Answer:
The time now is 7 pm
Step-by-step explanation:
Suppose that now is the time T.
We know that:
"if time is four hours from now, the time left till midnight would be a quarter that if it is one hour from now".
Then:
if we define midnight as 12, and we assume that T is in the pm range.
Then the "time left till midnigth, assuming that the time is four hours from now" will be written as (12 - (T + 4))
With this in mind, we can write the problem as:
12 - (T + 4) = (1/4)*( 12 - (T + 1))
Now we can solve this for T.
12 - T - 4 = (1/4)*(12 - T - 1)
8 - T = (1/4)*(11 - T)
4*(8 - T) = 11 - T
32 - 4*T = 11 - T
32 - 11 = -T + 4*T
21 = 3*T
21/3 = T
7 = T
Then T = 7 pm
The time now is 7 pm
The population Pa of insect A after t years is given by the equation
Pa = 1.3(1-0.038)^t
while the population Pb of insect B after t years is
Pb = 2.1(1-0.046)^t
We equate the above expressions to find the number of years t it will take the two populations to be equal:
Pa = Pb
1.3(1-0.038)^t = 2.1(1-0.046)^t
1.3(0.962)^t = 2.1(0.954)^t
These are the equations that can be used to determine how long it will be before the populations of the two species are equal.
We can now solve for t:
(0.962)^t / (0.954)^t = 2.1/1.3
(0.962/0.954)^t = 2.1/1.3
After taking the log of both sides of our equation, number of years t is
t = log (2.1/1.3) / log (0.962/0.954)
t = 57 years
Therefore, it will take 57 years for the population of insect A to equal the population of insect B.
Answer:
<h2>
The eleventh term of the sequence is 64</h2>
Step-by-step explanation:
The sequence given is an arithmetic sequence
14, 19, 24, …………., 264
The nth term of an arithmetic sequence is given as;
Tn = a+(n-1)d where;
a is the first term = 14
d is the common difference = 19-14=24-19 = 5
n is the number of terms = 11(since we are to look for the eleventh term of the sequence)
substituting the given values in the formula given;
T11 = 14+(11-1)*5
T11 = 14+10(5)
T11 = 14+50
T11 = 64
The eleventh term of the sequence is 64
