Which of the following could be the ratio between the lengths of the two legs

jekas [21]

The gcf is 7 for both

6 0

3 years ago

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

Solve for x. thank you in advance, please answer my other questions as well im having a tough time

klio [65]

Answer:

$3/4$

Step-by-step explanation:

$log_{(5)} (\sqrt[4]{125})$

$\frac{log(\sqrt[4]{125}) }{log(5)}$

$=0.75$

8 0

3 years ago

Quadrilateral CDEF is a rhombus. What is DCG?

svlad2 [7]

Answer:

62°

Step-by-step explanation:

The diagonals of a rhombus are perpendicular bisectors of each other, and each bisects the angle at a vertex of the rhombus. So, ∠DCG is the complement of ∠CDG, which is congruent to ∠EDG. We believe the marking 28° is intended to apply to ∠EDG, which would mean that ...

m∠DCG = 90° - 28°

m∠DCG = 62°

6 0

3 years ago

If f(x) = -3x-2, find the value f(-2)+9

Nookie1986 [14]

Answer:

13

Step-by-step explanation:

f(-2) means you want to find the y value when x=-2. Plug in x=-2 into the f(x) equation to get: [-3(-2)]-2 = 6-2 = 4.

so f(-2)=4

But the question asks for f(-2)+9. So you add 9 to f(-2) which is 9+4 = 13

4 0

4 years ago