1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
MArishka [77]
3 years ago
10

50 points! I understand A. and B. but I would really appreciate help with C.

Mathematics
1 answer:
FromTheMoon [43]3 years ago
7 0

Answer:

51.72\text{ cells per hour}

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:

P(t)=6.10t^2-9.28t+16.43

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]

Expand:

P'(t)=\frac{d}{dt}[6.10t^2]+\frac{d}{dt}[-9.28t]+\frac{d}{dt}[16.43]

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]

Differentiate. Use the power rule:

P'(t)=6.10(2t)-9.28(1)

Simplify:

P'(t)=12.20t-9.28

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

P'(5)=12.20(5)-9.28

Multiply:

P'(5)=61-9.28

Subtract:

P'(5)=51.72

This tells us that at <em>exactly</em> t=5, the rate of growth is 51.72 cells per hour.

And we're done!

You might be interested in
What does 7m- m equal
Norma-Jean [14]
7m-m\rightarrow7m-1m=m(7-1)\rightarrow6m

7m-m is equal to 6m.

4 0
1 year ago
A number cube is rolled. Find the Probability. (4 or 5)​
nikklg [1K]

Answer: 2/6 or 33%

Step-by-step explanation: Hope this helps <3

6 0
2 years ago
BRAINLIEST!
kodGreya [7K]
<span>4y - 12x = 20 
4y = 12x + 20
  y = 3x + 5
parallel has same slope = 3

answer
</span><span>A. Y = 3x - 1 </span>
4 0
3 years ago
One person wants to get a 95% z-confidence interval with a margin of error of at most 15 based on a population standard deviatio
Bess [88]

Answer:

n=(\frac{1.96(60)}{15})^2 =61.46 \approx 62  

So the answer for this case would be n=62 rounded up to the nearest integer  

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

\bar X represent the sample mean for the sample  

\mu population mean

\sigma=60 represent the population standard deviation  

n represent the sample size (variable of interest)  

Confidence =95% or 0.95

The margin of error is given by this formula:  

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}} (1)  

And on this case we have that ME =15, and we are interested in order to find the value of n, if we solve n from equation (1) we got:  

n=(\frac{z_{\alpha/2} \sigma}{ME})^2 (2)  

The critical value for 95% of confidence interval is provided, z_{\alpha/2}=1.96, replacing into formula (2) we got:  

n=(\frac{1.96(60)}{15})^2 =61.46 \approx 62  

So the answer for this case would be n=62 rounded up to the nearest integer  

6 0
3 years ago
PLEASE HELP! WILL GIVE BRAINLIEST!!
Maslowich

Your answer is -6+3i.

6 0
3 years ago
Read 2 more answers
Other questions:
  • Use the quadratic formula to solve the equation.<br><br>-3x^2 - x - 3 = 0
    14·1 answer
  • Identify any outlier(s) in the data. <br> {79, 75, 125, 61, 78, 63, 88, 76, 68, 82, 67}
    5·1 answer
  • Factor 8X squared + 10x + 2​
    6·1 answer
  • HELP MEEEEEEEE PLZZZZ
    14·1 answer
  • I need to know the answer
    6·1 answer
  • Classify a triangle with sides measuring 5, 7 and 8.
    10·1 answer
  • 14. Taxi company A charges $2 per ride plus $0.25 per mile. Taxi company B charges $3 per ride plus $0.15 per mile. Which equati
    11·1 answer
  • function h(t) =-167 + 80t + 3 where t is the number of seconds after the ball is thrown. What is the value of h(t), two seconds
    15·1 answer
  • 1) 2(x + 3) = x - 4<br><br> 2) 4(5x-2)=2(9x+3)
    14·1 answer
  • Which equation can be simplified to find the inverse of y = 5x^2 + 10?<br>​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!