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Vilka [71]
2 years ago
6

The rate of change (dP/dt), of the number of people on an ocean beach is modeled by a logistic differential equation. The maximu

m number of people allowed on the beach is 1200. At 10 A.M., the number of people on the beach is 200 and is increasing at the rate of 400 per hour. Whats the differential equation which can describe this situation?
Mathematics
1 answer:
Kazeer [188]2 years ago
3 0

Answer:

\frac{dP}{dt} = 2.4P(1 - \frac{P}{1200})

Step-by-step explanation:

The logistic differential equation is as follows:

\frac{dP}{dt} = rP(1 - \frac{P}{K})

In this problem, we have that:

K = 1200, which is the carring capacity of the population, that is, the maximum number of people allowed on the beach.

At 10 A.M., the number of people on the beach is 200 and is increasing at the rate of 400 per hour.

This means that \frac{dP}{dt} = 400 when P = 200. With this, we can find r, that is, the growth rate,

So

\frac{dP}{dt} = rP(1 - \frac{P}{K})

400 = 200r(1 - \frac{200}{1200})

166.67r = 400

r = 2.4

So the differential equation is:

\frac{dP}{dt} = rP(1 - \frac{P}{K})

\frac{dP}{dt} = 2.4P(1 - \frac{P}{1200})

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arah is at a miniature exhibit. There is a model of a skyscraper. Underneath the model was a ratio. It said:

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If the model is 38 inches tall, how Sarah use this information to find the actual height of the skyscraper?

In this concept, you will learn how proportions are used to find actual and scale dimensions using a scale ratio.

Using Proportions to Find Dimensions

A scale is a ratio that shows the relationship between the representation of an object and the real measurement of an object. Toy makers use scale ratios to make models of cars and airplanes that are proportional to the real thing. Architects use scale drawings to plan the design of buildings.

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Let’s look at a scale drawing of a sculpture. In the drawing, the sculpture is 4 inches tall. The scale is 1 inch : 4 feet. It scale can be written as

1 in4 ft

(Note: Inch is abbreviated “in.” or with the double prime mark, ″. Foot/feet is abbreviated “ft” or with the single prime mark, ′.)

A drawing with this scale tells you that 1 inch on paper is equal to 4 feet in real life. If the drawing is 4 inches tall, use the scale to find the actual height of the sculpture.

First, create a proportion using equivalent ratios. Remember to write the corresponding units in the numerator and in the denominator. The actual height of the sculpture is represented by the variable x.

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Then, cross multiply and simplify the equation to find the value of x.

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Which of the following is a monomial ? 9/x 11x2 20x9-7x 20x -14
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Step-by-step explanation:

I suppose that the options are:

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b) 11x^2

c) 20x^9-7x

d) 20x -14

First, a polynomial is something like:

aₙx^n + .... + a₂*x^2 + a₁*x^1 + a₀*x^0

Where n is the degree of the polynomial,  the therms a are the coefficients, and aₙ is the leading coefficient.

Depending on the number of terms of the polynomial, it takes different names.

If we have only one term, it is called a monomial, if it has two terms, it is called a binomial, and so on.

So if we want to find a monomial, then we need to look at the options with only one term.

The options with only one term are options a and b.

But option a is a quotient (we have a negative power of x: 9/x = 9*x^-1)

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3 years ago
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7 0
3 years ago
Holly made 12 pair of earrings for each of her girlfriends. To wrap the pairs individually, she creates a simple cardboard gift
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Answer:

3280cm²

Step-by-step explanation:

We are told the gift box is folded into a Pyramid with a square base.

Hence, we are to find the Surface Area of a square pyramid

From the question, we are given:

Length of the base of the square = 10cm

Triangle

Side length = 10cm

Height = 8 2/3 cm

A square Pyramid has 5 faces: 4 triangles and 1 square.

Step 1

Find the Area of the square

Formula = Side length² this is because all the side of a square is equal.

Length of the base = 10cm

Area of the square = (10cm)²

= 100cm²

Step 2

Find the Area of the triangle. We are told the 4 triangles are equilateral, which means their side are equal.

Hence, for one triangle.

Area of a triangle = 1/2 × base × height

Base = side length = 10cm

Height = 8 2/3 = 8.6666666667cm

Area of a triangle = 1/2 × 10 × 8.6666666667

Area of a triangle = 43.333333333cm²

Since we have 4 triangles

We would have : 4 × 43.333333333cm²

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The Area of the 4 equilateral triangles =

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Step 3

The Surface area of the Square Pyramid

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= 100cm² + 173.33333333cm²

= 273.33333333cm²

Therefore, the minimum amount of cardboard needed to make one gift box = 273.33333333cm²

Step 4

The minimum amount of cardboard Holly needs to create 12 gift boxes to wrap each pair of earrings individually is calculated as: 12 × 273.33333333cm²

= 3280cm²

7 0
3 years ago
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