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Ivahew [28]
3 years ago
9

Find the slope of the curve r=cos(2theta) at theta=pi/6.. . Must this be solved parametrically? If so, why?

Mathematics
1 answer:
lara31 [8.8K]3 years ago
6 0

By converting into parametric equations,

<span><span>x(θ)=r(θ)cosθ=cos2θ<span>cosθ
</span></span><span>y(θ)=r(θ)sinθ=cos2θsinθ</span></span>

By Product Rule,

<span>x'(θ)=−sin2θcosθ−cos2θsinθ</span>

<span>x'<span>(π/2)</span>=−<span>sin(π)</span><span>cos<span>(π/2)</span></span>−<span>cos(π)</span><span>sin<span>(π/2)</span></span>=1</span>

<span>y'(θ)=−sin2θsinθ+cos2θcosθ</span>

<span>y'<span>(π/2)</span>=−<span>sin(π)</span><span>sin<span>(π/2)</span></span>+<span>cos(π)</span><span>cos<span>(π/2)</span></span>=0</span>

So, the slope m of the curve can be found by

<span>m=<span>dy/dx</span><span>∣<span>θ=<span>π2
</span></span></span>= <span><span>y'<span>(π/2)/</span></span><span>x'<span>(π/2)
</span></span></span></span>=0/1

=0

I hope my answer has come to your help. Thank you for posting your question here in Brainly.

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What is the squre root of 32 divided by five plus the square root of 18 divided by 7
Marta_Voda [28]
Hi!

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The answer is <span>0.767715934

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A school is building a rectangular soccer field that has an area of 6000 square yards .the soccer field.must be 40 yards longer
LekaFEV [45]

Answer:

The equation in standard form is:

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Step-by-step explanation:

Let the length of the field be x yards.

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Thus, the width of the field would be (x-40) yards

Now, to calculate the area of the field, we simply multiply the length of the field by the width of the field.

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Answer:

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Start with y = 9x - 5 and substitute the coordinates of the given point (-1, 6):

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