LAW OF EXPONENT-PROPORTION-VARIATION.pptx

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1. MARC JERVIN BITONG, RME (2023) INSTRUCTOR 1 MECHANICAL ENGINEERING PROGRAM

2. SCHEDULE Tuesday 9AM-11AM Friday 8AM-10AM

3. ALGEBRA 2

4. LAW OF EXPONENT ADVANCE ALGEBRA CHAPTER 1

5. Law of Exponent The laws of exponents, also known as the rules of exponents, are fundamental principles in algebra that describe how to handle mathematical operations involving exponents. “EXPONENT” is a symbol written above and to the right of mathematical expression to indicate the operation of raising to a power

6. Law of Exponent PRODUCT RULE QUOTIENT RULE POWER RULE POWER OF A PRODUCT RULE ZERO EXPONENT RULE NEGATIVE EXPONENT RULE

7. PRODUCT RULE If you multiply two expressions with the same base, you add the exponents: EXAMPLE  

8. QUOTIENT RULE If you divide two expressions with the same base, you subtract the exponents: EXAMPLE  

9. POWER RULE If you raise an exponent to another exponent, you multiply the exponents: EXAMPLE  

10. POWER OF A PRODUCT RULE If you raise a product to an exponent, you raise each factor to the exponent: EXAMPLE  

11. ZERO EXPONENT RULE Any non-zero base raised to the zero power is equal to one: EXAMPLE  

12. NEGATIVE EXPONENT RULE A negative exponent indicates a reciprocal: EXAMPLE  

13. Try this! ANSWER:  

14. THANK YOU

15. Proportion and Variation CHAPTER 1

16. PROPORTION A proportion is an equation that states that two ratios are equivalent. In mathematics, proportions are used to express the equality of two fractions or ratios. Proportions are useful in solving problems involving ratios and comparisons between quantities . Basic Concept

17. PROPORTION Cross-Multiplication- To determine whether two ratios form a proportion, you can use cross-multiplication. This involves multiplying the numerator of one ratio by the denominator of the other ratio, and then comparing the products. If the products are equal, the ratios form a proportion:

18. PROPORTION EXAMPLE 1. 2.

19. Variation A mathematical function that relates the values of one variable to those of other variables Ex. 1. The area of a circle varies as the square of its radius 2. The volume of cylinder varies as the square of its radius and height  

20. Different Types of Variation Direct Variation Inverse Variation Joint Variation Combined Variation

21. Direct Variation A variation in which the quotient of two variables is constant. The statement “y varies directly with x” or “y is directly proportional to x” then y= kx , where k is the constant of variation.

22. Direct Variation EXAMPLE If it is known that y varies directly as x and that y=32 when x=4. A) find the variation constant and equation of variables. B) what is the value of y when The circumference of a circle varies directly with its diameter. If the circumference of a 7 cm in diameter circle is , what is the circumference of circle whose diameter is 10cm? 15cm? 18cm? 20cm?  

23. Inverse Variation A variation in which the product of two variables is constant. The statement “y varies inversely with x” or “ y is inversely proportional to x”, then , where k is the constant of variation.  

24. Inverse Variation EXAMPLE 1. If it is known that y varies inversely as x and that y=24 when x=0.3 A) find the variation constant and equation of variation. B) what is the value of y when x=0.25? 2. The time t required to finish a certain job varies inversely as the number of persons p who work on the job (assume that they do the same amount of work.). If 15 persons are required to finish painting a house in 5 hrs , how long would it take three person to finish the same job?