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s2008m [1.1K]
3 years ago
6

(TIMED HELP) The population model describing the population of antelope in an area is:

Mathematics
1 answer:
Elena L [17]3 years ago
6 0

Answer:

Step-by-step explanation:

The population model describing the population of antelopes in the area is

Pn+1 = [1.75(Pn)^2/(Pn-1)] + 32 - Pn

where n represents the number of years.

In the first year, the number of antelopes is given as 89, to find the number of antelopes for the second year, it means we are looking for P(1+1) = P2. We will substitute 1 for n and 89 for Pn+1

It becomes

Pn+1 = [1.75(Pn)^2/(Pn-1)] + 32 - Pn

P2 = [1.75×89^2 / (89 - 1)] + (32 -89)

P2 = [13861.75 / 88] - 57

P2 = 101

To find P3, we will substitute 101 for Pn+1 and 2 for n. It becomes

P3 = [1.75×101^2 / (101 - 1)] + (32 -101)

P3 = [17851.75 / 100] - 69

P3 = 110

To find P4, we will substitute 110 for Pn+1 and 3 for n. It becomes

P4 = [1.75×110^2 / (110 - 1)] + (32 -110)

P4 = [21175 / 109] - 78

P4 = 116

To find P5, we will substitute 116 for Pn+1 and 4 for n. It becomes

P5 = [1.75×116^2 / (116 - 1)] + (32 -116)

P5 = [23548 / 115] - 84

P5 = 121

To find P6, we will substitute 121 for Pn+1 and 5 for n. It becomes

P6 = [1.75×121^2 / (121 - 1)] + (32 -121)

P6 = [25621.75 / 120] - 89

P6 = 125

To find P7, we will substitute 125 for Pn+1 and 6 for n. It becomes

P7 = [1.75×125^2 / (125 - 1)] + (32 -125)

P7 = [27343.75 / 124] - 93

P7 = 128

To find P8, we will substitute 128 for Pn+1 and 7 for n. It becomes

P8 = [1.75×128^2 / (128 - 1)] + (32 -128)

P8 = [28672 / 127] - 96

P8 = 130

To find P9, we will substitute 130 for Pn+1 and 7 for n. It becomes

P9 = [1.75×130^2 / (130 - 1)] + (32 -130)

P9 = [29575 / 129] - 98

P9 = 131

To find P10, we will substitute 131 for Pn+1 and 7 for n. It becomes

P10= [1.75×131^2 / (131 - 1)] + (32 -131)

P10= [30031.75 / 130] - 99

P10 = 132

The correct option is C

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nikdorinn [45]

Answer:

<em>Area of polygon D = 10 square units</em>

Step-by-step explanation:

<u>Given:</u>

Polygon <em>C </em>has an area of 40 square units.

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<u></u>

<u>To find:</u>

The area of polygon D = ?

<u>Solution:</u>

When any polygon is scaled to half, then all the sides of new polygon are half of the original polygon.

And the area becomes one-fourth of the original polygon.

Let us consider this by taking examples:

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Area of a right angled triangle is given by:

A = \dfrac{1}{2} \times Base \times Height\\\Rightarrow A = \dfrac{1}{2} \times 6 \times 8 = 24\ sq\ units

If scaled with a factor \frac{1}{2}, the sides will be 3, 4 and 5.

New area, A':

A' =\dfrac{1}{2} \times 3 \times 4 = 6\ sq\ units = \dfrac{1}4\times A

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  • Let us consider a rectangle now.

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Area of a rectangle, A = Length \times Width = 8 \times 10 = 80 sq units.

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New Area, A' = 4 \times 5 =20 sq units

So, \bold{A' = \frac{1}4 \times A}

Now, we can apply the same in the given question.

\therefore Area of polygon D = \bold{\frac{1}{4}}\times Area of polygon C

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Part B

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