The following two functions have a common input, year t: R gives the average price, in dollars, of a gallon of regular unleaded gasoline, and P gives the purchasing power of the dollar as measured by consumer prices based on 2010 dollars. (a) Using function notation, show how to combine the two functions to create a new function giving the price of gasoline in constant 2010 dollars R(tdollars gallon (RP(t dollars gallon 2010 dollars P(t) dollars (at pump) R(t) dollars. P(tdollars (at pump) 2010 dollars (R P)(t) 2010 dollars gallon gallon Rit dollars . Pt dollars (at pump) 2010 dollars (R P(t dollars gallon gallon OR(t) dollars gallon 2010 dollars P(t) 2010 dollars gallon P(t) dollars (at pump) (R OR(t)dollars gallon 2010 dollars P(t) dollars (at pump) = (R + P)(t 2010 dollars gallon (b) What are the output units of the new function? O2010 dollars per gallon Odollars per gallon gallons per dollar 2010 dollars per dollar (at pump) Ogallons per 2010 dollar

The total cost C for a manufacturer during a given time period is a function of the number N of items produced during that period. To determine a formula for the total cost, we need to know the manufacturer's fixed costs (covering things such as plant maintenance and insurance), as well as the cost for each unit produced, which is called the variable cost. To find the total cost, we multiply the variable cost by the number of items produced during that period and then add the fixed costs.Suppose that a manufacturer of widgets has fixed costs of $9000 per month and that the variable cost is $14 per widget (so it costs $14 to produce 1 widget). (a) Use a formula to express the total cost C of this manufacturer in a month as a function of the number of widgets produced in a month. (Use N as the number of widgets produced in a month.)C =    (b) Express using functional notation the total cost if there are 225 widgets produced in a month.C(  )Calculate the total cost if there are 225…

The linearization of a function works best when it is used to approximate a function, meaning behaviour and value, close to the point of tangency.  A. True B. False

Level curves (isothermals) are shown for the water temperature (in °C) in Long Lake (Minnesota) in 1998 as a function of depth and time of year. Estimate the temperature in the lake on October 7 (day 280) at a depth of 5 m and on June 9 (day 160) at a depth of 10 m. X°C (day 280 and depth 5 m) X°C (day 160 and depth 10 m) Enter a number. Depth (m) 0 sti 10- 15+ 12 16 + 120 20 160 20 Day of 1998 16 200 240 280