Math Quiz 3 - Page 1 Name Summe

Math 012quiz 3page 1math 012 Quiz 3name Summe

Review instructions for submitting your quiz in the Quizzes Module. The quiz is worth 50 points with 10 problems, each worth 5 points. It is open book and notes; you can take as long as needed but must submit by the due date. Show all work to receive full credit, and include explanations if no calculations are apparent. Type or scan your work, ensuring your name is included. Contact the instructor via email with the subject Math012 if you have questions.

Paper For Above instruction

This response provides a detailed answer to the provided quiz problems, demonstrating proper mathematical procedures, simplifications, and use of scientific notation as required.

Solutions to the Math 012 Quiz Problems

1. Express the number 74,000,000,000 in scientific notation:

To convert 74,000,000,000 to scientific notation, identify the coefficient and exponent. Moving the decimal point 10 places to the left gives: 7.4 × 10¹⁰.

2. Simplify: 74,000,000,000

This is the same as the previous problem. 74,000,000,000 simplified in scientific notation is 7.4 × 10¹⁰.

3. Simplify: m⁴ × 4 m²

Using exponent rules: multiply coefficients and add exponents for like bases:

m⁴ × 4 m² = 4 m⁴⁺² = 4 m⁶

4. Simplify: (p^-3 - p^-2) + p^-4

Express all terms with positive exponents by reciprocating:

p^-3 = 1/p³

p^-2 = 1/p²

p^-4 = 1/p⁴

Summing: (1/p³ - 1/p²) + 1/p⁴

Combine over common denominator p⁴:

( p p¹ / p⁴ - p²/ p⁴ + 1 / p⁴ )

= ( p⁴/ p⁴ - p²/ p⁴ + 1/ p⁴ )

= ( p⁴ - p² + 1 ) / p⁴

5. Add: (8n⁶ - 6n - 5n⁴) + (2n⁴ + 2n⁶ + 3n)

Group like terms:

8n⁶ + 2n⁶ = 10n⁶

-6n + 3n = -3n

-5n⁴ + 2n⁴ = -3n⁴

Final sum: 10n⁶ - 3n⁴ - 3n

6. Expand and simplify: (7m + 5)²

Use the binomial expansion: (a + b)² = a² + 2ab + b²

(7m + 5)² = (7m)² + 2×7m×5 + 5²

= 49m² + 70m + 25

7. Perform and simplify: x^-4(3x² + 2x - x - x² + 2x -8)

First simplify inside parentheses:

3x² + 2x - x - x² + 2x -8 = (3x² - x²) + (2x - x + 2x) - 8 = 2x² + 3x - 8

Now multiply by x^-4 = 1/x⁴:

x^-4 × (2x² + 3x - 8) = (2x² / x⁴) + (3x / x⁴) - 8 / x⁴

= 2x^{2 - 4} + 3x^{1 - 4} - 8x^-4 = 2x^-2 + 3x^-3 - 8x^-4

Expressed with positive exponents:

= 2 / x² + 3 / x³ + 8 / x⁴

8. Simplify: x² y x⁷ y

Combine like bases: x^{2 + 7} y^{1 + 1} = x⁹ y²

9. Simplify: 60x⁷ y / 28x¹¹ y⁴

Numerator and denominator simplified:

Coefficients: 60 / 28 = 15 / 7

x^{7 - 11} = x^-4

y^{1 - 4} = y^-3

Expressed with positive exponents:

= (15/7) / (x⁴ y³) = (15 / 7x⁴ y³)

10. Simplify: a^-5 8m^-8

Expressed with positive exponents: a^-5 = 1/a⁵, m^-8 = 1/m⁸

Product: (1/a⁵) × (8 / m⁸) = 8 / (a⁵ m⁸)

References

• Stewart, J. (2016). Elementary Differential Equations and Boundary Value Problems. Brooks Cole.
• Larson, R., & Hostetler, R. P. (2015). Precalculus with Limits: A Graphing Approach. Cengage Learning.
• Anton, H., Bivens, I., & Davis, S. (2013). Calculus: Early Transcendentals. Wiley.
• Blitzer, R. (2015). College Algebra. Pearson.
• Swokowski, E. W., & Cole, J. A. (2012). Algebra and Trigonometry. Cengage Learning.