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Nothing wrong with "Research"....LOL!!!!

Yes thank you, that's actually where I learned how to do it haha.

A: Construct the angle bisector of angle R.

BTW.....here's this step-by-step....pretty easy, actually  !!!

https://www.mathsisfun.com/geometry/construct-triangleinscribe.html

5.  If the directrix  is  above the vertex, as in this case,  this parabola turns downward

So.....p  = the distance from the directrix to the vertex  = 5

So....we have the form

-4py  = x^2

-4(5)y = x^2

-20y  = x^2      divide both sides by -20

y  = (-1/20)x^2

6)  First.. in the form  x  = ay^2  ...the vertex is at the origin

x = (1/24)y^2    multiply both sides by 24

24x = y^2

We have the form

4px  = y^2         so   4p  = 24  ⇒   p  = 6

This parabola opens to the right  so  the focus  is   (0 + p, 0)  = (0 + 6 , 0 )  = (6, 0)

The directrix   is    x =  0 - p   ⇒  x  = 0 - 6  ⇒  x  = -6

The first one is A

Thank you a ton.

So it's basically just plugging with sin and cos?

sin θ   =   cos( 90° - θ )

So.....

sin 41°   =   cos( 90° - 41° )

sin 41°  =  cos x      Plug in   cos( 90° - 41° )   for  sin 41°

cos( 90° - 41° )   =   cos x

cos 49°   =   cos x

49°   =   x      

2.

Find  x  if  h(x)  =  9

h(x)  =  (1/4)x + 6         Plug in  9  for  h(x) .

9   =   (1/4)x + 6           Now solve this equation for  x . Subtract  6  from both sides.

3   =   (1/4)x                 Multiply both sides by  4 .

12  =  x

3.

Find  n  if  f(n)  =  f(3n + 1)

If  f(n)  =  f(3n + 1)   , then   n  must equal  3n + 1  .

n  =  3n + 1     Subtract  3n  from both sides of this equation.

n - 3n  =  1      Combine like terms.

-2n  =  1          Divide both sides by  -2 .

n  =  -1/2

What’s the difference?

You're a legend mate.

it comes up as math error

C  will be supplemental to A

So

A + C  =  180

89 + C  =  180      subtract 89 from both sides

C  = 91°

1.

(h - f)(4)   =   h(4) - f(4)

h(4)  =  (1/4)(4) + 6

h(4)  =  1 + 6

h(4)  =  7

f(4)  =  5(4) - 9

f(4)  =  20 - 9

f(4)  =  11

(h - f)(4)   =   h(4) - f(4)

(h - f)(4)   =   7 - 11

(h - f)(4)   =   -4

This is known as a cyclic quadrilateral......the opposite angles are suppllementary

So

x^2 + 78  + 10x + 46  = 180

x^2 + 10x + 124  =  180       subtract 180 from both sides

x^2 + 10x - 56  =  0  factor

(x - 4) ( x + 14)  = 0

Setting each factor to 0  and solving for x  produces

x = 4       and   x  =  -14

Reject the second since it produces negative angles

So  C  =   10(4)  + 46   =  86°

Find AI using Pythagoras:

AI² = (AC/2)² + (18+5)²

where AC² = 5² + 7²

To find angle AIE first find length EI.

EI² = (EH/2)² + 5²   and EH = AC

Having found AI and EI, now use the cosine rule to find AIE:

cos(AIE) = (AI² + EI² - 18²)/(2*AI*EI) so AIE = cos^-1((AI² + EI² - 18²)/(2*AI*EI))

I’ll leave you to crunch the numbers!

Your transformation rule is correct  !!!!!

The scale factor .....( since the radius is a linear measure)  from Circle 1  to Circle 2  is  just   9 / 15  =

3/5

Thank you for all your help. I tried doing this one multiple times by myself, but I didn't know it was equal to 180 instead of 3.14.

Very nice, hectictar  !!!

Just give me 15 minutes, I need a break

you are a GENIUS! LOVE YOU XX

I can!

In this case pi is equal to 180 degrees, not 3.14159265358979323846...

2pi/3 is (2*180)/3 = 120. The center angle is 120 degrees which is 1/3 of the whole circle. 

All we need to do is find the length of the circumference. 

24 * 2 * pi = 48 pi 

48 pi / 3 = 16 pi 

16pi is the final answer. 

Since the sine and cosine are co-functions, the sum of these two angles will  =  90°

So we have

[x + 34 ]  + [ 2x + 20]   =  90    simplify

3x + 54  = 90     subtract 54 from both sides

3x  = 36      divide both sides by 3

x = 12