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if z varies jointly as x and y and z
Ask: if z varies jointly as x and y and z is 40 when x is 8 and y is 5 what is z when x is 9 and y is 25
JOINT VARIATION
EQUATION:
[tex]z = kxy[/tex]
————————
[tex]40 = k(8)(5)[/tex]
[tex]k = frac{40}{(8)(5)} [/tex]
[tex]k = frac{40}{40} [/tex]
[tex]k = 1[/tex]
————————
[tex]z = 1xy[/tex]
[tex]z = (1)(9)(25)[/tex]
[tex]z = 225[/tex]
Final Answer:
z = 225
Learn more about joint variation:
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If y varies directly as x and z, and y
Ask: If y varies directly as x and z, and y = 130 when x = 2 and z = 5, what is y when x = 8 and z = 6?
Answer:
y = 624
Solution:
y = kxz
130 = k(2)(5)
130 = 10k
[tex] frac{130}{10} = frac{10k}{10} \ 13 = k[/tex]
y = kxz
y = (13)(8)(6)
y = 624
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if z varies directly as x and y, and z
Ask: if z varies directly as x and y, and z = 90 when x = 3 and y = 6. What is z when x = 4 and y = 8?
[tex]quad[/tex]JOINT VARIATION
[tex]qquad[/tex]z varies directly as x and y
[tex]\[/tex]
[tex]bold {EQUATION:}[/tex][tex]boxed{tt z=kxy}[/tex] where k is the constant of the variation.
[tex]bold {GIVEN:}[/tex]
- z = 90 when x =3 and y = 6
[tex]bold {UNKNOWN:}[/tex]
- constant of the variation k
- z when x =4 and y = 8
[tex]bold {SOLUTION:}[/tex]
First, we will find the value of k,
[tex] begin{array}{c} largett z = kxy \ \ large tt 90 = k(3)(6) \ \ large tt 90 = 18k \ \ Large tt frac{90}{18} = frac{18k}{18} \ \ large tt boxed{ tt k = 5} end{array}[/tex]
Now, we will substitute the value of k to find z when x = 4 and y = 8.
[tex] begin{array}{l} large tt z = kxy \ \ large tt z = (5)(4)(8) \ \ large red{ boxed{ tt z = 160}}end{array}[/tex]
[tex]\[/tex]
[tex]thereforeboxed{textsf{z = 160 when x = 4 and y = 8.}}[/tex]
[tex]\ \[/tex]
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Suppose z varies as y and inversely as x, and
Ask: Suppose z varies as y and inversely as x, and z = 12 when x = 8 and y = 24.
What is x when z = 16?
y
Answer:
x = 6
y = 32
Step-by-step explanation:
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If y varies jointly as x and z, find the
Ask: If y varies jointly as x and z, find the constant of variation and missing value.
1. If y = 24 when x = 2 and z = 3, what is y when x = 18 and z = 5?
2. If y = 12 when x = 6 and z = 4, what is x when y = 36 and z = 72?
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z varies jointly as x and y. and z =
Ask: z varies jointly as x and y. and z = 60 when x = 3 and y = 4. What is the constant (k)?
What is z when x=6 and y=4?
Answer:
k = 5
z = 120
Step-by-step explanation:
z = kxy
60 = k(3)(4)
60 = 12k
5 = k
z = 5xy
z = 5(6)(4)
z = 5(24)
z = 120
If z varies directly as x, z = 60 and
Ask: If z varies directly as x, z = 60 and x = 5, what is x when z = 6?
x = 1/2
If z varies directly as x, z = 60 and x = 5, what is x when z = 6?
[tex]z = kx \ 60 = k(5) \ 60 = 5k \ frac{60}{5} = frac{5k}{5} \ k = 12 \ \ constant : of : variation : = 12[/tex]
[tex]z = kx \ 6 = (12)(x) \ 6 = 12x \ frac{6}{12} = frac{12x}{12 } \ x = frac{1}{2} [/tex]
If z varies directly as x, z = 60 and
Ask: If z varies directly as x, z = 60 and x = 5, what is z when x =8?
Answer:
z=yx (the variable depends)
60=5y
divide both sides by 5
12=y or y=12
x=8
z=?
z=(12)(8)
z=96
If z varies directly as x, z = 60 and
Ask: If z varies directly as x, z = 60 and x = 5, what is x when z = 6?
Answer:
x = 1/2
Step-by-step explanation:
z = kx
60 = k 5
60 divided by 5 is 12
k = 12
6 = (12) x
6 divided by 12 is 1/2
x – 1/2
1. If y = 12 when x = 6 and
Ask:
1. If y = 12 when x = 6 and z = 4, what is x when y = 36 and z = 72?
2. If y = 24 when x = 2 and z = 3, what is y when x = 18 and z = 5?
Answer:
1. 18
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