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1) [15 points] Use the Extended Euclidean Algorithm to write the GCD of 1183 and 826 as a linear combination of themselves. Show the computations explicitly! [Hint: You should get 7 for the GCD!]2) [13 points] Compute the LCD of 1183 and 826 [the same numbers above!].3) [15 points] Find the remainder of the division of 94821532 when divided by 5 [i.e., what is 94821532congruent to modulo 5]. Show your computations explicitly!4) [15 points] Give the set of all solutions of the system4x ≡ 5 (mod 15)5x ≡ 22 (mod 33)[Hint: The system does have solution(s)!]5) [12 points] Suppose thatm = 2a· 32· 5b· 73,n = 25· 3c· 54· 7d,gcd(m, n) = 25· 32· 5 · 72,lcm(n, m) = 27· 32· 54· 73.Find a, b, c and d.6) [15 points] Let a, b and c be positive integers and suppose that there are r, s, t ∈ Z such thatra + sb + tb = 1.Prove that gcd(a, b, c) = 1.7) [15 points] Let p be a prime. Prove that for any integer a such that p - a, the equationxp-1 - x + a = 0 never has an integral [i.e., in Z] solution.[Hint: As I've mentioned before, if an equation has an integral solution, it has a solution moduloany m.]
Find the equation of the regression line. Graph the line . Determine the slope and y-intercept of the regression line.
A jeweler has three small solid spheres made of silver, of radius 2 mm, 6 mm, and 6 mm. He decides to melt these down and make just one sphere out of them. What will the radius of this larger sphere be?
In 2007, a bank was offering 4.39% interest on its online Orange Savings Account, with interest reinvested quarterly. Find the associated exponential model for the value of a $4,000 deposit after t years.
Find a function that relates dollars to Euros, find a function that relates Euros to yen and what is g(f(1000))?
Take 4900 draws from this distribution. Graph the histogram & give the mean and variance of this sample. (Hand in only the histogram and the results for mean and variance).
passes under it. How fast is the distance s(t) between the bicycle and balloon increasing 6 seconds later?
Determine which coin is the counterfeit coin in as few weightings as possible. Does your method also allow you to state whether the counterfeit coin is heavy or light?
determine the stability of the critical point for both the linearized and nonlinear system using the linearization process (that is, explicitly writed own the linearized system at (1,1) and use the eigen values of the corresponding coefficient mat..
Assuming that the speaker and the cat fanciers met by traveling in opposite directions, what is the answer and how many kittens are being transported
A balloon rises at the rate of 8 feet per second from a point on the ground 60 feet from an observer. Find the rate of change of the angle of elevation when the balloon is 25 feet above the ground.
A 5000-lb wrecking ball hangs from a 20-ft cable of density 5 lb/ft attached to a crane. Calculate the work done if the crane lifts the ball from ground level to 20 ft in the air by drawing in the cable.
Find the indefinite integral of f(x) and Find the compression x when the energy - Evaluate the integrals using integration by parts.
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