6. (a) use the complementary function and particular integral method to solve the differential equation: dx2 dx given that y(0) 6 and y (0) 3. state, with reasons, whether the system represented by this equation is stable or not. (15 marks) (b) (i) using the substitution t = 1 +x2 show that. (ii) hence, using separation of variables, obtain the general solution of the differential equation dy (ii) given the inital condition y(0) 2 obtain the particular solution of the differential (10 marks) equation given in part (ii).

5,600 x 10^3 = a) 560 b) 5,000,600 c) 5,600,000 d) 56,000

The larger of two number is 4 less than twice the smaller number. the sum is 41. find the numbers

Cone w has a radius of 8 cm and a height of 5 cm. square pyramid x has the same base area and height as cone w. paul and manuel disagree on how the volumes of cone w and square pyramid x are related. examine their arguments. which statement explains whose argument is correct and why? paul manuel the volume of square pyramid x is equal to the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is three times the volume of cone w. this can be proven by finding the base area and volume of cone w, along with the volume of square pyramid x. the base area of cone w is π(r2) = π(82) = 200.96 cm2. the volume of cone w is one third(area of base)(h) = one third(200.96)(5) = 334.93 cm3. the volume of square pyramid x is (area of base)(h) = (200.96)(5) = 1,004.8 cm3. paul's argument is correct; manuel used the incorrect formula to find the volume of square pyramid x. paul's argument is correct; manuel used the incorrect base area to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect formula to find the volume of square pyramid x. manuel's argument is correct; paul used the incorrect base area to find the volume of square pyramid x.