joint variation

joint variation

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  A. PreliminariesDirections: Ifthe statement “y varies jointly with respect to x and z” and the equation is in the form “y = kxz” (where k is the constant), translate each statement into a mathematical sentence using this pattern. 1. s varies jointly as r and t 2. V varies jointly as l, w, and h 3. N varies jointly as 𝑀1 and 𝑀2 4. A varies jointly as b and the square of c 5. The electrical voltage V varies jointly as the current I and the resistance R.
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  Joint Variations
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  Joint Variation isthe same as direct variation with two or more variables. The statement “a varies jointly as b and c” means a = kbc, or 𝒌 = 𝒂 𝒃𝒄 where k is the constant of variation.
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  Illustrative Example 1: Thepressure P of gas varies jointly as its density D, and its absolute temperature T. Solutions: P = kDT where k is the constant of variation
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  2. Find anequation of variation where a varies jointly as b and c, and a = 24 when b = 2 and c = 3. Solutions: A = kbc 24 = k(2)(3) 24 = 6k k = 4 Therefore, a = 4bc is the required equation of variation.
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  3. The areaof a rectangle varies jointly as the length and the width, and whose A = 72 sq. cm when l = 12 cm and w = 2cm. Find the area of the rectangle whose length is 15 cm and whose width is 3 cm. Solutions: A = klw 72 = k(12)(2) 72 = 24k k = 3 Therefore, when l = 15 cm and w = 3 cm, A = klw A = 3(15)(3) A = 135 sq.cm
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  a. What isjoint variation?
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  b. How dowe transform mathematical statement in joint variation equation?
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  Directions: Solve forthe value of the constant k of variation, then find the missing value. 1. If y varies jointly as the product of x and z, and y = 105 when x = 5 and z = 7, find y when x = 9 and z = 10. 2. If y varies jointly as the product of x and z, and y = 1000 when x = 10 and z = 20, find y when x = 8 and z = 10. 3. A varies jointly with l and w, when A = 24, l = 3 and w = 2. Find A when l = 12 and w = 7
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  1.y=270 2.y=360 3.A=336
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  Exercise #2.__. Directions:Solve the following and BOX your final answer 1. y varies jointly as x and z, find y if x =3, k = 6 and z = 9 2. c varies jointly as a and b. If c = 45 when a = 15 and b = 3, find c when a = 21 and b = 8.
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  1. m variesjointly as n and p. If p = 4 when m = 72 and n = 2, find p when m = 12 and n = 8. 2. q varies jointly as g and the square of b. If q = 105 when g = 14 and b = 5, find q when g = 10 and b = 14 3. 4.
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  1. y =162 2.c = 168 3. p = 𝟏 𝟔 4. q = 588
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  Joint Variation isthe same as direct variation with two or more variables. The statement “a varies jointly as b and c” means a = kbc, or 𝒌 = 𝒂 𝒃𝒄 where k is the constant of variation.
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  Assignment # 2.Solve: 1. z varies jointly with x and y. If x=2, y=3 and z=4, write the variation equation and find z when x=−6 and y=2. 2. z varies jointly with x and y. If x=5, y=−1 and z=10, write the variation equation and find z when x=−12 and y=7.
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  3. z variesjointly with x and y. If x=7, y=3 and z=−14, write the variation equation and find z when x=8 and y=3 4.Study a. What do you mean by the word combined? b. What is combined variation? c. What mathematical statement represents combined variation?
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  1. 2. 3.