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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.]
a triangle field with vertice OPQ has sides OP=402 meters, PQ=388 meters, and QO=254 meters. find the perpendicular distance from the vertex P to the opposite side?
A car is traveling at 100 km/h when the driver sees an accident 80 m ahead and slams on the brakes. What constant deceleration is required to stop the car in time to avoid a pileup?
There were 116 fewer blue balloons than white ones. How many balloons of each color did Marty inflate?
It is estimated that y , the number of items of a particular commodity (in millions)sold in the united States in year x represents the number of years since 1990 , is given the formula y=1.38x+3.49.
1. the way we feel emotionally and the way we feel physically are increasingly seen as single parts of a whole.nbsp
Description of Directional Derivative and how the dot product can be used to justify that the gradient points in the direction of maximum of a function.
Find coefficients An and Bn such that this is satisfied.
There are 5 pirates and a pot of 100 gold pieces. All the pirates have different ranks. The most senior pirate has to propose a split of the gold, such that at least half of the pirates agree.
in a time study of a process the average time to complete a unit was 36.5 minutes the performance rating of the worker
It is known that 20% of old cars cannot pass the emission test . Four old cars are selected randomly . x is the number of card in the sample that cannot pass the emission test.
A spherical ballon is being inflated at the rate of 5 cubic inches a minute. At what rate is the radius changing after ten minutes?
A plane travels 170 miles on a bearing of N18 degree e and then changes its course to N 49 E and travels 120 mi . find the total distance traveled north and the east.
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