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How do you find the direct variation equation if z is directly proportional to r when #r=412#, #z=51.5#?

Answer 1

Eva Adamson

Direct variations are expressed in the form

#y = kx#

where #k# is a constant

For your problem, #z # is directly proportional to #r#

#z = kr#

#51.5 = k(412)#

#k = 51.5/412#

#k = 1/8#

#=> z = 1/8r#

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Answer 2

Savannah Anderson

To find the direct variation equation when z is directly proportional to r, use the formula ( z = kr ), where k is the constant of proportionality. Substitute the given values for r and z into the equation and solve for k:

( 51.5 = k \times 412 )

( k = \frac{51.5}{412} )

( k = 0.125 )

Therefore, the direct variation equation is ( z = 0.125r ).

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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.