Answer:

Step-by-step explanation:
So, the function, P(t), represents the number of cells after t hours. 
This means that the derivative, P'(t), represents the instantaneous rate of change (in cells per hour) at a certain point t. 
C) 
So, we are given that the quadratic curve of the trend is the function: 

To find the <em>instanteous</em> rate of growth at t=5 hours, we must first differentiate the function. So, differentiate with respect to t: 
![\frac{d}{dt}[P(t)]=\frac{d}{dt}[6.10t^2-9.28t+16.43]](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdt%7D%5BP%28t%29%5D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B6.10t%5E2-9.28t%2B16.43%5D)
Expand: 
![P'(t)=\frac{d}{dt}[6.10t^2]+\frac{d}{dt}[-9.28t]+\frac{d}{dt}[16.43]](https://tex.z-dn.net/?f=P%27%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B6.10t%5E2%5D%2B%5Cfrac%7Bd%7D%7Bdt%7D%5B-9.28t%5D%2B%5Cfrac%7Bd%7D%7Bdt%7D%5B16.43%5D)
Move the constant to the front using the constant multiple rule. The derivative of a constant is 0. So: 
![P'(t)=6.10\frac{d}{dt}[t^2]-9.28\frac{d}{dt}[t]](https://tex.z-dn.net/?f=P%27%28t%29%3D6.10%5Cfrac%7Bd%7D%7Bdt%7D%5Bt%5E2%5D-9.28%5Cfrac%7Bd%7D%7Bdt%7D%5Bt%5D)
Differentiate. Use the power rule: 

Simplify: 

So, to find the instantaneous rate of growth at t=5, substitute 5 into our differentiated function: 

Multiply: 

Subtract: 

This tells us that at <em>exactly</em> t=5, the rate of growth is 51.72 cells per hour. 
And we're done!
 
        
             
        
        
        
Answer:
84/90
Step-by-step explanation:
Let 0.9333....... be x.
10x = 9.3333....... & 100x = 93.33333.......
So,
=> 100x - 10x = 93.33333...... - 9.333333.....
=> 90x = 84
=> x = 84/90
 
        
                    
             
        
        
        
Answer:
A
Step-by-step explanation:
 
        
             
        
        
        
Answer:
14.7%
Step-by-step explanation:
82/12 = 100/x
x= 14.7
 
        
             
        
        
        
Complementary angles add up to 90 degrees. We know that AXB is 20 degrees, and AXB is complementary to CYD and FZE. So CYD and FZE are 90-20, so each angle is 70 degrees
CYD = 70 degrees
FZE = 70 degrees
CYD + FZE = 70 + 70 = 140