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Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
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- Let f and g be functions from the positive integers to the positive integers defined by the equations f(x) = 3x + 1, g(x) = x2 + 2, h(x) = 7x - 3 Find the compositions a) g°h (x) b) g° f (x)arrow_forwardFind all solutions, if any, to: (a) 7x=3(mod 11) (b) 4x=1(mod 6)arrow_forwardNelson-Oppen Use the Nelson-Oppen procedure to prove that the following formula over the theories of uninterpreted functions and linear real-valued arithmetic is unsatisfiable: g(f(x – 2)) = x + 2 A g(f(y)) = y – 2A (y +1= x – 1)arrow_forward
- A circle in the XY-coordinate system is specified by the center coordinates (x, y) and radius (r). Read the values for 2 circles- x1, y1, r1 for C1 and x2, y2, r2 for C2. (i) Determine whether the 2 circles intersect. To solve the problem it suffices to check if the distance between the 2 centers is lesser than the sum of radii of the 2 circles. (ii) Find the smallest circle that encloses the two circles and return its center coordinates and radius. programming language - carrow_forwardA discharge factor is a ratio which compares the mass flow rate at the end of a channel or nozzle to an ideal channel or nozzle. The discharge factor for flow through an open channel of parabolic cross-section is: K = 1.2 [V16x +1+ In(V16x² +1+4x)]³ 4x where x is the ratio of the maximum water depth to breadth of the channel at the top of the water. Determine the discharge factors for x in the range 0.45 to 0.90 in steps of 0.05. Script e C Reset I MATLAB Docume 1 %Give values for x: 2 3 %Solve for K: 4arrow_forwardQ2: Apply De Morgan's theorem to (A.B+A. B)arrow_forward
- 4) Similar to Goldbach’s Conjecture, Lagrange’s Conjecture says that every odd Natural number can be written as a sum of primes a and b in the form “a + 2*b”. Show that this Conjecture is true by finding a and b for the following numbers: a) 15 b) 25.arrow_forwardFind the value of Marrow_forwardDuring a journey, a car accelerates from (10 m/s) to (20 m/s) in (5 sec). Calculate the acceleration of the car: 2.5 О 3.0 1.5 2.0 A bullet of mass 20g is found to pass two points 30m apart in a time interval of 4s. Calculate the kinetic energy of the bullet if it moves with constant speed. * 0.562J O 5J 2J O 2.5Jarrow_forward
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