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Tanya [424]
2 years ago
8

Can someone help me pls

Mathematics
2 answers:
Elena-2011 [213]2 years ago
5 0

For MN to be tangent, angle N would need to be 90 degrees making the triangle a right triangle.

Using the Pythagorean theorem uses the base and the height to see if it equals what is shown for the hypotenuse. If it does it is tangent.

Hypotenuse = SQRT(18^2 + 80^2)

Hypotenuse = sqrt(324 + 6400)

Hypotenuse = sqrt(6724)

Hypotenuse = 82

This matches the 82 shown in the picture, so it is a right triangle, making MN tangent to circle L.

motikmotik2 years ago
4 0

Answer:

the only explanation to this is segment MN is tangent to circle L because it touches the circle L in one point

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Compute the derivative dy/dx using the power, product, and chain rules. Given

x³ + y³ = 11xy

differentiate both sides with respect to x to get

3x² + 3y² dy/dx = 11y + 11x dy/dx

Solve for dy/dx :

(3y² - 11x) dy/dx = 11y - 3x²

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The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when

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Substitute y into into the original equation:

x³ + (3/11 x²)³ = 11x (3/11 x²)

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(3/11)³ x⁶ - 2x³ = 0

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One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with

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y = 3/11 x²

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y = (11•³√4)/3

So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).

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Step-by-step explanation:

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