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marin [14]
2 years ago
9

Given that AXB is complementary to both CYD and FZE, and mAXB = 36°, what is mCYD + mFZE?

Mathematics
1 answer:
anyanavicka [17]2 years ago
7 0
Complementary angles always equal 90°
So here is how to find what mCYD + mFZE equal 
mCYD + mFZE + mAXB
mCYD + mFZE + 36° = 90°
Subtract 
mCYD + mFZE = 54°
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Maurinko [17]

Hello from MrBillDoesMath!

Answer:

x = 1/2 (1 +\- i sqrt(23))

Discussion:

x \3x - 2 =   (x/3)*x - 2   =  (x^2)/3 - 2     (*)

1 \3x - 4   =  (1/3)x - 4                               (**)

(*) = (**)   =>

(x^2)/3 -2 = (1/3)x - 4        => multiply both sides by 3

x^2 - 6 = x - 12                 => subtract x from both sides

x^2 -x -6 = -12                   => add 12 to both sides

x^2-x +6  = 0

Using the quadratic formula gives:

x = 1/2 (1 +\- i sqrt(23))

Thank you,

MrB

4 0
2 years ago
How cos π/3=1/2?<br>having some problems learning continuity.
Bingel [31]

You can show that \cos\frac\pi3=\frac12 by constructing a triangle.

Take two points, O(0, 0) and A(1, 0), and let B be the point on the unit circle such that the angle between the line segments OA and OB is \frac\pi3 radians.

Since both A and B lie on the circle, the line segments OA and OB both have length 1 (same as the circle's radius). We finish constructing the triangle by connect A and B.

Since OB and OA have the same length, triangle OAB is isosceles, but more than that, it's also equilateral. Why? Because the interior angles of any triangle always add to \pi radians. We know one of the angles is \frac\pi3 radians, which leaves a contribution of \frac{2\pi}3 radians between the remaining angles A and B. Angles A and B must be congruent (because OAB is isosceles), which means they also have measure \frac\pi3 radians.

Next, draw an altitude of the triangle through point B, and label the point where it meets the "base" OA, C. Since OAB is equilateral, the altitude BC is also a perpendicular bisector. That means OC has length \frac12, and by definition of \cos we have

\cos\dfrac\pi3=\dfrac{OC}{OB}=\dfrac{\frac12}1=\dfrac12

3 0
3 years ago
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