Question A rod of length L lies along the x axis with its left end at the origin. It has a nonuniform charge density λ = αx, where α is a positive constant. Calculate the electric potential at point B , which lies on the perpendicular bisector of the rod a distance b above the x axis. (Use the following as necessary: α, ke, L, b, and d.)

James (mass 90.0 kg) and Ramon (mass 60.0 kg) are 20.0 m apart on a frozen pond. Midway between them is a mug of their favorite beverage. They pull on the ends of a light rope stretched between them. When James has moved 6.0 m toward the mug, how far and in what direction has Ramon moved?

2. In the above circuit, the initial conditions are all zero and the op-amp is ideal. (15 pts) A. Determine the transfer function, 𝐻(𝑠)=𝑉𝑂(𝑠)𝑉𝐼(𝑠) in one of the following forms: i) 𝐻(𝑠)=𝑘𝑐𝑠2+𝑏𝑠+𝑐 , where 𝑘,𝑏 and 𝑐 are constants; ii) 𝐻(𝑠)=𝑘𝑠2𝑠2+𝑏𝑠+𝑐 , where 𝑘,𝑏 and 𝑐 are constants; iii) 𝐻(𝑠)=𝑘𝑏𝑠𝑠2+𝑏𝑠+𝑐 , where 𝑘,𝑏 and 𝑐 are constants; iv) 𝐻(𝑠)=𝑘𝑠2+𝑐𝑠2+𝑏𝑠+𝑐 , where 𝑘,𝑏 and 𝑐 are constants. B. Determine the type of filter implemented by the circuit. C. If the circuit is a low-pass or high-pass filter, do Parts i and ii. If the circuit is a band-pass or band-reject filter, do Parts iii. i) Determine the order of the filter. ii) Find the values for the relevant components that will yield a gain of 8 under the requirement that ALL resistors must have a resistance greater than or equal to 1kΩ. iii) Find the values for the relevant components that will yield a bandwidth of 𝛽=12500 rad/s and a gain of 8 at the resonance frequency under the requirement that ALL resistors must have a resistance greater than or equal to 1kΩ. с RO R + V;(t) + Vo(t) bs 2. In the above circuit, the initial conditions are all zero and the op-amp is ideal. (15 pts) A. Determine the transfer function, H(S) Vo(s) in one of the following forms: V;(s) i) H(S) =k Sa+bs+c' where k, b and c are constants; s2 ii) H(S) = k where k, b and c are constants; 52+bs+c' iii) H(S) = k where k, b and c are constants; $2+bs+c' Sa+C iv) H(S) = k where k, b and c are constants. $2+bs+c' B. Determine the type of filter implemented by the circuit. C. If the circuit is a low-pass or high-pass filter, do Parts i and ii. If the circuit is a band- pass or band-reject filter, do Parts iii. i) Determine the order of the filter. ii) Find the values for the relevant components that will yield a gain of 8 under the requirement that ALL resistors must have a resistance greater than or equal to 1kl. iii) Find the values for the relevant components that will yield a bandwidth of B = 12500 rad/s and a gain of 8 at the resonance frequency under the requirement that ALL resistors must have a resistance greater than or equal to 1kN.

Q1) Assuming the passive sign convention, sketch the voltage which develops across the terminals of a 2.5 F capacitor in response to the current waveforms (3marks) a) i(t) (A) d t(s) 1 2 3 b) i(t) (A) 2 t(s) 2 3 c) i(t) (A) 3 t(s) 0 1 2 3

Let the functions of f,g and h be defined as follows: f:R → R, f(x) = 4x -3 g:R→ R, g(s) = x2 + 1 h:R → R, h(x) = Find rules for the following functions with domain and codomain R: i) f o f ii) f o g iii) g o f iv) f o h ſi if x>0 1 > 10 if x < 0 X

Q1) Assuming the passive sign convention, sketch the voltage which develops across the terminals of a 2.5 F capacitor in response to the current waveforms (3marks) a) i(t) (A) 2 t(s) 0 2 2 3 -21 b) i(t) (A) 2 3 0 1 2 3 -2 c) i(t) (A) 3 t(s) 0 1 2 3

help A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in: 4: 331.2 409.5 311.0 326.5 316.8 349.8 309.7 6: 424.1 347.2 361.0 404.5 331.0 348.9 381.7 8: 396.4 366.2 351.0 357.1 409.9 367.3 382.0 10: 351.7 452.9 461.4 433.1 410.6 384.2 362.6 12: 417.4 441.8 419.9 410.7 473.4 441.2 465.8 in USE SALT Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. lo Ho: Mq #M2 * Hz * M4 #45 M: all five 4's are equal O Ho: M1 = M2 M3 = 44 = 45 Ma: at least two M's are unequal O HO = H2 = Uz = 44 = Ms Ma: all five w's are unequal 10 Hoi My & My & Hz * M4 #45 Ma: at least two m's are equal Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.) Degrees of freedom Sum of Mean Squares Squares Source f Treatments Error Total Give the test statistic. (Round your answer to two decimal places.)