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garik1379 [7]
3 years ago
14

Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 2 cos 5θ

Mathematics
2 answers:
Finger [1]3 years ago
5 0

Answer:

The graph is symmetric about the x-axis.

Step-by-step explanation:

1. Symmetry about the x-axis: If the point (r, θ ) lies on the graph, then the point  (r, -θ ) or (-r, π - θ ) also lies on the graph.

2. Symmetry about the y-axis: If the point (r, θ ) lies on the graph, then the point (r,  π - θ ) or (-r, -θ ) also lies on the graph.

3. Symmetry about the origin: If the point (r, θ ) lies on the graph, then the point (-r, θ ) or (r, π + θ ) also lies on the graph.

The given polar equation is

r=2\cos (5\theta)

Check the equation by (r, -θ).

r=2\cos (-5\theta)=2\cos (5\theta)=r

Therefore, the graph is symmetric about the x-axis.

Check the equation by (-r, -θ).

-r=2\cos (-5\theta)=2\cos (5\theta)=r\neq -r

Therefore, the graph is not symmetric about the y-axis.

Check the equation by (-r, θ).

-r=2\cos (5\theta)=2\cos (5\theta)=r\neq -r

Therefore, the graph is not symmetric about the origin.

murzikaleks [220]3 years ago
3 0
Looking at the graph, we'll notice that there is a local maximum at x=0 and it looks similar on both sides of the y axis, therefore making it symmetric around the y axis given the options
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The ratio of the number of mystery books to the number of science fiction books is 4:3. The ratio of the number of science ficti
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7 0
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Find the equation of the tangent line to the curve y equals left parenthesis x minus 3 right parenthesis superscript 7 baseline
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We have been given the expression to be y=(x-3)^7(x+1)^2

Since we need to find the tangent at a point, we will have to find the derivative of y as the slope of the tangent at a given point on the curve is always equal to value of the derivative at that point.

Thus, we have to find \frac{dy}{dx}=\frac{d}{dx} (x-3)^7(x+1)^2

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y'_{x=4}=Slope of the tangent of y at x=4=m

Thus, m=(4-3)^6(4+1)(9\times4+1)=185

Now, the equation of the tangent line which passes through (x_{1}, y_{1}) and has slope m is given by:

y-y_{1}=m(x-x_{1})

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Which can be simplified to y=185x-740+25=185x-715

Thus, y=185x-715

This is the required equation of the tangent.

3 0
3 years ago
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