1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
liberstina [14]
2 years ago
9

. A population of rabbits oscillates 25 above and below an average of 129 during the year, hitting the lowest value in January (

t = 0). a. Find an equation for the population, P, in terms of the months since January, t. b. What if the lowest value of the rabbit population occurred in April instead?
Mathematics
1 answer:
Burka [1]2 years ago
7 0

Answer:

Because we know that here we have an oscillation, we can model this with a sine or cosine function.

P = A*cos(k*t) + M

where:

k is the frequency

A is the amplitude

M is the midline

We know that at t = 0, we have the lowest population.

We know that the mean is 129, so this is the midline.

We know that the population oscillates 25 above and below this midline,

And we know that for t = 0 we have the lowest population, so:

P = A*cos(k*0) + 129 = 129 - 25

P = A + 129 = 129 - 25

A = -25

So, for now, our equation is

P = -25*cos(k*t) + 129

Because this is a yearly period, we should expect to see the same thing for t = 12 (because there are 12 months in one year).

And remember that the period of a cosine function is 2*pi

Then:

k*12 = 2*pi

k = (2*pi)/12 = pi/6

Finally, the equation is:

P = -25*cos(t*pi/6) + 129

Now we want to find the lowest population was in April instead:

if January is t = 0, then:

February is t = 2

March is t = 3

April is t = 4

Then we would have that the minimum is at t = 4

If we want to still use a cosine equation, we need to use a phase p, such that now our equation is:

P = -25*cos(k*t + p) + 129

Such that:

cos(k*4 + p) = 1

Then:

k*4 + p = 0

p =  -k*4

So our equation now is:

P = -25*cos(k*t  - 4*k) + 129

And for the periodicity, after 12 months, in t = 4 + 12 = 16, we should have the same population.

Then, also remembering that the period of the cosine function is 2*pi:

k*12 - 4*k = 2*pi

k*8 = 2*pi

k = 2*pi/8 = pi/4

And remember that we got:

p = -4*k = -4*(pi/4) = -pi

Then the equation for the population in this case is:

P = -25*cos( t*pi/4 - pi) + 129

You might be interested in
The tabel shows the amount of miles of Cheryl travels 4 each day.About how many miles did she travel during the 4 days?
OLga [1]
4 times 4=16 So in four days, Cheyrl traveled 16 miles.
8 0
3 years ago
What is multiplication in 2 paragraphs
Ivanshal [37]

Four bags with three marbles per bag gives twelve marbles (4 × 3 = 12).

Multiplication can also be thought of as scaling. Here we see 2 being multiplied by 3 using scaling, giving 6 as a result.

Animation for the multiplication 2 × 3 = 6.

4 × 5 = 20. The large rectangle is composed of 20 squares, each having dimensions of 1 by 1.

Area of a cloth 4.5m × 2.5m = 11.25m2; 4½ × 2½ = 11¼

Multiplication (often denoted by the cross symbol "×", by a point "⋅", by juxtaposition, or, on computers, by an asterisk "∗") is one of the four elementary mathematical operations of arithmetic; with the others being addition, subtraction and division.

The multiplication of whole numbers may be thought as a repeated addition; that is, the multiplication of two numbers is equivalent to adding as many copies of one of them, the multiplicand, as the value of the other one, the multiplier. The multiplier can be written first and multiplicand second (though the custom can vary by culture[1]).

{\displaystyle a\times b=\underbrace {b+\cdots +b} _{a}} a\times b=\underbrace {b+\cdots +b} _{a}

For example, 4 multiplied by 3 (often written as {\displaystyle 3\times 4} 3\times 4 and spoken as "3 times 4") can be calculated by adding 3 copies of 4 together:

{\displaystyle 3\times 4=4+4+4=12} 3\times 4=4+4+4=12

Here 3 and 4 are the factors and 12 is the product.

One of the main properties of multiplication is the commutative property: adding 3 copies of 4 gives the same result as adding 4 copies of 3:

{\displaystyle 4\times 3=3+3+3+3=12} 4\times 3=3+3+3+3=12

Thus the designation of multiplier and multiplicand does not affect the result of the multiplication[2].

The multiplication of integers (including negative numbers), rational numbers (fractions) and real numbers is defined by a systematic generalization of this basic definition.

Multiplication can also be visualized as counting objects arranged in a rectangle (for whole numbers) or as finding the area of a rectangle whose sides have given lengths. The area of a rectangle does not depend on which side is measured first, which illustrates the commutative property. The product of two measurements is a new type of measurement, for instance multiplying the lengths of the two sides of a rectangle gives its area, this is the subject of dimensional analysis.

The inverse operation of multiplication is division. For example, since 4 multiplied by 3 equals 12, then 12 divided by 3 equals 4. Multiplication by 3, followed by division by 3, yields the original number (since the division of a number other than 0 by itself equals 1).

Multiplication is also defined for other types of numbers, such as complex numbers, and more abstract constructs, like matrices. For some of these more abstract constructs, the order in which the operands are multiplied together matters. A listing of the many different kinds of products that are used in mathematics is given in the product (mathematics) page.

3 0
3 years ago
Read 2 more answers
Find the area of the rectangle
galben [10]
Rectangle is length multiplied by breadth
5 0
3 years ago
Read 2 more answers
"to find x in part a, you would need" to solve the equation x 2 – 25 =0. wh
musickatia [10]
X2 - 25 = 0

Add 25 on each side.

x2 = 25

Divide by 2 on each side.

x = 12.5
3 0
3 years ago
What ratio shows 20:12 written in simplest form?
arsen [322]

It is 5:3 or 5/3

Divide it by 4

4 0
2 years ago
Read 2 more answers
Other questions:
  • Estimate then find the sum 324967+6233
    14·2 answers
  • 4x+3y= -1<br> 5x+4y= -1<br> solving by emilination or subtraction<br> please help :)
    14·1 answer
  • An engineer is designing a play set for an elementary school. The drawing above shows the detailed view for the pre-drilled hole
    8·1 answer
  • What is the product?<br> 42<br> 3<br> 흐<br> B<br> 18<br> 18
    12·1 answer
  • What is the equation of the line through (2, -4) and (0, 4)?
    11·1 answer
  • amanda baked 10 chocolate cupcakes and 6 blueberry cupcakes(a) what is the ratio of chocolate cupcakes to bluueberry cupcake?Wha
    9·2 answers
  • The highway mileage (mpg) for a sample of 9 different models of a car company can be found below.
    14·2 answers
  • SOMEONE PLEASE HELP! I don’t know how to do this !
    7·1 answer
  • 6) In problem 5, how much will he owe the bank after June 8?
    10·1 answer
  • Can someone please help mee (will give brainliest 20 points!!!)
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!