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3 years ago

Find the volume of the hemisphere shown. remember a hemisphere is half of a sphere. r = 5

1 answer:

3 0

As we know from geometry, the volume of any given sphere is

V = 4/3*πr³

Since a hemisphere is half of any given sphere, its volume should be

V = 4/3*πr³ ÷ 2
V = 2/3*πr³

This will be our working equation for finding the volume of hemisphere. Since r is already given to be 5 units, we substitute this to the working equation:

V = 2/3*π(5)³
V = 261.8 cubic units

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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

5. Write two or three sentences that describe how a chart differs from a table. -please help meh T-T

igomit [66]

Answer:

Key difference: Tables represent facts and figures in a row and column format. Charts represent data in a more graphical manner which may include lines, bars and circles.

CHART-graphical display of information wherein the information is illustrated in symbols such as bars, lines, or slices.

TABLE- a means of displaying data or information in rows and columns.

5 0

3 years ago

A pizza shop sells three sizes of pizza, and they track how often each size gets ordered along with how much they profit from ea

kari74 [83]

Answer:

μy = $6.56 ; σy = 2.77

Step-by-step explanation:

Given the data :

Mean μx= $8.56

Standard Deviation σx ≈ 2.77

Profit, Y on pizza with current promo :

Price off on pizza = $2

Y = x - 2

μx = E(x) = $8.56

μy = μ(x - 2)

μy = μx - $2

μy = $8.56 - $2

μy = $6.56

For the standard deviation of y

σx ≈ 2.77

σy = σ(x - 2)

σy = σx - 2

Constants are treated as 0 for standard deviation

σy = 2.77

8 0

3 years ago

The circumference of a circle varies directly as the diameter of a circle. When the diameter of a circle is 5, the circumference

Naya [18.7K]

Answer:

20.3 units

Step-by-step explanation:

Write and solve an equation involving ratios:

5 units 15.7 units

------------- = ----------------

9 units C

Cross-multiplying, we get 5C = 9(15.7), with C measured in "units."

Then 5C = 141.3, so that C = 141.3 units / 5 = 20.3 units.

5 0

3 years ago

Read 2 more answers

A) 4

Shkiper50 [21]

Answer:

i think c

Step-by-step explanation:

8 0

3 years ago