5 and 7 since rectangles must have a pair of each sides
(a) <TOR=pi/3 radians
To determine <TOR we use the fact that in the right-angled triangle ORT we know two sides:
|OT|=radius=8cm and |OR|=radius/2=4cm
and can use the sine:

and since <TRO=pi/2, it must be that

(b) The arc length is approximately 7.255 cm
In order to calculate the arc length QT, we need to first determine the length |ST| and the angle <OST.
Towards determining angle <OST:

Next, draw a line connecting P and T. Realize that triangle PTS is right-angled with <PTS=pi/2. This follows from the Thales theorem. Since R is a midpoint between P and O, it follows that the triangles ORT and PRT are congruent. So the angles <PTR and <OTR are congruent. Knowing <PTS we can determine angle <OTS:

and so the angle <OST is

Towards determining |TS|:
Use cosine:

Finally, we can determine the arc length QT:

<h2> <u>Answer</u> :</h2>

<h2><u>Solution</u> :</h2>
According to a Trigonometric Identity :

Now, let's solve for 





24x⁶ - 1029y³ =
3(8x⁶ - 343y³) =
3((2x²)³ - (7y)³) =
3(2x²-7y)(4x⁴ + 14x²y + 49y²)
Answer is <span>D) All of the above.</span>