a. To solve the equation for t, we need to isolate t.
Given: h = 7cos(π/3t)
1. Divide both sides by 7:
h/7 = cos(π/3t)
2. Take the inverse cosine of both sides to isolate t:
cos^(-1)(h/7) = π/3t
3. Multiply both sides by 3/π to solve for t:
t = 3cos^(-1)(h/7)/π
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 substitute these values into the equation and solve for t.
1. For h = 1 cm:
t = 3cos^(-1)(1/7)/π ≈ 0.53 seconds
2. For h = 3 cm:
t = 3cos^(-1)(3/7)/π ≈ 1.51 seconds
3. For h = 5 cm:
t = 3cos^(-1)(5/7)/π ≈ 2.26 seconds
Therefore, the times at which the weight is first at a height of 1 cm, 3 cm, and 5 cm above the rest position are approximately 0.53 seconds, 1.51 seconds, and 2.26 seconds, respectively.
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 show work in short term
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