Numerade

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16.323 3-12 Spr 2008 Start - evaluate cost associated with all possible terminal states $$J_2 = h(x_2) = (x_2)^2$$ 0 0 0.5 0.25 1 1 1.5 2.25 Given $x_1$ and possible $x_2$, can evaluate the control effort required to make that transition: $$u(1) = x_2 + u(1)$$ 0 0.5 1 1.5 0 0 0.5 1 1.5 0.5 -0.5 0 0.5 1 1 -1 -0.5 0 0.5 1.5 -1.5 -1 -0.5 0 which can be used to compute the cost increments: $$ \Delta J_{12}$$ 0 0.5 1 1.5 0 0 0.5 2 XX 0.5 0.5 0 0.5 2 1 2 0.5 0 0.5 1.5 XX 2 0.5 0 and costs at time t = 1 given by $J_1 = \Delta J_{12} + J(x_2)$ $$J_1$$ 0 0.5 1 1.5 0 0 0.75 3 XX 0.5 0.5 0.25 1.5 4.25 1 2 0.75 1 2.75 1.5 XX 2.25 1.5 2.25 16.323 3-11 Spr 2008 DP Example See Kirk pg.59: $$J = x^2(T) + A \int_0^T u^2(t) dt$$ with $\dot{x} = ax + u$, where $0 \le x \le 1.5$ and $-1 \le u \le 1$ Must quantize the state within the allowable values and time within the range $t \in [0,2]$ using $N=2$, $\Delta t = T/N = 1$. - Approximate the continuous system as: $$\dot{x} \approx \frac{x(t + \Delta t) - x(t)}{\Delta t} = ax(t) + u(t)$$ which gives that $$x_{k+1} = (1 + a \Delta t)x_k + (\Delta t)u_k$$ - Very common discretization process (Euler integration approximation) that works well if $\Delta t$ is small Use approximate calculation from previous section - cost becomes $$J = x^2(T) + A \sum_{k=0}^{N-1} u_k^2 \Delta t$$ Take $\lambda = 2$ and $a = 0$ to simplify things a bit. - With $0 \le x(k) \le 1.5$, take $x$ quantized into four possible values $x_k \in {0, 0.5, 1.0, 1.5}$ - With control bounded $|u(k)| \le 1$, assume it is quantized into five possible values: $u_k \in \{-1, -0.5, 0, 0.5, 1\}$ June 18, 2008 16.323 3-13 Take min across each row to determine best action at each possible $x_1 \rightarrow J(x_2)$ $$x_1 \rightarrow x_2$$ 0 → 0 0.5 → 0.5 1 → 0.5 1.5 → 1 Can repeat the process to find the costs at time t = 0 which are $$J_0 = \Delta J_{01} + J_1(x_1)$$ $$J_0$$ $x_0$ 0 0.5 1 1.5 0 0 0.75 2.75 XX 0.5 0.5 0.25 1.25 3.5 1 2 0.75 0.75 2 1.5 XX 2.25 1.25 1.5 and again, taking min across the rows gives the best actions: $$x_0 \rightarrow x_1$$ 0 → 0 0.5 → 0.5 1 → 0.5 1.5 → 1 So now we have a complete strategy for how to get from any $x_0$ to the best $x_2$ to minimize the cost - This process can be highly automated, and this clumsy presentation is typically not needed. June 18, 2008 June 18, 2008

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(1 point) Suppose that high temperatures in College Place during the month of January have a mean of 32.8°F. If you are told that Chebyshev's inequality says at most 12.5% of the days will have a high of 35.8°F or more, what is the standard deviation of the high temperature in College Place during the month of January? Round your answer to one decimal place. Answer: 1

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calculate ph of solution 9: using BCA and RICE chart: 15.0 mL of the 0.50 M acetic acid + 0.50 M sodium acetate mixture and 10.0 mL of 0.50 M HCl

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What best describes the stretch-shortening cycle? Select one: a. The use of elastic energy in the antogonist during a neuromuscular stretch. b. The use of elastic energy stored during the eccentric contraction phase to augment the concentric phase. c. The use of elastic energy to activate the agonist muscle during a static stretch. d. The use of elastic energy store within the antagonist muscle to improve the static stretch.

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4. Let A and B be two events. Show that if P(A) = 1 and P(B) = 1, then P(AB) = 1. 5. A point is selected at random from the interval (0, 2000). What is the probabil

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14 The DFD that shows an overview of organizational system is: Select one: a. Level-1 DFD b. Level-0 DFD c. Context DFD d. Level-n DFD

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The previous function it mentions is listed below: def draw_shape_line(fillSize, fillChar, preSize=0, preChar='', leftChar='', rightChar='') So if draw_shape_line(8, '*', preChar='A', preSize=3, leftChar='/', rightChar='\') is called the output is AAA/******** Diamond Shape You should implement the following functions to print a diamond shape. print_diamond(size, priorChar, fillChar). This function will call the draw_shape_line function described above to print the shape. It will use the priorChar to print the area prior to the diamond and the fillChar to print the area inside the diamond. The shape will have a height and a width of the given size. For example, when this function is called by print_diamond(10, '', 'T'), it should print the following shape: ****/ ***/ TT **/ TTTT LLLLLL/ LLLLLLLL/ TTTTTTTT/ /LLLLLL /LLLL* ***TT/ make_diamond. This function will prompt the user for entering the size, the edgeChar, and the fillChar. We limit the size to no more than 80 characters. The width of the diamond should be validated as no more than 20 characters and should also be even, or input should be taken again.

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5) Rice has an inelastic demand, but demand for Uncle Ben's Rice is relatively elastic. Explain why? (2 marks)

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Assume code is running in the main thread on an ARM processor, and then a subroutine is called. As part of the subroutine call: Select one: a. The program counter is pushed onto the stack, and the registers holding parameters for the subroutine are pushed onto the stack b. Processor flags are pushed onto the stack, the link register is pushed onto the stack, and the registers holding parameters for the subroutine are pushed onto the stack c. Processor flags are pushed onto the stack and the registers holding parameters for the subroutine are pushed onto the stack d. The link register is pushed onto the stack, and the registers holding parameters for the subroutine are pushed onto the stack e. The registers holding parameters for the subroutine are pushed onto the stack f. None of the other answers are correct.

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You are trying to drive to the mall. However, the road to get there is closed and you are required to take the detour. Because of the detour, how many more miles did you have to drive? [A] 6 miles [B] 13 miles [C] 17 miles [D] 23 miles

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dillon b.