P(t)=500(1+4t/(50+t^2 ))
P'(t) = 500 [(50+t^2).4 - 4t.2t]/(50+t^2)^2
by the quotient rule
500 (-4t^2 + 200)/(t^2 + 50)^2
Hence
P'(2) = 500 . (-16 + 200)/54^2 ~= 31.6
Answer:
2/5
Step-by-step explanation:
Hence, simplest form of 34/85 is 2/5.
Answer:
Step-by-step explanation:
In order to write the series using the summation notation, first we need to find the nth term of the sequence formed. The sequence generated by the series is an arithmetic sequence as shown;
4, 8, 12, 16, 20...80
The nth term of an arithmetic sequence is expressed as Tn = a +(n-1)d
a is the first term = 4
d is the common difference = 21-8 = 8-4 = 4
n is the number of terms
On substituting, Tn = 4+(n-1)4
Tn = 4+4n-4
Tn = 4n
The nth term of the series is 4n.
Since the last term is 80, L = 4n
80 = 4n
n = 80/4
n = 20
This shows that the total number of terms in the sequence is 20
According to the series given 4 + 8 + 12 + 16 + 20+ . . . + 80
, we are to take the sum of the first 20terms of the sequence. Using summation notation;
4 + 8 + 12 + 16 + 20+ . . . + 80 =
One of the major advantage of the two-condition experiment has to do with interpreting the results of the study. Correct scientific methodology does not often allow an investigator to use previously acquired population data when conducting an experiment. For example, in the illustrative problem involving early speaking in children, we used a population mean value of 13.0 months. How do we really know the mean is 13.0 months? Suppose the figures were collected 3 to 5 years before performing the experiment. How do we know that infants haven’t changed over those years? And what about the conditions under which the population data were collected? Were they the same as in the experiment? Isn’t it possible that the people collecting the population data were not as motivated as the experimenter and, hence, were not as careful in collecting the data? Just how were the data collected? By being on hand at the moment that the child spoke the first word? Quite unlikely. The data probably were collected by asking parents when their children first spoke. How accurate, then, is the population mean?
