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    Joint Variation: Group 3

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    Charles Daniell Santos
    Joint variation refers to a scenario where the value of one variable depends on two or more other variables when the other variables are held constant. The relationship can be expressed mathematically as an equation of variation where the variable is equal to the product of the other variables multiplied by a constant. Some examples provided show how to set up and solve equations of joint variation when given certain variable values to find unknown values. The last example demonstrates calculating the percentage change in an area that is jointly related to other variables when those variables change by a percentage.

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    Joint Variation: Group 3

    Uploaded by

    Charles Daniell Santos
    27 views12 pages
    Joint variation refers to a scenario where the value of one variable depends on two or more other variables when the other variables are held constant. The relationship can be expressed mathematically as an equation of variation where the variable is equal to the product of the other variables multiplied by a constant. Some examples provided show how to set up and solve equations of joint variation when given certain variable values to find unknown values. The last example demonstrates calculating the percentage change in an area that is jointly related to other variables when those variables change by a percentage.

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    Joint variation refers to a scenario where the value of one variable depends on two or more other variables when the other variables are held constant. The relationship can be expressed mathematically as an equation of variation where the variable is equal to the product of the other variables multiplied by a constant. Some examples provided show how to set up and solve equations of joint variation when given certain variable values to find unknown values. The last example demonstrates calculating the percentage change in an area that is jointly related to other variables when those variables change by a percentage.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    27 views12 pages

    Joint Variation: Group 3

    Uploaded by

    Charles Daniell Santos
    Joint variation refers to a scenario where the value of one variable depends on two or more other variables when the other variables are held constant. The relationship can be expressed mathematically as an equation of variation where the variable is equal to the product of the other variables multiplied by a constant. Some examples provided show how to set up and solve equations of joint variation when given certain variable values to find unknown values. The last example demonstrates calculating the percentage change in an area that is jointly related to other variables when those variables change by a percentage.

    Copyright:

    © All Rights Reserved
    Download as PPTX, PDF, TXT or read online from Scribd
    Download as pptx, pdf, or txt
    of 12

    JOINT VARIATION

    Group 3
    What is Joint Variation?
    •  Joint Variation refers to a scenario in which the
    value of one variable depends on two, or more,
    other variables when the other variables are held
    constant.
     y = kx
    '' y varies jointly as x and z ''
    ''y is proportional to x and z''
    2
                                                                            

    Translate each statement into a mathematical sentence.


     1.) P varies jointly as q and r. 
                         P= kqr
     2.) V varies jointly as 1, w and h.
                        V=kLwh
      3) The electrical voltage V varies jointly as the current I and
       the resistance R.
                         V=kIR
    Solve for the constant k, then find the missing value. Z varies
    jointly as x and y and z = 60 , when x = 5 and y = 6.

    a) Find z when x = 7 and y = 6    b) Find x when 3 = 72 and y = 4


         Z=kyx         k=2 
     z = 2xy  z = 2xy
     z = 2(7)(6) 72 = 2x(4)
     z = 84 72/8 = 8x/8
         9 = x
    Examples;

    1. Find the equation of variation where  a varies jointly as b and c, and 


    a=36  when  b=3  and  c=4.

    a = kbc a = 36  b = 3 c = 4

    36 = k(3)(4) a = 3bc – equation of variation 


    36 = 12k
    36/12 = 12k/12
      3=k
    Examples;
    2. Z varies jointly as x and y. If z = 60 when x = 5 and y = 6, find z when x
    = 7 and y = 6.

    z = kxy  z = 60 y = 6 x = 5 z = 2xy             x = 7 y = 6
    60 = k(5)(6)  z = 2(7)(6)
    60 = 30k  z = 84
    60/30 = 30k/30
        2=k
    1. The variable x is in joint variation with y and z. When the values of y and z are
    4 and 6, x is 16. What is the value of x when y = 8 and z =12?

    Solution: 
    The equation for the given problem of joint variation is  x = Kyz where K is
    the constant.

    For the given data 16 = K × 4 × 6  or, K = 46.

    So substituting the value of K the equation becomes  x = 4yz/6

    Now for the required condition  x = 4×8×126  = 64

     Hence the value of x will be 64. 


    2. A is in joint variation with B and square of C. When A = 144, B = 4 and C = 3.
    Then what is the value of A when B = 6 and C = 4? 

    Solution: 
    From the given problem equation for the joint variation is A = KBC2 

    From the given data value of the constant K is K = BC2A K = 4×3^21/44 = 36/144 = 
    ¼.
    Substituting the value of K in the equation A = BC24 A = 6×424 = 24
    3. The area of a triangle is jointly related to the height and the base of the
    triangle. If the base is increased 10% and the height is decreased by 10%, what
    will be the percentage change of the area? 

    Solution:
    We know the area of triangle is half the product of base and height. So the joint 
    variation equation for area of triangle is A = bh2bh2 where A is the area, b is
    the base and h is the height. Here 1212 is the constant for the equation. 
    Base is increased by 10%, so it will be b x 110100110100 = 11b1011b10.
     Heightis decreased by 10%, so it will be h x 9010090100 = 9h109h10. So
    the new area after the changes of base and height is 11b10×9h10211b10×9h102
    = (9910099100)bh2bh2 = 9910099100A. So the area of the triangle is decreased
    by 1%.
    4. A rectangle’s length is 6 m and width is 4 m. If length is doubled and width is halved, how much the
    perimeter will increase or decrease? 

    Solution:
    Formula for the perimeter of rectangle is P = 2(l + w) where P is perimeter, l is length and w is width.

    This is joint variation equation where 2 is constant. 

    So P = 2(6 + 4) = 20 m

    If length is doubled, it will become 2l. 

    And width is halved, so it will become w2.

    So the new perimeter will be P = 2(2l + w2) = 2(2 x 6 + 42) = 28 m.

    So the perimeter will increase by (28 - 20) = 8 m.


    LET'S TRY THIS!
    1.  a varies jointly as b and c.
     a = k b c
    2. h is jointly proportional to i and j.
     h = k i j

    3. m varies jointly as n and p.


    m=knp
    4. s is jointly proportional to t and v.
    s=ktv
       THANK YOU!!!

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