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3 years ago

Pls help me. rlly need help. question in picture. pls hurry

Mathematics

1 answer:

Goshia [24]3 years ago

7 0

Answer:

$(x-9)(x-6)$

Step-by-step explanation:

Factor $x^2-15x+54$

Find two numbers that add up to -15 and multiply to 54 (hint hint, two negatives makes a positive hint hint):

$-9, -6$

Rewrite the expression:

$(x-9)(x-6)$

<em>Finito.</em>

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Age Problem. Please help. I suck at these.

eimsori [14]

Let Cynthia's age be C, then Abigail's age A

since Abigail is 8 years older, her age A = C+8.

20 years ago Cynthia's she was C-20 and Abigail was A-20=3(C-20)

A-20=3C-60
A=3C-40
but we just said A=C+8
so 3C-40=C+8
2C=48
C=24
A=24+8=32

Cynthia's age is 24 and Abigail's age is 32

7 0

3 years ago

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

3 years ago

At a dog park , there are 10 black dogs, 5 brown dog, 2 white dog, and 12 multi color dogs

Sophie [7]

What question are you trying to ask?

5 0

3 years ago

Read 2 more answers

Which of the below descriptions shows a possible HAMILTON PATH?

Vadim26 [7]

Option B: FECBAD is the Hamilton path

Explanation:

Given that ABCDEF is a graph with vertices A,B,C,D,E and F

We need to determine the Hamilton path.

Since, we know that a Hamilton path is a path that touches every vertex in a graph exactly once.

Option A: EFADECBA

The path touches the vertices E and A twice.

Hence, the path EFADECBA is not a Hamilton path.

Therefore, Option A is not the correct answer.

Option B: FECBAD

The path touches every vertex in the graph exactly once.

Hence, the path FECBAD is a Hamilton path.

Therefore, Option B is the correct answer.

Option C: ADEFBD

The path touches the vertex A twice because when the path travels from F to B the only way to travel through A.

Hence, the path ADEFBD is not a Hamilton path.

Therefore, Option C is not the correct answer.

Option D: ADECBAFE

The path touches the vertices E and A twice.

Hence, the path ADECBAFE is not a Hamilton path.

Therefore, Option D is not the correct answer.

8 0

3 years ago

What is the circumference of the circle?

True [87]

Step-by-step explanation:

What is the circumference of the circle?

f) 52 cm2

e) 2610 cm2

5 0

3 years ago

Pls help me. rlly need help. question in picture. pls hurry​

Pls help me. rlly need help. question in picture. pls hurry