W varies inversely as the square of t. If W = 12 when t = 2. Find t when W = 27. Options : 27t = 24 27t2=48 108 = 12t2 12t=54
Question
W varies inversely as the square of t.
If W = 12 when t = 2. Find t when W = 27.
Options :
- 27t = 24
- 27t² = 48
- 108 = 12t²
- 12t = 54
Solution
The problem states that "W varies inversely as the square of t". This can be written as W = k/(t^2), where k is the constant of variation.
Step 1: Find the constant of variation (k) We know that W = 12 when t = 2. Substituting these values into the equation gives us 12 = k/(2^2) or 12 = k/4. Solving for k gives us k = 12 * 4 = 48.
Step 2: Find t when W = 27 Now we know that W = 48/(t^2). We can substitute W = 27 into the equation and solve for t. This gives us 27 = 48/(t^2).
Step 3: Solve for t To solve for t, we first multiply both sides of the equation by t^2 to get 27t^2 = 48. Then, we divide both sides by 27 to isolate t^2, giving us t^2 = 48/27.
Finally, we take the square root of both sides to solve for t. This gives us t = sqrt(48/27) = 1.33 (rounded to two decimal places).
So, the correct option is none of the given options.
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