1. If x varies jointly as yz and x=8 when y=4,z=3. find x when y=6,z=4

Solution:
`x prop yz`

`=>x=k*yz`

Now, `x=8" when "y=4,z=3`

`=>8=k*4*3`

`=>8=k*12`

`=>k=(8)/(12)`

`=>k=2/3`

Hence, `x=2/3*yz`

we have to find `x" when "y=6,z=4`

`=>x=2/3*6*4`

`=>x=2/3*24`

`=>x=16`

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2. If x varies jointly as y^3z and x=8 when y=4,z=3. find x when y=6,z=4

Solution:
`x prop y^3z`

`=>x=k*y^3z`

Now, `x=8" when "y=4,z=3`

`=>8=k*4^3*3`

`=>8=k*192`

`=>k=(8)/(192)`

`=>k=1/24`

Hence, `x=1/24*y^3z`

we have to find `x" when "y=6,z=4`

`=>x=1/24*6^3*4`

`=>x=1/24*864`

`=>x=36`

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3. x prop yz and x=8 when y=4,z=3. find x when y=6,z=4

Solution:
`x prop yz`

`=>x=k*yz`

Now, `x=8" when "y=4,z=3`

`=>8=k*4*3`

`=>8=k*12`

`=>k=(8)/(12)`

`=>k=2/3`

Hence, `x=2/3*yz`

we have to find `x" when "y=6,z=4`

`=>x=2/3*6*4`

`=>x=2/3*24`

`=>x=16`

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4. x prop y^3/z and x=8 when y=4,z=3. find x when y=6,z=4

Solution:
`x prop y^3/z`

`=>x=k*y^3/z`

Now, `x=8" when "y=4,z=3`

`=>8=k*4^3/3`

`=>8=k*64/3`

`=>k=8*3/64`

`=>k=3/8`

Hence, `x=3/8*y^3/z`

we have to find `x" when "y=6,z=4`

`=>x=3/8*6^3/4`

`=>x=3/8*54`

`=>x=81/4`

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