Xy=1 in polar coordinates

2 answers:

8 0

$xy=1\iff (r\cos\theta)(r\sin\theta)=r^2\sin\theta\cos\theta=\dfrac12r^2\sin2\theta=1$
$\implies r^2=2\csc2\theta$
$\implies r=\sqrt{2\csc2\theta}$

where we ignore the second root and use the convention that $r>0$ .

Goshia [24]3 years ago

3 0

Answer:

The answer is r^2 * sin 2(theta) = 2!

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Pani-rosa [81]

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Step-by-step explanation:

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Sholpan [36]

This is a linear relationship. The slope-intercept form of the linear equation is:

$y=mx+c$

Where,

m is the rate of change (positive if increasing rate and negative if decreasing rate)
c is the y intercept, or the initial value

Rate of change is 2.5 quarts per minute (it is decreasing so m is -2.5)

Initial value is 50 quarts, so c is 50.

Plugging in the values we get $y=-2.5x+50$ .

Changing variables to w instead of y and t instead of x, gives us,

$w=50-2.5t$ . Where w is warts of water left in the tub and t is the time in minutes.

There is no viable solution when t=30 because at t=20, w=0 ( $0=50-2.5(20)$ ). It means after 20 minutes, there is no water left. So t=30 minutes doesn't make sense.