For Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree > 2 • Compound inequality 2 x x − 4 + 7 = 2 x 2 − 3 x + 5 − 2 + x
For Exercises 1-20, a. Identify the type of equation or inequality (some may fit more than one category). b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible. • Linear equation or inequality • Quadratic equation • Rational equation • Absolute value equation or inequality • Radical equation • Equation in quadratic form • Polynomial equation degree > 2 • Compound inequality 2 x x − 4 + 7 = 2 x 2 − 3 x + 5 − 2 + x
Solution Summary: The author explains that the linear equation is x=2 and the solution sets to the inequalities in interval notation.
a. Identify the type of equation or inequality (some may fit more than one category).
b. Solve the equation or inequality. Write the solution sets to the inequalities in interval notation if possible.
• Linear equation or inequality
• Quadratic equation
• Rational equation
• Absolute value equation or inequality
• Radical equation
• Equation in quadratic form
• Polynomial equation
degree
>
2
• Compound inequality
2
x
x
−
4
+
7
=
2
x
2
−
3
x
+
5
−
2
+
x
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
After a great deal of experimentation, two college senior physics majors determined that when a bottle of French champagne is shaken several times, held upright, and uncorked,
its cork travels according to the function below, where s is its height (in feet) above the ground t seconds after being released.
s(t)=-16t² + 30t+3
a. How high will it go?
b. How long is it in the air?
+6x²+135x+1) (0≤x≤10). a) Find the number of units
The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is given by P(x) = In (-x²+6x² + 135x+
that should be sold in order to maximize the total profit. b) What is the maximum profit?
The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the
population in the year 2000 was 22600.
(a) Find a function that models the population t years after 2000 (t = 0 for 2000).
Your answer is P(t)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer should be an integer)
College Algebra with Modeling & Visualization (5th Edition)
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