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2 years ago

The Blue devils had won 37.5 games. they had played 24 games altogether. how may games had they won?

1 answer:

4 0

The Blue Devils are trying to sell us a bridge and a bill of goods.
But we are sharp, and we are not falling for their story.

We are smart enough to spot two glaring weaknesses in their story.

1). There is no way to win .5 of a game.

2). There is no way to win 37 games if you've
only played 24 so far.

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The Department of Agriculture is monitoring the spread of mice by placing 100 mice at the start of the project. The population,

uranmaximum [27]

Answer:

Step-by-step explanation:

Assuming that the differential equation is

$\frac{dP}{dt} = 0.04P\left(1-\frac{P}{500}\right)$ .

We need to solve it and obtain an expression for $P(t)$ in order to complete the exercise.

First of all, this is an example of the logistic equation, which has the general form

$\frac{dP}{dt} = kP\left(1-\frac{P}{K}\right)$ .

In order to make the calculation easier we are going to solve the general equation, and later substitute the values of the constants, notice that $k=0.04$ and $K=500$ and the initial condition $P(0)=100$ .

Notice that this equation is separable, then

$\frac{dP}{P(1-P/K)} = kdt$ .

Now, intagrating in both sides of the equation

$\int\frac{dP}{P(1-P/K)} = \int kdt = kt +C$ .

In order to calculate the integral in the left hand side we make a partial fraction decomposition:

$\frac{1}{P(1-P/K)} = \frac{1}{P} - \frac{1}{K-P}$ .

So,

$\int\frac{dP}{P(1-P/K)} = \ln|P| - \ln|K-P| = \ln\left| \frac{P}{K-P} \right| = -\ln\left| \frac{K-P}{P} \right|$ .

We have obtained that:

$-\ln\left| \frac{K-P}{P}\right| = kt +C$

which is equivalent to

$\ln\left| \frac{K-P}{P}\right|= -kt -C$

Taking exponentials in both hands:

$\left| \frac{K-P}{P}\right| = e^{-kt -C}$

Hence,

$\frac{K-P(t)}{P(t)} = Ae^{-kt}$ .

The next step is to substitute the given values in the statement of the problem:

$\frac{500-P(t)}{P(t)} = Ae^{-0.04t}$ .

We calculate the value of $A$ using the initial condition $P(0)=100$ , substituting $t=0$ :

$\frac{500-100}{100} = A}$ and $A=4$ .

So,

$\frac{500-P(t)}{P(t)} = 4e^{-0.04t}$ .

Finally, as we want the value of $t$ such that $P(t)=200$ , we substitute this last value into the above equation. Thus,

$\frac{500-200}{200} = 4e^{-0.04t}$ .

This is equivalent to $\frac{3}{8} = e^{-0.04t}$ . Taking logarithms we get $\ln\frac{3}{8} = -0.04t$ . Then,

$t = \frac{\ln\frac{3}{8}}{-0.04} \approx 24.520731325$ .

So, the population of rats will be 200 after 25 months.

6 0

2 years ago

James has decided to start saving for a cruise over the summer. His money is currently in the local bank modeled by the function

IgorLugansk [536]

Answer:

s ( x ) = 102, a ( x ) = 8 ( x + 2 )

A function that combines the two:

f ( x ) = s ( x ) + a ( x ) = 102 + 8 ( x + 2 ) =

= 102 + 8 x + 16

final answer : f ( x ) = 8 x + 118

7 0

2 years ago

Factor the expression.<br> 30-4n

zheka24 [161]

Hope this is what you are looking for the answer is 2(15-2n)

7 0

2 years ago

Read 2 more answers

Estimate the quotient of 394.6 divided by 9

N76 [4]

The answer rounded to the tenths place is 43.8, to the hundredths place is 43.84

8 0

2 years ago

Adult tickets to a play cost $22 tickets for kids cost $15. Tickets for a group of 11 cost a total of $228. How many children an

Zina [86]

Answer:Number of children = 2 and number of adults = 9 attended the play

Step-by-step explanation:

Step 1

Let the number of children be represented as x

and the number of adults in the group be represented as as y

such that the total number of the group that went to the play

= x+y=11--- equation 1

And the total cost paid for the play will be expressed as

15x+ 22y= 228------ equation 2

Step 2-- Solving

x+y=11--- equation 1

15x+ 22y= 228------ equation 2

B y elimination method, multiply equation 1 by 15 to give equation 3 and then subtract from equation 2

15x+ 22y= 228------ equation 2

15x+15Y= 165----- equation 3

7y=63

y= 63/7= 9

y= adults = 9

therefore x = number of children will be

x+y=11

x+ 9=11

x= 11-9= 2

In the group that attended the play, Number of children = 2 and number of adults = 9

8 0

2 years ago