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4 years ago

Find an equation equivalent to xy = 1 in polar coordinates.

Mathematics

2 answers:

Xelga [282]4 years ago

8 0

Answer:

r²sinθcosθ = 1 OR r²sin2θ = 2

Step-by-step explanation:

Polar coordinates are represented in of the radius r and angle θ.

In the x axis:

x = rcosθ

Along the y-axis:

y = rsinθ

Rectangular coordinate to polar coordinate will be:

(x, y) = (rcosθ, rsinθ)

To convert the equation xy = 1 to polar coordinate, we will substitute the value of x and y in its polar form into the given equation to have:

(rcosθ)(rsinθ) = 1

r²sinθcosθ = 1...(1)

From the trigonometry identity

Sin2θ = 2sinθcosθ

Sinθcosθ = sin2θ/2...(2)

Substituting equation 2 into 1:

r²(sin2θ/2) = 1

r²sin2θ = 2

igomit [66]4 years ago

4 0

Answer:

Step-by-step explanation:

Just took the test on Edge 2020

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Nonamiya [84]

Answer:

x = -8/b

Step-by-step explanation:

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Combine like terms

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Divide by b

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3 years ago

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frozen [14]

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4 years ago

The function that represents bruce’s elevation in feet over time in hours is an exponential function that starts at 1,505 feet.

Strike441 [17]

Answer:

<h3>The function for Bruce’s elevation is $f(x)=1505(6)^x$ and because b=6 that is greater than 0, it is an exponential growth function.</h3>

Step-by-step explanation:

We are given initial Bruce’s elevation = 1,505 feet.

Each successive hour, his average elevation change for the hike becomes 6 times the previous hourly elevation change.

We know, the exponential function $f(x)=a(b)^x$ , where a is the initial value, b is the growth factor and x is the exponent represents time in hours.

Therefore, initial value a=1505, growth factor b for exponential function $f(x)=a(b)^x$ is 6.

Plugging a=1505 and b=6 in $f(x)=a(b)^x$ , we get

$f(x)=1505(6)^x$

Also note, if b>0, it would be an exponential growth function.

<h3>Therefore, the function for Bruce’s elevation is $f(x)=1505(6)^x$ and because b=6 that is greater than 0, it is an exponential growth function.</h3>

8 0

4 years ago