]2 years ago

7 0

Step-by-step explanation:

By using Implicit Differentiation,

d/dx (y² + xy - x²) = d/dx (11x)

d/dx (y²) + d/dx (xy) - d/dx (x²) = 11

2y * dy/dx + x * dy/dx + y - 2x = 11

dy/dx (2y + x) = 11 + 2x - y

dy/dx = (11 + 2x - y) / (2y + x).

At the point (2, 3), we have x = 2, y = 3.

=> dy/dx = (11 + 2(2) - (3)) / (2(3) + (2))

= 12 / 8 = 1.5.

P.S. Your question is weird because (2,3) is not on the graph, let me know what is the correct question thanks!

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Evgesh-ka [11]

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Height = 14.4

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The diagonals meet at right angles. Interesting property.

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You can find the other side of the the triangle by using the Pythagorean Theorem

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b = 9

The area of this right angle = 9 * 12/2 = 54

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Step-by-step explanation:

From the figure it is clear that:

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For y:

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