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Question 1

For the given power system, A = 1 2 8 0 ° Ω , B = ( 2 0 – j 2 5 ) Ω , and C = ( 8 0 + j 6 0 ) Ω . Note that 4 4 0 V is an rms value. Find the reactive power. The reactive power of the given power system is ( ◻ ) kVAR.

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For the given power system, A=1280°Ω,B=(20-j25)Ω, and C=(80+j60)Ω. Note that 440 V is an rms value. Find the reactive power. The reactive power of the given power system is ( ◻ ) kVAR.

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Question 2

6–15. Members AB and BC can each support a maximum compressive force of 800 lb, and members AD, DC, and BD can support a maximum tensile force of 2000 lb. If a = 6 ft, determine the greatest load P the truss can support

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6–15. Members AB and BC can each support a maximum compressive force of 800 lb, and members AD, DC, and BD can support a maximum tensile force of 2000 lb. If a = 6 ft, determine the greatest load P ...

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Question 3

Fig. 2 shows the activations in the three hidden units of a shallow network. The slopes in the hidden units are 1.0, 1.0, and -1.0, respectively, and the joints in the hidden units are at positions 1/6, 2/6, and 4/6. Find values of ϕ0, ϕ1, ϕ2, and ϕ3 that will combine the hidden unit activations as ϕ0+ϕ1h1+ϕ2h2+ϕ3h3 to create a function with four linear regions that oscillate between output values of zero and one. The slope of the leftmost region should be positive, the next one negative, and so on. How many linear regions will we create if we compose this network with itself? How many will we create if we compose it with itself K times?

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Fig. 2 shows the activations in the three hidden units of a shallow network. The slopes in the hidden units are1.0, 1.0, and -1.0, respectively, and the joints in the hidden units are at positions 1/6, 2/6, and 4/6. ...

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Question 4

Fig. 2 shows the activations in the three hidden units of a shallow network. The slopes in the hidden units are 1.0, 1.0, and -1.0, respectively, and the joints in the hidden units are at positions 1/6, 2/6, and 4/6. Find values of ϕ0, ϕ1, ϕ2, and ϕ3 that will combine the hidden unit activations as ϕ0+ϕ1h1+ϕ2h2+ϕ3h3 to create a function with four linear regions that oscillate between output values of zero and one. The slope of the leftmost region should be positive, the next one negative, and so on. How many linear regions will we create if we compose this network with itself? How many will we create if we compose it with itself K times?

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Fig. 2 shows the activations in the three hidden units of a shallow network. The slopes in the hidden units are1.0, 1.0, and -1.0, respectively, and the joints in the hidden units are at positions 1/6, 2/6, and 4/6. ...

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Question 5

Consider two neural networks that map a scalar input x to a scalar output y. The first network is shallow and has D = 95 hidden units. The second is deep and has K = 10 layers, each containing D = 5 hidden units. How many parameters does each network have? How many linear regions can each network make? Which would run faster?

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Consider two neural networks that map a scalar input x to a scalar output y. The first network is shallow andhas D = 95 hidden units. The second is deep and has K = 10 layers, each containing D ...

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Question 6

Consider a deep neural network with a single input, a single output, and K hidden layers, each of which contains D hidden units. Show that this network will have a total of 3D + 1 + (K − 1)D(D + 1) parameters.

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Consider a deep neural network with a single input, a single output, and K hidden layers, each of which containsD hidden units. Show that this network will have a total of 3D + 1 + (K − 1)D(D + ...

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Question 7

Consider a network with Di = 1 input, Do = 1 output, and K = 10 layers, with D = 10 hidden units in each. Would the number of weights increase more if we increased the depth by one or the width by one? Provide your reasoning.

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Consider a network with Di = 1 input, Do = 1 output, and K = 10 layers, with D = 10 hidden units in each.Would the number of weights increase more if we increased the depth by one or ...

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Question 8

Consider a deep neural network with Di = 5 inputs, Do = 1 output, and K = 20 hidden layers containing D = 30 hidden units each. What is the depth of this network? What is the width?

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Consider a deep neural network with Di = 5 inputs, Do = 1 output, and K = 20 hidden layers containingD = 30 hidden units each. What is the depth of this network? What is the width?

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Question 9

Show that: ReLU h β1+λ1 ·Ω1ReLU [β0+λ0 · Ω0x] i =λ0λ1 · ReLU 1 λ0λ1 β1+Ω1ReLU 1 λ0 β0+Ω0x , where λ0 and λ1 are non-negative scalars, Ωk is the weights matrix that are applied to the k-th layer (contribute to the (k + 1)-th layer) and βk is the the vector of biases that contribute to hidden layer k + 1. From this, we see that the weight matrices can be rescaled by any magnitude as long as the biases are also adjusted, and the scale factors can be re-applied at the end of the network. Hint: Use non-negative homogeneity property of the ReLU function.

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Show that: ReLU h β1+λ1 ·Ω1ReLU [β0+λ0 · Ω0x] i =λ0λ1 · ReLU 1 λ0λ1 β1+Ω1ReLU 1 λ0 β0+Ω0x , where λ0 and λ1 are non-negative scalars, Ωk is the weights matrix that are applied to the k-th layer (contribute to the (k + 1)-th layer) and βk is the the vector of biases that contribute to hidden layer k + 1. From this, we see that the weight matrices can be rescaled by any magnitude as long as the biases are also adjusted, and the scale factors can be re-applied at the end of the network. Hint: Use non-negative homogeneity property of the ReLU function.

2. Show that:ReLUhβ1+λ1 ·Ω1ReLU [β0+λ0 · Ω0x]i=λ0λ1 · ReLU 1λ0λ1β1+Ω1ReLU 1λ0β0+Ω0x ,where λ0 and λ1 are non-negative scalars, Ωk is the weights matrix that are applied to the k-th layer (contributeto the ...

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Question 10

Consider composing the two neural networks in Fig. 1. Draw a plot of the relationship between the input x and output y′ for x ∈ [−1, 1].

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Consider composing the two neural networks in Fig. 1. Draw a plot of the relationship between the input x and output y′ for x ∈ [−1, 1].

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