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Vlad1618 [11]
2 years ago
10

Every year, monarch butterflies migrate approximately 2,500 miles from the Great Lakes to central Mexico where they spend their

winters. They travel at a speed of 18 miles per hour. In flight, they flap their wings 500 times per minute. About how many times will a single Monarch butterfly flap its wings in order to make the entire trip from the Great Lakes to central Mexico?
Mathematics
1 answer:
Ghella [55]2 years ago
4 0

Answer:Dec 18, 2009 — How far do you think you will travel as you migrate from your winter home to ... average stick of gum weighs four times as much as your new monarch body. ... Once you spend a minute or two thinking about life as a butterfly, click on the ... have the farthest journey of all, nearly 4,000 kilometers (2,500 miles).

Step-by-step explanation:

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Answer:

72π (in terms of pi)

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family of solutions of the second-order DE y y 0. Find a solution of the second-order IVP consisting of this differential equati
Anna35 [415]

Answer:

y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}

Step-by-step explanation:

Given

y=c_1e^x +c_2e^{-x

y(1) = 0

y'(1) =e

Required

The solution

Differentiate y=c_1e^x +c_2e^{-x

y' = c_1e^x - c_2e^{-x}

Next, we solve for c1 and c2

y(1) = 0 implies that; x = 1 and y = 0

So, we have:

y=c_1e^x +c_2e^{-x

0 = c_1 * e^1 + c_2 * e^{-1}

0 = c_1 e + \frac{1}{e}c_2 --- (1)

y'(1) =e implies that: x = 1 and y' = e

So, we have:

y' = c_1e^x - c_2e^{-x}

e = c_1 * e^1 - c_2 * e^{-1}

e = c_1 e - \frac{1}{e}c_2 --- (2)

Add (1) and (2)

0 + e = c_1e + c_1e + \frac{1}{e}c_2 - \frac{1}{e}c_2

e = 2c_1e

Divide both sided by e

1 = 2c_1

Divide both sides by 2

c_1 = \frac{1}{2}

Substitute c_1 = \frac{1}{2} in 0 = c_1 e + \frac{1}{e}c_2

0 = \frac{1}{2} e+ \frac{1}{e}c_2

Rewrite as:

\frac{1}{e}c_2 = -\frac{1}{2} e

Multiply both sides by e

c_2 = -\frac{1}{2} e^2

So, we have:

y=c_1e^x +c_2e^{-x

y = \frac{1}{2}e^x -\frac{1}{2} e^2 * e^{-x}

y = \frac{1}{2}e^x -\frac{1}{2} e^{2-x}

6 0
3 years ago
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