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3 years ago

Complete the equation for the given graph of the parabola

Mathematics

1 answer:

Anarel [89]3 years ago

4 0

The graph of any quadratic equation y=ax2+bx+c y = a x 2 + b x + c , where a, b, and c are real numbers and a≠0 a ≠ 0 , is called a parabola. When graphing parabolas, find the vertex and y-intercept. ... This y-value is a maximum if the parabola opens downward, and it is a minimum if the parabola opens upward.
Vertex: (−1, 3)
Y-intercept: (0, 5)
X-intercepts: None
Extra points: (−3, 11), (−2, 5), (1, 11)

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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

3 years ago

Which of the following options represents the graph of the function shown below?

grigory [225]

I think the answer is B but not sure about "11" in A

4 0

3 years ago

Read 2 more answers

write an equation in slope intercept form for the line that passes through (4, -4) and is parallel to 3x+4x=2y-9

photoshop1234 [79]

Answer:

$\large\boxed{y=\dfrac{7}{2}x-18}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

Convert the equation of a line 3x + 4x = 2y - 9 to the slope-intercept form:

$3x+4x=2y-9$

$7x=2y-9$ add 9 to both sides

$7x+9=2y$ divide both sides by 2

$\dfrac{7}{2}x+\dfrac{9}{2}=y\to y=\dfrac{7}{2}x+\dfrac{9}{2}$

Parallel lines have the same slope. Therefore we have the equation:

$y=\dfrac{7}{2}x+b$

Put the coordinates of the point (4, -4) to the equation:

$-4=\dfrac{7}{2}(4)+b$

$-4=7(2)+b$

$-4=14+b$ subtract 14 from both sides

$-18=b\to b=-18$

Finally we have the equation:

$y=\dfrac{7}{2}x-18$

8 0

3 years ago

Two friends, Devon and Bryce, are working together at the Oakland Cafe today. Devon works every 2 days, and Bryce works every 9

ludmilkaskok [199]

Answer:

11 days before they worked together

5 0

3 years ago

Please help me with the work because i dont understand this.

Alexandra [31]

Answer:

The dimension are 20 ft by 15 ft

Step-by-step explanation:

A = l*w

P = 2(l+w)

we know the area = 300

and the perimeter = 70

300 = lw

70 = 2 (l+w)

divide by 2

70/2 = 2/2 (l+w)

35 = l+w

subtract w

35-w = l+w-w

35 -w =l

substitute this into 300 = lw

300 = (35-w) * w

distribute

300 = 35w - w^2

subtract 300 from each side

0 = -w^2 +35w - 300

divide by -1

0 = w^2 - 35w + 300

factor

0= (w-15) (w-20)

using the zero product property

w-15 = 0 w-20 =0

so w=15, w=20

if w=15 then l=35 -w l = 35-15 l=20

if w=20 then l=35-w l= 35-20 = 15

The dimension are 20 ft by 15 ft

7 0

3 years ago