5. If \( x^{2}+y^{2}+6 x+8 y+1=0 \), find \( \frac{d x}{d y} \) in terms of \( x \) and \( y \quad 5 \) marks

\( : \int _ { - 3 } ( x ^ { 2 } + 7 x - 8 ) d x \)

2) La ecuación del movimiento de una particula está dada por: \( s(t)=t^{3}-3 t \) Encontrar: a) La velocidad como función de \( t \) b) La aceleración después de 4 segundos. c) la aceleración cuando la velocidad es cero.

2. \( y=\frac{3^{\sqrt{x}}}{\lg (3-x)} \)

A national fast food company has just analyzed the effect of the latest sales promotion. It has determined that the sales decay for its milkshakes is given by \( S=285,000 e^{-0.7 x} \), where \( S \) is the weekly sales and \( x \) is the number of weeks that have passes since the end of the sales promotion. a) Determine the sales 2 weeks after the end of the promotion: Round answer to 2 decimal places. Sales \( =\$ \) b) If no new campaign is started, how many weeks after the end of the promotion will sales drop below 30,000 ? Round answer to 1 decimal place. Num. weeks =

Find the average rate of change of \( h(x)=-2 x^{2}-5 x \) from \( x=-4 \) to \( x=1 \). Simplify your answer as much as possible.