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olga55 [171]
3 years ago
10

Let C be the circle in the xy plane centered at (5,0) with radius 2, and let S be the resulting surface in R3 when you rotate C

around the y axis. a. Draw a picture of S. b. Find an equation for the tangent plane to S at the point (3 2, 3, 3 2). c. Find the surface area of S.

Mathematics
1 answer:
guajiro [1.7K]3 years ago
7 0

Answer:

Please see attachment

Step-by-step explanation:

Please see attachment

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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) Which graph shows the solution of the system of inequalities 2x - y<-6 and y < 2x - 3?
liq [111]

Answer:

B

Step-by-step explanation:

4 0
3 years ago
Use the drawing tool(s) to form the correct answer on the provided number line. Consider the given functions. Function 1 Functio
Anna007 [38]

Both functions decrease at (-1, 2)

<h3>How to determine the decreasing intervals of the function?</h3>

The complete question is added as an attachment

The polynomial function f(x) is represented by the graph.

From the graph, the polynomial function decreases at (-2, 2)

The absolute function is given as;

f(x) = =5|x + 1| + 10

The vertex of the above function is

Vertex = (-1, 10)

Because a is negative (a= -5), the vertex is a maximum.

This means that the function decreases at (-1, ∞)

So, we have

(-2, 2) and (-1, ∞)

Combine both intervals

(-1, 2)

This means that both functions decrease at (-1, 2)

See attachment 2 for the number line that represents the interval where both functions are decreasing

Read more about function intervals at:

brainly.com/question/27831985

#SPJ1

3 0
2 years ago
What is 1 2/3+3 3/4=
STALIN [3.7K]

Answer:

5 5/12

Step-by-step explanation:

2/3 + 3/4 = 1 5/12 + 3+1

= 5 5/12

7 0
3 years ago
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Hello once again please help me out in pre cal
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Answer:

the answer is D 8.8

Step-by-step explanation:

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3 years ago
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