Fuency Set up let statements for appropriate expressions and using these expressions set up an equation that allows you to find each number deseribed. Be sure to find EACH integer you are looking for. (a) Find two consecutive integers such that ten more than twice the smaller is seven less than three times the larger.

1) The domain of the function \( f(x)=\sqrt{2 x+6} \) is: a) \( ]-\infty,-3] \) b) \( [-3, \infty[ \) c) \( [3, \infty[ \) d) \( ]-3, \infty[ \)

The vertical position \( y \) (in feet) of a rock \( t \) seconds after it was dropped from a cliff is given by the formula \( y=-16 t^{2}+14 t+200 \). The base of the cliff corresponds to \( y=0 \). How many seconds will it take for the rock to hit the ground at the base of the cliff? 3 seconds 6 seconds 8 seconds 4 seconds

The equation \( y=2\left(3^{\prime}\right) \) shows the number of infected people from an outbreal of the norovirus. The variable \( y \) represents the number of infected people, an \( t \) represents time in weeks. In how many weeks will the number of infected people reach \( 1,458 ? \) a.) 6 weeks b.) 5 weeks c.) 10 weeks d.) 12 weeks

ii) A numerical integration technique [Note: the work done is given by the area under the curve]

(b) let the systen of differential equations be given by \[ \frac{d x}{d t}=-x y+x(1-x) \] \[ \frac{d y}{d t}=-3 x^{2} y+2 y\left(1-\frac{y^{2}}{2}\right) \] (i) Determine the \( x-i \) socines and \( y \) - isoclines and tee signs of \( \frac{d z}{d t} \) and dy/dt. (ii) Determine the equilibrium points of the system.