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Hi, normally when we try to analyse a structural beam with composite section, we apply transformed section method or so. But what if two beams are just put together (one onto another one) instead of having a composite relation (e.g. glued together), how am I going to analyse the forces and...

Hello everyone. I have a question about compressive strength of concrete. It is said that (in my country) 150 mm x 150 mm x 150 mm concrete cube is used for concrete testing. Someone asks me why 100 mm x 100 mm x 100 mm is not used. In fact, I know that sometimes it is allowed or even preferred...

And you mentioned that there should not be Cin? Does this mean there are no cascading inputs?

I have a question about the XOR gates. Are those XOR gates for doing 2's complement (i am thinking in this way)? But I know that 2's complement is not just inverting 1 and 0, but also needs to add 1 after that. It seems that the above design cannot do that?

A truth table looks like this? because I have never drawn a truth table for such a design...so I searched on google...

I think it should be using 2's complement.

Homework Statement Hi, it's me again. Now I am going to design a 4-bit magnitude comparator using just ONE 4-bit adder and infinitely large number of gates (AND, OR, NOT, NAND, NOR, XOR, XNOR) for signed numbers (negative binary). Homework Equations A > B => A3barB3 + A2barB2x3 +...

Homework Statement Okay, This time it's an exam question. I am doing some past papers and there are questions about comparators which are not introduced in this course (this course is preliminary course for engineering students who are interested in electrical, electronic or computer...

thank you for your kindness

then 1 - 0.52 = 3/4

so the probability of getting HH is p2? Then the required probability is 1- p2?

If it is HT, then no matter the next one is T or H, TH already occurs before HH, right? If it is TT, then also no matter the next one is T or H, TH already occurs before HH, right? If it is TH, then obviously no matter the next one is T or H, TH already occurs before HH, right? Just the case if...

so if there is no HH, then it is alright? Let the probability of getting a H be p. Then the required prob. is 1 - p2?

Actually TT, HT,TH all means TH must occur before HH, right?

Should I indeed use conditional probability? In case I have a T at the 1st trial, then it already achieves the event that TH appears before HH?

Oh Sorry... I have a typo in the question... The correct question is "T,H before HH"

but it seems 0.5*0.5*0.5*... , gets you 0...

1?

Which two? TH and HT? 0.5*0.5 + 0.5*0.5 = 0.5?

So simply calculate the first case?

Same?

I don't quite understand your question... The prob. of getting a head or a tail is 1/2? Is this what you are asking?

Homework Statement A fair coin is continually flipped. What is the probability that the pattern T,H occurs before the pattern H,H, where T and H respectively denote Tail and Head of a coin? Homework Equations Prob. = (n r) (pr)(1-p)n-r The Attempt at a Solution I am thinking whether the...

because question 1 is P(acceptable)...so I use it directly...

So is this P(more than 2 tests) = 1 - [ P(1st acceptable) + P(1st rejected, 2nd accpetable) ] = 1 - [ p + (1-p)p ] wrong?

I understand 1st and 3rd question now. For 2nd question, my approach now is let p be the P(accpetable) in 1st question. P(more than 2 tests) = 1 - [ P(1st acceptable) + P(1st rejected, 2nd accpetable) ] = 1 - [ p + (1-p)p ]. Is this correct?

Homework Statement Due to the pollution from the industry around an apple farm, the apples grown there may be contaminated by heavy metals. It is believed that the amount of heavy metals in an apple of the farm follows the Normal distribution. N(16,16) which has a mean μ = 16 units and σ = √16...

Homework Statement Given sin x = (eix - e-ix) / 2i, I want to prove that arcsin x = -i ln(ix + √1 - x2) Homework Equations I know about the Euler's formula and complex number. But I have never learned about complex logarithms. The Attempt at a Solution I try to use x = sin y. But it seems...

Sorry. My typo... It should be (e2πi/5)5, so it equals 1.

I can solve it now. Thanks.

You mean I can make two pairs into the form (x−r)(x−r∗) that makes them real?

You mean this pair are conjugates to each other?

I can get (x - 1)(x4 + x3 + x2 + x + 1), but then what to do? To decompose (x4 + x3 + x2 + x + 1) into 2 more?

Homework Statement Decompose x5 - 1 into the product of 3 polynomials with real coefficients, using roots of unity. Homework Equations As far as I know, for xn = 1 for all n ∈ ℤ, there exist n distinct roots. The Attempt at a Solution [/B] So, let ω = e2πi/5. I can therefore find all the 5th...

IN = 2.6 x 10-3 A and RN = Rth I had thought about using superposition... But when I attempted to do this question, I hadn't clearly understood these theorems. My lecturer just taught too fast... I couldn't really get myself familiar with these theorems just from what he taught in class. So I...

Hi. It's me again. Right now I have some troubles with Thevenin's and Norton's theorem. Here is the circuit. I have to find the thevenin voltage Vth and thevenin resistance Rth and solve the circuit when there is a 2000Ω resistor connected to A and B. Then, I try to solve it... First, for the...

Thank you very much.

Here is the circuit. I have to find the voltage across each resistor and the current i1 and i2. My attempts are the following: By KCL, i2 + i1 = 0.1 A By KVL, 3 - 5 - 100i1 + 1100i2 = 0 ∴ i1 = 0.09 A, i2 = 0.01A ∴ Voltage across 100Ω resistor = 0.09 × 100 = 9 V, voltage across 1100Ω resistor...

I know all these... the non-inverting and inverting op-amp... I simply can't distinguish them easily...so I prefer deriving the equations every time...

R1 = 5R2 R3 = (1/5)R4 there might be some calculation mistakes...

I think I was taught the superposition theorem... I just simply get confused at the line joining node D and E... As no current flow through these two nodes (or just 1 node as their potentials are the same), so current from C to D means from C to E?

So are node D and E having same potential?

Sorry.. I want to say V at E = V at D a typo

Hi. I have moved on to the next question. There is something I am confused. The question wants us to express Rf in terms of R such that vo = -15vi. After doing the last task, I think I understand the flow of solving it. But here still exists a problem. My attempts and question are listed in...

I solve it... I had never thought of using comparing coefficients... turns out to be not too difficult...Thanks everyone

In the following circuit, compute the values of R1 and R3 in terms of R2 and R4, such that vo is always equal to v1 - 5v2. I have marked 3 nodes, A, B and C. v+ = v- as assumption for the op-amp. Consider node A. v- = v+ = v1 × (R2 / (R1+R2)) Consider node B and C. (v- - v2) / R3 = (vo -...

Yeah typo...sorry the 2 is redundant

So my second try is correct? Better to let w1, w2, w3, w4, w5 instead of x...?

Let u = [1, 2, 3, -1, 2]T, v = [2, 4, 7, 2, -1]T in ℝ5. Find a basis of a space W such that w ⊥ u and w ⊥ v for all w ∈ W. I think the question is quite easy. Given this vector w in the space W is orthogonal to both u and v. I can only think of w being a zero vector. But would this be too...