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Hitman42 [59]
3 years ago
12

In this problem, y = c1ex + c2e−x is a two-parameter family of solutions of the second-order de y'' − y = 0. find a solution of

the second-order ivp consisting of this differential equation and the given initial conditions. y(0) = 1, y'(0)= 8
Mathematics
1 answer:
Nonamiya [84]3 years ago
3 0
<span>y(1) = 0 y'(1) = e y" = c1ex + c2e-x y' = c1ex - c2e-x for solving c1, 0 = c1e1 + c2e-1 this implies that c1 = - (c2/e2) and to solve c2 e1 = (-c2e-2)e1 - c2e-1 e1 = (-2c2e-1) c2= - (e1/2e-1) = - (e2/2) c1 = - (c2/e2) = (e2/2e2) Therefore y =(e2/2e2)ex - (e2/2)e-x</span>
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12

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A world record was set for the men’s 100-m dash in the 2008 Olympic Games in Beijing by Usain Bolt of Jamaica. Bolt "coasted" ac
Andrei [34K]

Answer:

a) v = 12.21m/s

a = 4.07 m/s²

b)v = 11.24m/s

a =  3.75 m/s²

Step-by-step explanation:

a) Dividing the moviment into two parts:

I - With acceleration

v = v₀ + at

s = s₀ + v₀t + at²/2

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x = v/3.3²/2

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II - Uniform

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t = 9.69 - 3 = 6.69s

s = s₀ + vt

100 = x + v*6.69

100 = x + 6.69v

As x = 3v/2

100 = 3v/2 + 6.69v

100 = 1.5v + 6.69v

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b) Dividing the moviment into two parts:

I - With acceleration

v = v₀ + at

s = s₀ + v₀t + at²/2

  • v₀ = 0
  • s₀ = 0
  • a = ?
  • v = ?
  • t = 3s
  • s = x

v = v₀ + at

v = 3a ⇒ a = v/3

s = s₀ + v₀t + at²/2

x = v/3.3²/2

x = 3v/2

II - Uniform

s = s₀ + vt

s = 200

s₀ = x

v = v

t = 19.30 - 3 = 16.30s

s = s₀ + vt

200 = x + v*16.3

100 = x + 16.3v

As x = 3v/2

200 = 3v/2 + 16.3v

200 = 1.5v + 16.3v

200 = 17.8v

v = 11.24m/s

a = v/3 = 3.75 m/s²

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3 years ago
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Answer:

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