Learning Materials
Features
Discover
Chapter 2: Problem 38
Perform the operation and write the result in standard form. $$(\sqrt{3}+\sqrt{15} i)(\sqrt{3}-\sqrt{15} i)$$
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
For each function, identify the degree of the function and whether the degree of the function is even or odd. Identify the leading coefficient and whether the leading coefficient is positive or negative. Use a graphing utility to graph each function. Describe the relationship between the degree of the function and the sign of the leading coefficient of the function and the right-hand and left-hand behavior of the graph of the function. (a) \(f(x)=x^{3}-2 x^{2}-x+1\) (b) \(f(x)=2 x^{5}+2 x^{2}-5 x+1\) (c) \(f(x)=-2 x^{5}-x^{2}+5 x+3\) (d) \(f(x)=-x^{3}+5 x-2\) (e) \(f(x)=2 x^{2}+3 x-4\) (f) \(f(x)=x^{4}-3 x^{2}+2 x-1\) (g) \(f(x)=x^{2}+3 x+2\)
Use the position equation $$s=-16 t^{2}+v_{0} t+s_{0}$$ where \(s\) represents the height of an object (in feet), \(v_{0}\) represents the initial velocity of the object (in feet per second), \(s_{0}\) represents the initial height of the object (in feet), and \(t\) represents the time (in seconds). A projectile is fired straight upward from ground level \(\left(s_{0}=0\right)\) with an initial velocity of 128 feet per second. (a) At what instant will it be back at ground level? (b) When will the height be less than 128 feet?
Write the polynomial (a) as the product of factors that are irreducible over the rationals, (b) as the product of linear and quadratic factors that are irreducible over the reals, and (c) in completely factored form. \(f(x)=x^{4}-4 x^{3}+5 x^{2}-2 x-6\) (Hint: One factor is \(\left.x^{2}-2 x-2 .\right)\)
Write the polynomial as the product of linear factors and list all the zeros of the function. $$f(x)=x^{4}-16$$
The numbers \(N\) (in millions) of students enrolled in schools in the United States from 2000 through 2009 are shown in the table. $$\begin{array}{|c|c|}\hline \text { Year } & \text { Number, \(N\) } \\\\\hline 2000 & 72.2 \\\2001 & 73.1 \\\2002 & 74.0 \\\2003 & 74.9 \\\2004 & 75.5 \\\2005 & 75.8 \\\2006 & 75.2 \\\2007 & 76.0 \\\2008 & 76.3 \\\2009 & 77.3 \\\\\hline\end{array}$$ (a) Use a graphing utility to create a scatter plot of the data. Let \(t\) represent the year, with \(t=0\) corresponding to 2000. (b) Use the regression feature of the graphing utility to find a quartic model for the data. (A quartic model has the form \(a t^{4}+b t^{3}+c t^{2}+d t+e,\) where \(a, b\) \(c, d, \text { and } e \text { are constant and } t \text { is variable. })\) (c) Graph the model and the scatter plot in the same viewing window. How well does the model fit the data? (d) According to the model, when did the number of students enrolled in schools exceed 74 million? (e) Is the model valid for long-term predictions of student enrollment? Explain.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine