Answer:
5(15+4)
Step-by-step explanation:
I think this is the answer. I don't understand the question but I did factor out the problem
Answer:
Vertical angles are across from each other on any two intersecting lines and are always congruen
Answer:
My proof is in the explanation.
Step-by-step explanation:
This is a two-column proof.
One column for statements and the other for the reason for that statement.
Hopefully it shows up well on your screen. Let me know if it doesn't.
Statement | Reason
1) CD is the perpendicular 1) Given
bisector of AB
2) AD=DB 2) Definition of bisector
3) CD=CD 3) Reflexive property
4) mAngleCDA=90 4) Definition of perpendicular
5) mAngleCDB=90 5) Definition of perpendicular
6) mAngleCDA=mAngleCDB 6) Substitution property
7) Corresponding parts of each 7) SAS
triangle are congruent (side-angle-side)
8) AC=CB 8) The two triangles are ............................................................................congruent so
the corresponding parts ............................................................................are
congruent.
The slope of the tangent line to the curve at a point <em>(x, y)</em> is d<em>y</em>/d<em>x</em>. By the chain rule, this is equivalent to
d<em>y</em>/d<em>θ</em> × d<em>θ</em>/d<em>x</em> = (d<em>y</em>/d<em>θ</em>) / (d<em>x</em>/d<em>θ</em>)
where <em>y</em> = <em>r(θ)</em> sin(<em>θ</em>) and <em>x</em> = <em>r(θ)</em> cos(<em>θ</em>). Then
d<em>y</em>/d<em>θ</em> = d<em>r</em>/d<em>θ</em> sin(<em>θ</em>) + <em>r(θ)</em> cos(<em>θ</em>)
d<em>x</em>/d<em>θ</em> = d<em>r</em>/d<em>θ</em> cos(<em>θ</em>) - <em>r(θ)</em> sin(<em>θ</em>)
Given <em>r(θ)</em> = cos(3<em>θ</em>), we have
d<em>r</em>/d<em>θ</em> = -3 sin(3<em>θ</em>)
and so
d<em>y</em>/d<em>x</em> = (-3 sin(3<em>θ</em>) sin(<em>θ</em>) + cos(3<em>θ</em>) cos(<em>θ</em>)) / (-3 sin(3<em>θ</em>) cos(<em>θ</em>) - cos(3<em>θ</em>) sin(<em>θ</em>))
When <em>θ</em> = <em>π</em>/3, we end up with a slope of
d<em>y</em>/d<em>x</em> = (-3 sin(<em>π</em>) sin(<em>π</em>/3) + cos(<em>π</em>) cos(<em>π</em>/3)) / (-3 sin(<em>π</em>) cos(<em>π</em>/3) - cos(<em>π</em>) sin(<em>π</em>/3))
d<em>y</em>/d<em>x</em> = -cos(<em>π</em>/3) / sin(<em>π</em>/3)
d<em>y</em>/d<em>x</em> = -cot(<em>π</em>/3) = -1/√3
Answer: γ≈14.71deg
or
165.29deg
Step-by-step explanation:
