Jake ran several laps around a 14mile track. then he ran 212miles on a trail. in all he ran 4 miles. write and solve an equation for l, the number of laps jake ran.

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Ответ:

chartrow7

12.11.2021

Mathematics

The location of A' is A'(x,y) = (2,-1) .

Step-by-step explanation:

We know the location of A in rectangular form and must transform it into polar form, which is represented by magnitude (), dimensionless, and direction ( $\theta$ ), measured in sexagesimal degrees. Let suppose that rotation is counterclockwise and around the origin:

Magnitude

$r = \sqrt{x^{2}+y^{2}}$ (1)

Direction

$\theta = \tan^{-1}\frac{y}{x}$ (2)

The location of A' is determined by the following expression:

$A'(x,y) = (r\cdot \cos (\theta+180^{\circ}), r\cdot \sin (\theta+180^{\circ}))$

If we know that A(x,y) = (-2, 1) , then the location of A' is:

$r = \sqrt{(-2)^{2}+1^{2}}$

$r =\sqrt{5}$

$\theta = \tan^{-1}\left(\frac{1}{-2}\right)$

$\theta \approx 153.435^{\circ}$

$A'(x,y)=(\sqrt{5}\cdot \cos (153.435^{\circ}+180^{\circ}), \sqrt{5}\cdot \sin (153.435^{\circ}+180^{\circ}))$

A'(x,y) = (2,-1)

The location of A' is A'(x,y) = (2,-1) .

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