3. JOINT VARIATION
οΆJoint variation is a direct relationship between three or more
quantities
οΆThe statement βy varies jointly as x and zβ is translated as
y=kxz
οΆTo find the value of k k=
π¦
π₯π§
:
π¦
π₯π§
=
ππ₯π§
π₯π§
k=
π
5. TRANSLATING JOINT VARIATION
STATEMENT INTO
MATHEMATICAL STATEMENT
EXAMPLE:
1)The area A of a parallelogram varies
jointly as the base b and attitude h:
A= kbh
7. TRANSLATING JOINT VARIATION
STATEMENT INTO
MATHEMATICAL STATEMENT
EXAMPLE:
3) The heat h produced by an electrical lamp
varies jointly as the resistance r and the
square of the current l:
H = πππ2
9. SOLVING PROBLEMS
INVOLVING JOINT
VARIATION1) Find the equation of variation where a varies jointly as b and
a=36 when b=3 and c=4
Solution: a=kbc k=
π
ππ
k=
36
3(4)
k=3
A=3bc (equation of variation)
a=kbc
36
(3)(4)
=
π (3)(4)
(3)(4)
10. SOLVING PROBLEMS
INVOLVING JOINT VARIATION
2) Z varies jointly as x and y and z=10 when x=5 and y=6 find
z when x=7 and y=6
Solution: z=kxy k=
π§
π₯π¦
k=
60
5(6)
k=2 z=2xy
z=2(7)(6) z=84
π§
π₯π¦
=
ππ₯π¦
π₯π¦
z=kxy
60
(5π₯6)
=
π(5)(6)
(5)(6)
11. SOLVING PROBLEMS
INVOLVING JOINT VARIATION
3) The weight w of a cylindrical metal varies jointly as its length l and
the square of the diameter d of its base.
a. If w=6 kg when l=6 cm and d=3 cm find the equation of variation.
b. Find l when w=10 kg and d=2 cm.
c. Find w when d=6 cm and l=1.4 cm w=6 l=6 d=3 cm
W=πππ2