Steven needs to buy t theme park tickets for himself and his family. Each ticket costs $80,and the number of tickets he needs to buy can be modeled by the expression `t^2-4t-90=6` when `t gt 0`. What is the total cost of the theme park tickets that Steven Purchased?

For his 18th birthday in February Peter plants to turn a hut in the garden of his parents into a swimming pool with an artifical beach. In order to estimate the consts for heating the water and the house , peter obtains the data for the natural gas combustion and its price. What is the total energy (in MJ) needed for Peter's "winter swimming pool" calculated in 1.3 and 1.4? How much natural gas will he need, if the gas heater has an efficiency of 90.0% ? What are the different costs for the use of either natural gas or electricity ? Use the values given by PUC for your calculations and assume 100% efficiency for the electric heater. Table 1: Composition of natural gas {:("Chemical substance","mol fraction x",D_(1)H^(@)(KJ mol^(-1))^(-1),S^(@)(J mol^(-1)K^(-1))^(-1),C_(p)^(@)(J mol^(-1)K^(-1))^(-1)),(CO_(2(g)),0.0024,-393.5,213.6,37.1),(N_(2(g)) ,0.0134,0.0,191.6,29.1),(CH_(2(g)),0.9732,-74.6,186.3,35.7),(C_(2)H_(3 (g)),0.0110,-84.0,229.2,52.2),(H_(2)O_(g),-,-285.8,70.0,75.3),(H_(2)O_(g),-,-241.8,188.8,33.6),(H_(2)O_(g),-,0.0,205.2,29.4):} Equation J=E(A.Deltat)^(-1) =!! lambda "wall" . DeltaT. d^(-1) , where J= energy flow E along a temperature gradient (wall direction Z) par area A and time Deltat , d-wall thickness , lambda wall -heat conductivity , DeltaT - difference in temperature between the inside and the outside of the house.

The drama department at a middle school wants to determine the price to charge for tickets to a show . If the price is too low, there won't be enough money to cover expenses. If its too high, they may not get a big enough audience. The teacher estimates that the profit, P, in dollars per show, can be represented by P=-(t-12)^2+100 , where t is the price of a ticket in dollars . When the profit is 0, the drama department breaks even . What is the lowest ticket price for which the department breaks even ?

The director of the Blue Rose club must decide what to charge for a ticket to the club’s performance of The Music Man. If the price is set too low, the club will lose money, and if the price is too high, people won’t come. From past experience she estimates that the profit P from sales (in hundreds) can be approximated by P(x)=-x^(2)+22x-40 where x is the cost of a ticket and 0le x le 25 thousand rupees. What is the lowest cost of a ticket that would allow the club to break even.