B.A. Mathematics Mississippi State UniversityM.S. MathematicsMississippi State UniversityPh.d. Curriculum & InstructionUniversity of Mississippi
Solve the quadratic equation by factoring.$$x^{2}+4 x-21=0$$
Use a graphing utility to graph $f(x)=\ln \left(x^{2}-4\right)$, $\mathrm{g}(x)=\ln (x+2)+\ln (x-2),$ and $h(x)=\ln (x+2) \ln (x-2)$ in the same viewing screen. Determine the domain where two of the functions give the same graph.
Medication. The amount of medication that an infant requires is typically a function of the baby's weight. The number of milliliters of an antiseizure medication $A$ is given by $A(x)=\sqrt{x}+2,$ where $x$ is the weight of the infant in ounces. In emergencies there is often not enough time to weigh the infant, so nurses have to estimate the baby's weight. What is the function that represents the actual amount of medication the infant is given if his weight is overestimated by 3 ounces?
Draw a graph whose domain is $(-\infty, 5]$ and whose range is $[2, \infty)$. Is your graph a function? Discuss why or why not.
In your own words, describe how to graph a piecewise-defined function.
Factor each trinomial by grouping. Exercises 9 through 12 are broken into parts to help you get started.$$15 x^{2}+11 x+2$$
Objective: Use a variable to represent an unknown in a Biblical passage and write algebraic expressions to estimate a value from the passage.
Read 1 Kings 6:1-4.What was the area in square feet of the floor space of the temple excluding the porch?Hint: Research the equivalents of a cubit. The equivalent of each above measurement in Feet is about 90 feet long, 30 feet wide and 45 feet high or about 27 meters long, 9 meters wide, and 14 meters high.How do I write algebraic expressions to estimate a value from the passage?
The different methods of graphing a line. How do you do it? Doyou find the slope method easier than plotting points? Why or whynot?There are different ways of deciding if a relation is afunction. Which do you find easiest? Give an example of a functionfrom daily life or something that relates to your major.
A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 28 ft/s. Its height in feet after t seconds is given by y = 28t - 13t^2.
A. Find the average velocity for the time period beginning when t=1 and lasting:0.01 s:0.005 s:0.002 s:0.001 s:
NOTE: For the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator. Estimate the instantaneous velocity when t=1.
Five friends (Amari, Blake, Emerson, Jamie, and Kai) have a weekly meetup for dinner. During the first week, Amari and Kai pay $50 each to cover the group's expenses. During the second week, Blake pays $30, Emerson pays $50, and Jamie pays $30. During the third week, Amari pays $35, Blake pays $15, Emerson pays $20, and Kai pays $45. During the fourth week, Amari pays $35 and Jamie pays $70. The five friends then decide to split all of the dinners equally and calculate who owes who how much money.
a.) Who ends up owing money and how much does each person owe?b.) Write out the fewest transactions needed to 'settle up' (make it so everyone paid the same amount). Example: Kai pays Amari $20
Fanny and Elena enjoy roller coasters. Whenever a new roller coaster opens near their town, they try to be among the first to ride. One Saturday, the two friends decide to ride a new coaster. While waiting in line, Fanny notices that part of this coaster resembles the graph of a polynomial function that they have been studying in their math class. The brochure for the coaster says that, for the first 10 seconds of the ride, the height of the coaster can be determined by H(t) = 0.3t^3 - t^2 + 21t where t is the time in seconds and h is the height in meters.
1. Find the height of the coaster at t = 0 seconds. Explain why this answer makes sense.2. Evaluate H(10) to find the height of the roller coaster at t = 10 seconds.3. Graph H(t) using a calculator or a computer program for t = 0 to t = 10 seconds.4. During the first 10 seconds of the ride, is the roller coaster going up and/or going down? Is the slope constant?
Gerald is in training for the next Tour de France. He practices by riding a lap around a set route in his neighborhood. Each day his time is 4 minutes faster than on the previous day. In total he spent 10 hours in training over 4 days. Determine his lap time on the last day of practice. Give your answer in minutes.
