Explain how to use a graph of the function f(x) to find f(3).
2 answers:
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The given displacement at time, t, is
p(t) = 2 sin(t³) + 5 cos(t³)
The initial equilibrium position is
p(0) = 5
To determine future equilibrium postions, define
f(t) = p(t) - 5 = 2 sin(t³) + 5 cos(t³ - 5
The derivative of f(t) is
f'(t) = (3t²)[2 cos(t³) - 5sin(t³)]
Equilibrium is established when f(t) = 0.
To solve this equation numerically, we shall use the Newton-Raphson method, given by.
t(n+1) = t(n) - f[t(n)]/f'[(t(n)], n=0,1,2, ...,
As a guess, let (0) = 1.
The iterative solution for t is shown below.
n t(n)
--- -----------
0 1.0000
1 0.9344
2 0.9147
3 0.9130
4 0.9130
The solution converges rapidly to t = 0.913 s.
The graphical solution (shown below) confirms the numerical solution.
Answer:
The weight first reaches the equilibrium position in 0.913 sec.
p(t) = 2 sin(t³) + 5 cos(t³)
The initial equilibrium position is
p(0) = 5
To determine future equilibrium postions, define
f(t) = p(t) - 5 = 2 sin(t³) + 5 cos(t³ - 5
The derivative of f(t) is
f'(t) = (3t²)[2 cos(t³) - 5sin(t³)]
Equilibrium is established when f(t) = 0.
To solve this equation numerically, we shall use the Newton-Raphson method, given by.
t(n+1) = t(n) - f[t(n)]/f'[(t(n)], n=0,1,2, ...,
As a guess, let (0) = 1.
The iterative solution for t is shown below.
n t(n)
--- -----------
0 1.0000
1 0.9344
2 0.9147
3 0.9130
4 0.9130
The solution converges rapidly to t = 0.913 s.
The graphical solution (shown below) confirms the numerical solution.
Answer:
The weight first reaches the equilibrium position in 0.913 sec.
Answer:
The number of turbines is 74
Step-by-step explanation:
* Lets explain how to solve the problem
- Four 3 megawatt wind turbines can supply enough electricity
to power 3000 homes
∴ The number of turbines is 4
∵ Each turbine give 3 megawatt
∴ The four turbines give ⇒ 4 × 3 = 12 megawatt
- This quantity give enough electricity to power 3000 homes
∴ The number of homes for the 12 megawatt is 3000
- We need to find how many turbines can cover enough electricity
to power 55,000 homes, so we must to know the quantity of
electricity that be enough to power 55,000 homes
* <em>Lets use the cross multiplication to solve the problem</em>
∵ megawatt : number of homes
12 : 3,000
? : 55,000
- <em>By using cross multiplication</em>
∴
∴ The enough electricity to power 3000 homes = 220 megawatt
∵ Each turbine gives 3 megawatt
- Find the number of turbines divides the total megawatt by the the
megawatt of one turbine
∴ The number of turbines = 220 ÷ 3 = 73.3
- If we take 73 only the electricity will not be enough to cover all
homes, so we must to take 74 turbines
∴ The number of turbines is 74