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  1. ichabodgrant

    Non-composite beam analysis

    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...
  2. ichabodgrant

    Size of specimen and compressive strength of concrete

    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 prefered...
  3. ichabodgrant

    Comparator design using a 4-bit adder

    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 +...
  4. ichabodgrant

    Op-amp as a comparator (analog-to-digital conversion)

    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...
  5. ichabodgrant

    Probability question on fair coin

    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...
  6. ichabodgrant

    Probability and normal distribution

    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...
  7. ichabodgrant

    Prove arcsin x for its logarithm form

    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 learnt about complex logarithms. The Attempt at a Solution I try to use x = sin y. But it seems...
  8. ichabodgrant

    Decomposition using roots of unity

    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...
  9. ichabodgrant

    Thevenin's and Norton's Theorem

    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...
  10. ichabodgrant

    Engineering Circuit with 2 voltage sources and 1 current source

    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...
  11. ichabodgrant

    Engineering Op-amp circuit analysis 2

    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...
  12. ichabodgrant

    Engineering Op-amp circuit analysis

    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 -...
  13. ichabodgrant

    Finding a basis of a space

    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...
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