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There are two essential tricks to grasp in this question. Firstly, since the equation has only one solution, the Discriminant that will be required would equal 0. Secondly, since we are given f(x) = 2 we ...

3x + y =23, 4x +4y=5212x+4y=92, 12x+12y=1568y=64y=8sub in3x+8=23, 3x=15x=5y=8x=5

solving horizontally, use v=s/t, where s=200, v=25(3)^1/2. Hence t=s/v=8/(3)^1/2 (where t is the time when the ball would reach the fort if it does not reach the ground)Solivng vertica...

∫ xsin3x dx takes the form of any integral ∫ (u)(dv/dx) dx.
∫ (u)(dv/dx) dx = uv - ∫ (v)(du/dx) dx
Taking u=x and dv/dx= sin3x. The equation can be re-written in the form uv - ∫ (v)(du/dx) dx....

Minimum point of Graph A:*complete square to find(x+2)^2 - 4 - 3 = 0(x+2)^2 - 7 = 0Therefore minimum point = (-2, -7)Minimum point of Graph B:(-2+3, -7+2) = (1, -5)*reverse complete the square method(x-1)...