The vertex where the two triangles touch forms a pair of vertical angles, so that the angles on opposites sides of the vertex are congruent. You're shown that two legs of both triangles are congruent. All this tells you that the two triangles are isosceles, and furthermore that they are similar because of the congruence of their "base" angles.
This means
Answer:
18245
Step-by-step explanation:
We have to use L.C.M,
L.C.M(20,24,32,38)
2|20,24,32,38
2| 10 ,12 ,16 ,19
2| 5 , 6 , 8 , 19
2| 5 , 3 , 4 , 19
2| 5 , 3 , 2 , 19
L.C.M = 2 x 2 x 2 x 2 x 2 x 2 x 5 x 3 x 19
= 18240
Now for each case remainder is 5,
So the number is 18240+5
=> 18245
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.
Answer:
(3, 4) and (5, 12)
Step-by-step explanation:
The points where the two curves intersect are the solutions to the system of equations:
(3, 4) and (5, 12)
