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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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Answer:

$92.50

Step-by-step explanation:

$72 - $35 = 37

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8 0
3 years ago
Two times the sum of a number and 8 subtracted from the number equals 6. What is the number that makes this statement true?
Zanzabum

Answer:

7

Step-by-step explanation:

let the no. be 'x'

By question,

2x-8=6

or, 2x =6+8

or,2x = 14

or,x = 7

therefore, the no. is 7.

5 0
3 years ago
5.5.5.5.4.4.4 in exponential form.
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5^4 and 4^3

hope it helps!

if not, sorry...

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3 years ago
(84x - 69y) - (65x + 34y)
Svetach [21]

(84x - 69y) - (65x + 34y)

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Combine for final answer:

19x -103y

6 0
3 years ago
47.9 less than k is -21.6
Law Incorporation [45]
K is equal to -69.5 K=69.5 You put it in an equation 47.9-K=-21.6Then you subtract 47.9 from both sides and you get K=69.5 
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