Suppose that y varies jointly with w and x and inversely with z and y=360 when w=8, x=25 and z=5. How do you write the equation that models the relationship. Then find y when w=4, x=4 and z=3?

Answer 1

#y =48# under the given conditions
(see below for the modelling)

If #color(red)y# varies jointly with #color(blue)w# and #color(green)x# and inversely with #color(magenta)z# then #color(white)("XXX")(color(red)y * color(magenta)z)/(color(blue)w *color(green)x) = color(brown)k# for some constant #color(brown)k#
GIven #color(white)("XXX")color(red)(y=360)# #color(white)("XXX")color(blue)(w=8)# #color(white)("XXX")color(green)(x=25)# #color(white)("XXX")color(magenta)(z=5)#
#color(brown)k=(color(red)(360) * color(magenta)(5))/(color(blue)(8) * color(green)(25))#
#color(white)("XX")=(cancel(360)^45 * cancel(5))/(cancel(8) * cancel(25)_5#
#color(white)("XX")= color(brown)9#
So when #color(white)("XXX")color(blue)(w=4)# #color(white)("XXX")color(green)(x=4)# and #color(white)("XXX")color(magenta)(z=3)#
#color(white)("XXX")(color(red)y * color(magenta)3)/(color(blue)4 * color(green)4) = color(brown)9#
#color(white)("XXX")color(red)y = (color(brown)9 * color(blue)4 * color(green)4)/color(magenta)3 = 48#
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Answer 2

The equation that models the relationship is ( y = \frac{{kwx}}{{z}} ). By substituting the given values for ( y ), ( w ), ( x ), and ( z ) into the equation ( y = \frac{{kwx}}{{z}} ), we can solve for ( k ). Then, we can use the value of ( k ) to find ( y ) when ( w = 4 ), ( x = 4 ), and ( z = 3 ).

( 360 = \frac{{8 \times 25 \times k}}{{5}} )

( k = \frac{{360 \times 5}}{{8 \times 25}} )

( k = 9 )

Now that we have ( k = 9 ), we can use it to find ( y ) when ( w = 4 ), ( x = 4 ), and ( z = 3 ):

( y = \frac{{4 \times 4 \times 9}}{{3}} = 48 )

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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