a. To solve the equation for t, we need to isolate t in the equation h=7cos(π/3t).
First, divide both sides by 7 to get:
h/7 = cos(π/3t)
Next, take the inverse cosine of both sides to solve for t:
t = (3/π)arccos(h/7)
b. To find the times at which the weight is first at a height of 1 cm, 3 cm, and 5 cm above the rest position, we need to substitute the respective heights into the equation and solve for t.
For h=1 cm:
t = (3/π)arccos(1/7) ≈ 0.70 seconds
For h=3 cm:
t = (3/π)arccos(3/7) ≈ 1.27 seconds
For h=5 cm:
t = (3/π)arccos(5/7) ≈ 1.64 seconds
Therefore, the weight is first at a height of 1 cm above the rest position at approximately 0.70 seconds, at a height of 3 cm above the rest position at approximately 1.27 seconds, and at a height of 5 cm above the rest position at approximately 1.64 seconds.
A weight is attached to a spring that is fixed to the floor. The equation h=7cos (π3t)
models the height, h, in centimeters after t seconds of the weight being stretched and released.
a. Solve the equation for t.
b. Find the times at which the weight is first at a height of 1 cm, of 3 cm, and of 5 cm above the rest position. Calculate your answer using radian angle measure. Round your answers to the nearest hundredth...
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