Joe drove 12 miles in the morning and 16 miles

One method of slowing the growth of an insect population without using pesticides is to introduce into the population a number o

Zielflug [23.3K]

To be clear, the given relation between time and female population is an integral:
 $t = \int { \frac{P+S}{P[(r - 1)P - S]} } \,
dP$

The problem says that r = 1.2 and S = 400, therefore substituting:
 $t = \int { \frac{P+400}{P[(1.2 - 1)P - 400]}
} \, dP$ 

= $
\int { \frac{P+400}{P(0.2P - 400)} } \, dP$

In order to evaluate this integral, we need to write this rational function in a simpler way:
 $\frac{P+400}{P(0.2P - 400)} = \frac{A}{P} +
\frac{B}{(0.2P - 400)}$ 

where we need to evaluate A and B. In order to do so, let's calculate the LCD:
 $\frac{P+400}{P(0.2P - 400)} = \frac{A(0.2P -
400)}{P(0.2P - 400)} + \frac{BP}{P(0.2P - 400)}$ 

the denominators cancel out and we get:
P + 400 = 0.2AP - 400A + BP
 = P(0.2A + B) - 400A

The two sides must be equal to each other, bringing the system:
 $\left \{ {{0.2A + B = 1} \atop {-400A =
400}} \right.$ 

Which can be easily solved:
 $\left \{ {{B=1.2} \atop {A=-1}} \right.$ 

Therefore, our integral can be written as:
 $t = \int { \frac{P+400}{P(0.2P - 400)} } \,
dP = \int {( \frac{-1}{P} + \frac{1.2}{0.2P-400} )} \, dP$ 
= $- \int { \frac{1}{P} \, dP +
1.2\int { \frac{1}{0.2P-400} } \, dP$ 
= $- \int { \frac{1}{P} \, dP +
6\int { \frac{0.2}{0.2P-400} } \, dP$ 
= - ln |P| + 6 ln |0.2P - 400| + C

Now, let’s evaluate C by considering that at t = 0 P = 10000:
0 = - ln |10000| + 6 ln |0.2(10000) - 400| + C
C = ln |10000| - 6 ln |1600|
C = ln (10⁴) - 6 ln (2⁶·5²)
C = 4 ln (10) - 36 ln (2) - 12 ln (5) 
 Therefore, the equation relating female population with time requested is:
t = - ln |P| + 6 ln |0.2P - 400| + 4 ln (10) - 36 ln (2) - 12 ln (5)

8 0

3 years ago

In the course of a short race, a car does 50,000 J of work in 7 s. What is the power of the car during the race? (round to the n

nirvana33 [79]

Answer:

Work done is the product of distance and force, it is measured in joules.

Power is the rate of work done given by dividing the work done by time

Power (watts)= workdone (J)/ time (s)

= 50,000J/7 sec

= 7142.857 watts

Therefore, the power of the car during the race was 7142.857 watts

Step-by-step explanation:

4 0

3 years ago

What do you notice? What do you wonder?

Rus_ich [418]

I need to see a picture

5 0

3 years ago

Jerry's team has played 8 games of basketball. During those 8 games his team scored 59, 66, 56, 63, 42, 55, 62 and 51. What is t

zavuch27 [327]

Answer:

To calculate the mean of a set of data, you have to work out the sum of the data (in this case, you need to work out the sum of all the points) and divide it by the number of data points there are (in this case, number of games played).

So you have to do:

(67 + 45 + 84 + 55 + 73 + 36 + 80 + 62 + 38)/9 = 60

The mean number of points is 60.

Step-by-step explanation:

please mark as brainiest

8 0

3 years ago

Read 2 more answers

Kristy ask Lonnie to think add 3 to it multiply the sum by 2 and the subtract 6 let n stand for lonnie starting number which exp

Kryger [21]

Answer:

2(n+3)-6

n=0

Step-by-step explanation:

2(3+n)-6=

Simplifying

2(3 + n) + -6 = 0

(3 * 2 + n * 2) + -6 = 0

(6 + 2n) + -6 = 0

Reorder the terms:

6 + -6 + 2n = 0

Combine like terms: 6 + -6 = 0

0 + 2n = 0

2n = 0

Solving

2n = 0

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Divide each side by '2'.

n = 0

Simplifying

n = 0

5 0

3 years ago