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:
The number is 4321
Step-by-step explanation:
Let the number be x
16 2/3% = (16x3+2)/3 % = 50/3 %
50/3 % of X = 72
50/300 x X =72
X=(72 x 300)/50
X=21600/50
X=4321
Answer:
4 and 6
Step-by-step explanation:
First, let's find all the pairs that add up to 10.
- 1 + 9, 2 + 8, 3 + 7, 4 + 6, and 5 + 5
Next, we find the difference between the addends for each pair.
- 9 - 1 = 8
- 8 - 2 = 6
- 7 - 3 = 4
- 6 - 4 = 2
- 5 - 5 = 0
As you can, see the numbers that add to 10 and have a different of 2 is 4 and 6.
Let x gallons be the amount of pure antifreeze that should be added to the 30% solution to produce a solution that is 65% antifreeze. Then the total amount of antifreeze solution will be x+3 gallons.
There are 30% of pure antifreeze in 3 gallons of solution, then
3 gallons - 100%,
a gallons - 30%,
where a gallons is the amount of pure antifreeze in given solution.
Mathematically,
Now in new solution there will be x+0.9 gallons of pure antefreeze.
x+3 gallons - 100%,
x+0.9 - 65%
or
Answer: he should add 3 gallons of pure antifreeze.
Answer: D
Step-by-step explanation:
Standard Deviation σ2 =
Σ(xi - μ)2/N
=(1 - 5.3)2 + ... + (9 - 5.3)2/10
=68.1/10
= 6.81
σ = √6.81
= 2.60959767014
B) σ2 =
Σ(xi - μ)2/N
=(3 - 61.7)2 + ... + (99 - 61.7)2/10
=58414.1/10
= 5841.41
σ = √5841.41
= 76.429117488036
C) (1 - 11.4)2 + ... + (1 - 11.4)2/10
=8758.4/10
= 875.84
σ = √875.84
= 29.59459410095
D) (79 - 79)2 + ... + (79 - 79)2/10
=0/10
= 0
σ = √0
= 0
I hope this helps, mark as Brainliest please.
