Answer:
QR=18
Step-by-step explanation:
QR/QO =QS/QP (proportionality theorem...OP||RS )
QR/39 =24/52 
52QR = 24(39)
52Q2=936
QR=18 
 
        
             
        
        
        
You have to complete the square to get it into vertex form.  Do this by setting the function equal to zero and at the same time moving the constant over to the other side of the equals sign so you have this: 

.  Now we can complete the square on the polynomial by taking half the linear term, squaring it, and adding it to both sides.  Our linear term is 4. Half of 4 is 2, and 2 squared is 4, so we add 4 to both sides: 

 and simplify to get 

.  In this process we have created a perfect square binomial on the left, which happens to be 

.  Now move the -6 back over by addition to get 

.  The vertex is found at (-2, 6), the third choice down.
 
        
        
        
M=4n+11 
-6n+8m=36
-6n + 8(4n+11) = 36
-6n + 32n + 88 = 36
26n = 36 - 88
26n = -52
n = -2
m = 4n+11 = 4(-2) + 11 = 3
Answer: (3, -2)
        
                    
             
        
        
        
The angular speed of the wheel is calculated as 52.36 radians per second
<h3>How to solve for the angular speed</h3>
The revolution of this wheel is said to be at 500 in a minute
This is also called the frequency of this wheel.
This can be written as 
500rev in 60 seconds. 500/60 = 8.333 per second
Angular speed is given as 
pi = 22/7
f = 8.333
Formular for angular speed = ω = 2*pi*f
w = 2 * 22/7 * 8.333
= 52.36 radians per second
Read more on angular speed here: 
brainly.com/question/6860269
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