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Question 437912: These are my questions. I have no clue how to do these. I need to know step by step how you got the solutions. Thank you!
1. Buildings often include stairways of steps with 7 inch risers and 11 inch treads. If one were to lay a board on such a stairway to make a temporary ramp, what would the grade, or slope, of the ramp be? (Round to the nearest hundredth.)
2. The amount of farmland in the United States (in millions of acres) can roughly be estimated by the linear equation A = -3t + 980, where A is the amount of farmland in acres and t is the number of years after 1990. Using this equation, approximately how many acres of farmland were there in 1995? In 2000? In 2010? What is the approximate rate of change for the amount of farmland, in acres, with respect to time, in years?
3. The cost, C, in hundreds of dollars, of a commercial telephone line for a business is given by C = 0.75m + 3, where m is the number of months that the telephone line has been in use. Find the cost of the phone line for 1 month, 2 months, 3 months, and 8 months. Insert a graph of this equation, using either Ian Vogt’s graphing website or MML, below.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! 1. The grade, or slope is simply the rise over the run:
Slope = rise/run = 7/11 = 0.64
2. Given A = -3t + 980
Since 1995 is 5 years after 1990, we substitute the value 5 in the equation
A(5) = -3(5) + 980 = 965 million acres
For the year 2000 we have:
A(10) = -3(10) + 980 = 950 million acres
And for 2010:
A(20) = -3(20) + 980 = 920 million acres
From 1990, when A = 980 to 2010 when A = 920 the change was 60 million acres in 20 years.
Therefore the rate of change is 60/20 = 3 million acres per year
Of course, we also can see this from the slope of the equation, -3.
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