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.
We want to write an inequality that tells how much Hannah should walk this week. The inequality will be:
x ≥ (3 + 3/4) mi
<h3>
Finding the inequality:</h3>
We know that she already did walk 2 3/4 miles this week, and she wants to walk at least 6 1/2 miles.
So to reach that minimum, she needs to walk:
(6 1/2)mi - (2 + 3/4) mi = (3 + 3/4) mi
And she can walk that or more, so the inequality is:
x ≥ (3 + 3/4) mi
Where x represents how much she will walk this week.
If you want to learn more about inequalities, you can read:
brainly.com/question/11234618
This relation is a function. None of the x-values repeat. Each y-value belongs to a specific x-value.
