B. \( 6^{\text {th }} \) week II. Work out (Show each siens learly) 6. In an arithmetic sequence, if the \( p^{\text {th }} \) term is \( q \) and the \( q^{\text {th }} \) term is \( p \), find the \( (p+q)^{\text {th }} \) term. Find the first term of the sequence \( 4,12,36,108 \ldots \) which exceeds 20,000 . 8 . Find \( S_{100} \) when the general term \( a_{n}=\frac{n}{n+1}-\frac{n+1}{n+2} \) 9 . Find the absolute maximum valuc of \( f(x)=2 \cos x+x \) on \( [0,2 \pi] \) ? 10. Find the interval on which \( f(x)=x \sqrt{x+1} \) (s increasing?

Norman and Suzanne own 31 shares of a fast-food restaurant stock and 76 shares of a toy company stock. On a particular day in 2021 , their stock portfolio consisting of these two stocks was worth \( \$ 7165 \). The fast-food restaurant stock was \( \$ 195.75 \) more per share than the toy company stock. What was the price of each stock on that day? The price per share of the fast-food restaurant stock is \( \$ 206 \). The price per share of the toy company stock is \( \$ \square \).

Kevin and Randy Muise have a jar containing 66 coins, all of which are either quarters or nickels. The total value of the coins in the jar is \( \$ 6.50 \). How many of each type of coin do they have?

Graph the line with the equation \( y=-\frac{1}{2} x-4 \)

Pratap Puri rowed 18 miles down a river in 2 hours, but the return trip took him \( 4 \frac{1}{2} \) hours. Find the rate Pratap can row in still water and find the rate of the current. Let \( x= \) rate Pratap can row in still water and \( y= \) rate of the current. What is the rate that Pratap rows in still water? Pratap can row at a rate of (Type an integer or a decimal.)

Graph the line with the equation \( y=-\frac{1}{2} x-1 \)