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:
Option C.
Step-by-step explanation:
It is given that the dilation rule is 
. It means the center of dilatation is point Q and scale factor is 2.5.
Scale factor is the ratio of distance from center to the image of a point and distance from center to the corresponding point.
It is given that QU=4 and scale factor = 2.5.
Multiply both sides by 4.
We know that
The distance between U' and U is 6 units.
Therefore, the correct option is C.
Answer: C
Step-by-step explanation:
Okay first set a comparison since the two triangles are similar
x-1/20=x-1+27/3x+8
x-1/20 = x+26/3x+8
cross multiply
20x+520=3x^2+8x-3x-8
3x^2-15x-528=0
3(x^2-5x-176)=0
im kinda lazy to factor this out so i used an online calculator right here but factor it out like a good kid
x=16, x=-11
it has to be positive so x=16
C
Distance=speed x time
so it would be 28 x 6=168
Answer:
359/4
Decimal: 89.75
Step-by-step explanation:
