Chapter 2:Variations Word Scramble
|
Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.
Normal Size Small Size show me how
Normal Size Small Size show me how
Question | Answer |
What are some examples of a constant of variation? | r=5c, r=10. They are all a form of y=kx^n where k is a nonzero constant and n is a positive number. |
Ex: The weight w of an adult animal of a given species is known to vary directly with the cube of its height h. a. Write an equation relating w and h. b. Identify the dependent and independent variables. | Solution: An equation for the direct varation is w=kh^3 b. Because w is given in terms of h, The dependent variable is w and the independent variable is h. |
What is an inverse-variation function? | Its a function with a formula of the form y=k/x^n, with k not equaling 0 and n being greater than 0. |
Ex: The number n of oranges you can pack in a box is approximentely inversely proportional to the cube of the average diameter d of oranges. Write an equation to express this relation. | Solution: The cube of the diameter of d^3. So, n is = k/d^3 |
The Fundamental Theorem of Variation | a. If y varies directly as x^n( That is, y=kx^n), and x is multiplied by c, then y is multiplied by c^n. b. If y varies inversely as x^n( That is, y=k/x^n), and x is multiplied by a nonzero constant c, then y is divided by c^n. |
Formula for Slope of a Line | =changes in vertical distance/ change in horizontal distance = change in dependent variable/ change in independent variable =rise/run |
Domain and range k>0 | The domain of the function with equation y=kx^2 is the set of all real numbers. When K > 0, the range is the set of nonnegative real numbers, and the parabola opens up. |
Domain and range k<0 | The range is thet set of nonpositive real numbers and the parabola opens down. That is, the vertex of the parabola is its maximum point. |
Created by:
kmalone30
Popular Math sets