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Warm-Up: October 31, 2011

Warm-Up: October 31, 2011. Simplify the following expressions. Monomials. Section 5-1. Monomial. A monomial is an expression that is a number, a variable, or the product of a number and one or more variables. Cannot contain: Addition or subtraction Variables in denominators

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Warm-Up: October 31, 2011

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  1. Warm-Up: October 31, 2011 • Simplify the following expressions

  2. Monomials Section 5-1

  3. Monomial • A monomial is an expression that is a number, a variable, or the product of a number and one or more variables. • Cannot contain: • Addition or subtraction • Variables in denominators • Negative exponents of variables • Fractional exponents of variables • Roots of variables (square root, cube root, etc.)

  4. Definitions • Constants are monomials without variables • 5, -7, 13 • A coefficient is the numerical factor of a monomial. • 3 is coefficient of x2 in 3x2 • -5 is the coefficient of xy in -5xy • The degree of a monomial is the sum of the exponents of its variables. • 5x3 has degree 3 • -2xy has degree 2 • Any constant has degree 0

  5. Power • A power is an expression of the form xn, or simply the exponent n. • Physics: Work overtime to get power.

  6. Simplify • In order for an expression to be simplified, the following must be true: • No parentheses • No negative exponents • All fractions simplified • No square roots in the denominator • No negative sign in the denominator

  7. Negative Exponents • Negative exponents move quantities to the other side of a fraction bar

  8. Product Rule

  9. Example 1 - Simplify

  10. You-Try #1 - Simplify

  11. Quotient Rule

  12. Example 2 – Simplify

  13. You-Try #2 – Simplify

  14. Properties of Powers

  15. Example 3 – Simplify

  16. You-Try #3 – Simplify

  17. Example 4 – Simplify

  18. You-Try #4 – Simplify

  19. Warm-Up: November 1, 2011 • Simplify

  20. Scientific Notation • Scientific notation is used to express very small or very large numbers • 1 ≤ a < 10 • n is an integer, and is the number of places to move the decimal point • If the number in standard notation is greater than 1, then n is positive. • If the number in standard notation is less than 1, then n is negative.

  21. Example 5 – Express in Scientific Notation

  22. You-Try #5 – Express in Scientific Notation

  23. Example 6 – Multiply in Scientific Notation

  24. You-Try #6 – Multiply in Scientific Notation

  25. Dimensional Analysis • Performing operations with units is called dimensional analysis. • Units behave in equations the same way that variables do.

  26. Example 7 • Using the formula d=vt (distance = velocity times time), calculate how long it takes light from the sun to reach Earth, a distance of 1.5x1011 m. Light travels at a velocity of 3.0x108 m/s.

  27. You-Try #7 • Using the formula d=vt (distance = velocity times time), calculate how long it takes light from the sun to reach Mars, a distance of 2.3x1011 m. Light travels at a velocity of 3.0x108 m/s.

  28. Assignment • Page 226 #19-59 odd

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