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1. Let a, b be positive integers, and write a = qb + r, where q, r are Elements of Z and0 (= or)< r < b. Suppose that d = gcd(a, b).
a) If r = 0 show that d = b.
b) If r > 0 show that d = gcd(b, r).
2. Use Problem 1 to find:
a) gcd(100; 3);
b) gcd(100; 82).
Total number of arrangements.
Frame an equation.
During the first seconds, the height h of a baseball after t seconds is given by h = -16t +108t + 4. Estimate the height of the ball after 4 seconds.
Determine the nature of the solutions of the equation. Find and label the vertex and the line of symmetry. Graph the function F(x) = -(1/3)x2.
Write a matrix system of equations for the amounts and of salt in the two tanks after t minutes. Solve the system using matrix methods. Calculate how long it takes for tank 2 to have a salt concentration of 1 pound per gallon.
Solve the given fraction
The height of a building is 1411 ft. How long would it take an object to fall to the ground from the top? Use the formula s=16t^2, where s is the distance
Let B = . Find each of the following. You may use a calculator to replace hand calculation for row reduction and finding the characteristic polynomial. Show your work; don't just write down the answers.
During a road trip, Tonya drove one-third the distance that Lana drove. Mark drove 15 miles more than Lana. The total distance they drove on the trip was 491. How many miles did each person drive?
In a certain year, solar and wind energy generation totaled 1000 24 trillion BTUs. Wind generated 52 trillion BTUs more than eight times that generated by solar energy. How much was generated by each source?
What potential solution did you obtain
Given the linear equation y= -3/7x-1, find the y-coordinates of the points (-7, ), (0, ), and (7, ). Please show all of your work. Plot those points and graph the linear equation.
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