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Z varies inversely as the cube of d. If z = 3 when d = 2, how do you find z when d is 4?

Answer 1

To find z when d is 4, we can use the inverse variation formula. The formula states that z is inversely proportional to the cube of d, which can be written as z = k/d^3, where k is the constant of variation.

To find the value of k, we can substitute the given values of z and d into the formula. When z = 3 and d = 2, we have 3 = k/2^3. Solving for k, we get k = 3 * 2^3 = 24.

Now that we have the value of k, we can use it to find z when d is 4. Substituting d = 4 and k = 24 into the formula, we get z = 24/4^3 = 24/64 = 3/8.

Therefore, when d is 4, z is equal to 3/8.

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Answer 2

Kennedy Adams

#z=3/8#

#z# varies inversely as the cube of #d# means #zprop1/d^3#

In other words #z=kxx1/d^3#, where#k# is a constant.

Now as #z = 3# when #d = 2# means

#3=kxx1/2^3# or #3=kxx1/8# or #k=8xx3=24#

Hence #z=24xx1/d^3=24/d^3#

Therefore when #d=4#,

#z=24xx1/4^3=24/64=3/8#.

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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.