Simplify. 5(x+2)-3(x-2)+7x= Please Help!!! Make it legit!

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

Which graph represents a linear function?

eduard

Answer:

That graph in the picture is not linear

Step-by-step explanation:

The graph does not go up or go down the same each unit

8 0

3 years ago

Read 2 more answers

Alexandra purchases two doughnuts and three cookies at a doughnut shop and is charged $3.30. Brianna purchases five doughnuts an

Gekata [30.6K]

Answer:1 donut=$0.75 and 1 cookie=$0.6

let c be the cookie and d be the dougnut

2d +3c = 3.30 ---eq 1
5d+ 2c = 4.95 ---eq 2

4 0

4 years ago

58% of students were girls, there are 450 students total. How many students are girls ?

Anastaziya [24]

Answer:

261

Step-by-step explanation:

450 (.58)= 261

check answer 261/450 =.58

4 0

3 years ago

HELLLPP ANY HELPS PLEASE I NEED HELP I AM RUNNING OUT OF TIME !!

Tju [1.3M]

Answer:

8

Step-by-step explanation:

3(x-2) = 18

=> 3x - 6 = 18

=> 3x = 24

=> x = 8 (Ans)

5 0

3 years ago