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vladimir1956 [14]
3 years ago
14

Suppose that w and t vary inversely and that t = 5/12

Mathematics
1 answer:
Svetlanka [38]3 years ago
8 0

Answer:

Option B. t=5/3w ;1/3

Step-by-step explanation:

We are told that w varies Inversely with t thus generally speaking w∝\frac{1}{t}  since they are inverted, <u>otherwise</u> if they were proportionally varied then w∝t. This means that there is a constant value ( a ) for which w is inversely proportional to t and can be mathematically expressed as:

w=\frac{a}{t}        Eqn. (1)

Now since we are given the values of w=4 and t=\frac{5}{12}, we can plug them in Eqn. (1) and find our constant of proportionality a as follow:

w=\frac{a}{t}\\ \\a=wt\\\\a=(4)(\frac{5}{12} )\\\\a=\frac{5}{3}

Now that we have our constant we can find the new t value for the second value of w=5 as follow:

w=\frac{a}{t} \\\\t=\frac{a}{w}\\ \\t=\frac{\frac{5}{3} }{5}\\\\t=\frac{5}{15}\\ \\t=\frac{1}{3}\\

Therefore based on the options give, we can see that Option B. is correct since

t=\frac{5}{3w} and for w=5, then t=\frac{1}{3}

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