Joint Variation - Translate mathematical statements of joint variations ans solving equations of the joint variation
- 1. An area (A) of a triangle varies jointly as the base (b) and the height (h).
- 2. An area (A) of a triangle varies jointly as the base (b) and the height (h). This is an example of a joint variation, in which one variable varies directly to two or more variables. In this case, what will happen to the base (b) and height (h) of the triangle if the area (A) of the triangle is doubled?
- 3. Objectives: a) Translate mathematical statements of joint variations into mathematical equations. b) Solve for the equation of the joint variation and its constant. c) Relate real-life scenarios where joint variation can be used.
- 4. k = constant of the variation 0 𝑦 =𝑘 𝑥𝑧 EQUATION OF JOINT VARIATION Translation to sentence: y varies jointly as x and z
- 5. k = constant of the variation 0 𝑦 =𝑘 𝑥𝑧 EQUATION OF JOINT VARIATION 𝑘= 𝑦 𝑥𝑧
- 6. k = constant of the variation 0 𝑦 =𝑘𝑥𝑧 EQUATION OF JOINT VARIATION An area (A) of a triangle varies jointly as the base (b) and the height (h).
- 7. An area (A) of a triangle varies jointly as the base (b) and the height (h). 𝐴= 𝑘 h 𝑏 Equation of Joint Variation
- 8. An area (A) of a triangle varies jointly as the base (b) and the height (h). 𝐴= 𝑘 h 𝑏 Equation of Joint Variation 𝑘= 𝐴 h 𝑏 Equation of the Constant of Joint Variation
- 9. Translate the following into a mathematical equation: 1) A varies jointly as b and c. 2) l varies jointly as m and n.
- 10. 1) A varies jointly as b and c. 2) l varies jointly as m and n. Translate the following into a mathematical equation: 3) The amount of Interest (I) varies jointly as the rate (r) and time (t). 4) The volume V of a box varies jointly as the length l, width w, and height h.
- 11. Solve for the value of k, and equation of the variation: 1) Find the equation of variation where y varies jointly as x and z, and y = 60, x = 4, and z = 5.
- 12. Solve for the value of k, and equation of the variation: 1) Find the equation of variation where y varies jointly as x and z, and y = 60, x = 4, and z = 5. 2) S varies jointly as r and q, and s = 8, r = 12, and q = 4.
- 13. 1) y varies jointly as w, and x, and y = 40, w = 4, and x = 2. 2) H varies jointly as D, and M, and H = 64, D = 16, and M = 8. 3) A varies jointly as b, c, and d, and A = 240, b = 6, c = 2 and d = 10. BOARD WORK: Find the constant and the equation of the joint variation of the following:
- 14. 1) P varies jointly as q and r. 2) The volume V of a pyramid varies jointly as the area of the base B and the altitude h. SW 3 A. Translate the following into a mathematical equation: B. Solve for the value of k, and equation of the variation when Z varies jointly as x and y: 1) Z = 200, x = 4, and y = 10 2) Z = 35, x = 7, and y = 20.