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4 years ago

2(y-1/2)=-(3y-1)+3 solve using distributive property

Mathematics

1 answer:

Rainbow [258]4 years ago

8 0

...I got Y=1..

Don't trust it though I am not certain that is the correct answer.

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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

How do you write 1 tenth as a decimal

Bingel [31]

"one tenth" as a decimal is 0.1 .

8 0

4 years ago

Read 2 more answers

Given: AACD is isosceles with angle D as the vertex angle. B is the midpoint of AC. AB= x + 5, BC= 2x - 3, and CD = 2x + 6. Find

Marina86 [1]

Answer:

70 units

Step-by-step explanation:

Given triangle ACD

AB = BC
CD = 2x + 6
AB = x + 5
BC = 2x - 3
P = ?

Perimeter is sum of the side lengths:

P = AD + CD + AC

AD = CD because D is vertex and the triangle is isosceles

AC = AB + BC because B is midpoint of AC

Then P is:

P = 2(2x + 6) + (x + 5) + (2x -3) = 4x + 12 + x + 5 + 2x - 3 = 7x + 14

Find the value of x from the AB = BC:

x + 5 = 2x - 3
2x - x = 5 + 3
x = 8

Then find the value of P:

P = 7*8 + 14 = 56 + 14 = 70 units

3 0

3 years ago

Solve for x:

Marta_Voda [28]

The answer is C.) x=15

7 0

3 years ago

in 2012 in costed $0.55 per mile to drive a sedan. How much would it cost if you drove it 13,000 miles

Aloiza [94]

Answer:

calculaotro soup

Step-by-step explanation:

5 0

3 years ago

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