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Lostsunrise [7]

3 years ago

6

Determine if the segment X is half the length, double the length, two thirds the length, or the same length as segment Y.

1 answer:

Ipatiy [6.2K]3 years ago

6 0

The right answer is The Same Length.
The triangle displayed is Isosceles. The explanation of this statement is the fact that the Line which is making a right angle it is also the one that slices the segment into equal segments. Mathematically speaking, in our triangle the
Median is perpendicular on the segment from which results that the triangle is Isosceles and x = y.

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Arisa [49]

ANSWER

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EXPLANATION

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Recall and use the product rule of logarithms.

$ln(AB) = ln(A ) + ln(B)$

This implies that:

$ln(y) = ln({x}^{2} ) + ln( \cos(x) )$

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We now differentiate implicitly to obtain;

$\frac{ {y}^{'} }{y} = \frac{2}{x} - \frac{ \sin(x) }{ \cos(x) }$

Multiply through by y,

${y}^{'} = y( \frac{2}{x} - \frac{ \sin(x) }{ \cos(x) ) })$

Substitute y=x²cosx to obtain;

${y}^{'} = {x}^{2} \cos(x) ( \frac{2}{x} - \frac{ \sin(x) }{ \cos(x) ) } )$

Expand:

${y}^{'} = 2x \cos(x) - {x}^{2} \sin(x)$

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