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Sample Question & Answer Of Algebra Homework Examples

MAT 142 College Mathematics

Question:

Every assignment must be typed and a sufficient amount of work shown. Use correct calculus notation.  Graphs must be done electronically (I do not want hand-drawn graphs.)  Directions for graphing using excel are available in blackboard.

You may ask for help with the assignments.

A car dealership keeps track of how much it spends on advertising each month and of its monthly revenue. From this information, the list of advertising expenditures and probably associated revenues are shown in the table below.

a. Find a cubic polynomial that models the data.

b. Find the first derivative and explain what it means in terms of the data.

c. Find the relative extremes and explain what they mean in terms of the problem.

d. Find the second derivative and explain what it means in terms of the data.

e. Find the point of diminishing returns and explain what it means in terms of the data.

Answer:

• a)The general cubic polynomial

y=ax³+bx²+cx+ d

There are four unknowns

Using (5,150) = 150= 125a +25 b +5c +d………………………………. (1)

Using (7,200) = 200 =343a +49b +7c +d………………………………... (2)

Using (9,250) =250=729a +81b+9c +d…………………………………… (3)

Using (11,325) = 325= 1331a +121b+11c+d…………………………... (4)

From equation 1 and 2 we get 218a +24b +2c =50……………… (5)

From equation 2 and 3 we get 386a +32b +2c =50……………… (6)

From equation 3 and 4 we get 602a +40b +2c=75………………….. (7)

On solving the above equation 5, 6, 7 we get;

a=0.52

b=-10.92

c=99.47 Read More...

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