Question A cylindrical blood vessel is partially blocked by the buildup of plaque. At one point, the plaque decreases the diameter of the vessel by 62.0%. The blood approaching the blocked portion has speed 𝑣0. Just as the blood enters the blocked portion of the vessel, what is its speed 𝑣, expressed as a multiple of 𝑣0?𝑣=

(17%) Problem l: An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: 0(t) = a + bt-ce where a = 2.9 rad, b = 0.35 rad/s2 and c = 0.045 rad/s3. Randomized Variables a= 2.9 rad b = 0.35 rad/s2 c= 0.045 rad/s3 20% Part (a) Determine an equation for the angular speed of the ride as a function of time, o(t). Write your answer using the symbols a, b, and c, instead of their numerical values. (1) = 2 bt-3ct? ✓ Correct! 20% Part (b) Besides at t= 0. at what time t, is the ride stopped? Give your answer in seconds. Correct! 5.19 20% Part (c) What is the magnitude of the angular displacement of the ride in radians between times t = 0 and t = t;? Δθ = Grade Summary Deductions 4% Potential 96% 7 8 9 HONE 11 ( E TA 4 6 sino cos tan cotan asino acos atan) acotan sinh cosh) tanh cotanh Degrees O Radians 1 2 3 - Submissions Attempts remaining: 3 (2% per attempt) detailed view 1 2% 2 2% + - 0 END NO BACKSPACE CLEAR Submit Hint Feedback I give up! Hints: 2% deduction per hint. Hints remaining: 3 Feedback: 2% deduction per feedback. A 20% Part (d) Determine an equation for the angular acceleration of the ride as a function of time, alt). Write your answer using the symbols a, b, and c, instead of their numerical values. A 20% Part (e) What is the angular acceleration in rad/s2 when the ride is at rest at t=tı?

a. Bank A offers three-year loans at 3.6% compounded quarterly. What nominal interest rate compounded monthly would a local bank have to offer you so that you would not be disadvantaged by choosing it? % Round to two decimal places b. Bank B offers four-year loans at 4.8% compounded monthly. What nominal interest rate compounded semi-annually would a local bank have to offer you so that you would not be disadvantaged by choosing it? % Round to two decimal places

2. For a wave characterized by the electric field E(2,t) = fax cos(6t - kc) + ýa, cos(ot-k+8) identify the polarization state, determine the polarization angles (y,x), and sketch the locus of E(0.t) for each of the following cases: a) ax = 3 V/m, ay = 4 V/m, and 8 = 0° b) az = 3 V/m, ay = 4 V/m, and 8 = 180° c) ax = 3 V/m, ay = 3 V/m, and 8 = 45°

Suppose that a borrower and a lender agree on the nominal interest rate to be paid on a loan. Then, inflation turns out to be lower than they both expected. Is the real interest rate on this loan higher or lower than expected? Does the lender gain or lose from this unexpected condition? Does the borrower gain or lose?

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