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
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Answer:
Answer:(0,3)Step-by-step explanation:The solution in a set of graphs is where they intersect. In this graph, they intersect at (0,3)
Answer:
31
Step-by-step explanation:
100-7= 93
93÷3=31
Answer:
m∠1=80°, m∠2=35°, m∠3=33°
Step-by-step explanation:
we know that
The sum of the interior angles of a triangle must be equal to 180 degrees
step 1
Find the measure of angle 1
In the triangle that contain the interior angle 1
∠1+69°+31°=180°
∠1+100°=180°
∠1=180°-100°=80°
step 2
Find the measure of angle 2
In the small triangle that contain the interior angle 2
∠2+45°+(180°-∠1)=180°
substitute the value of angle 1
∠2+45°+(180°-80°)=180°
∠2+45°+(100°)=180°
∠2+145°=180°
∠2=180°-145°=35°
step 3
Find the measure of angle 3
In the larger triangle that contain the interior angle 3
(∠3+31°)+69°+47°=180°
∠3+147°=180°
∠3=180°-147°=33°