Question

current learning objective: solving problems involving joint variation
question 8
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score: 0 of 1 point
the number of widgets that a manufacturing plant can produce (w) varies jointly with the number of workers (n) and the time that they have worked (t). find the constant of proportionality k to 2 decimal places if 635 workers work 19 hours and can produce 65030.35 widgets.
k = enter your answer
how many widgets (to 1 decimal place) can be produced by 650 workers in 29 hours?
w₀ = enter your answer
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Explanation:

Step1: Write the joint - variation formula

The formula for joint variation is \(W = knt\).

Step2: Solve for \(k\)

Given \(W = 65030.35\), \(n = 635\), and \(t=19\). Substitute these values into the formula:
\(65030.35=k\times635\times19\).
First, calculate \(635\times19 = 12065\).
Then, \(k=\frac{65030.35}{12065}\).
\(k = 5.39\) (rounded to two decimal places).

Step3: Use the value of \(k\) to find \(W_0\)

Now that \(k = 5.39\), \(n = 650\), and \(t = 29\).
Substitute into \(W=knt\):
\(W_0=5.39\times650\times29\).
First, \(650\times29=18850\).
Then, \(W_0=5.39\times18850\).
\(W_0 = 101601.5\)

Answer:

\(k = 5.39\)
\(W_0=101601.5\)