A weight is attached to the end of a spring. Its height after t seconds is given by the equation h(t)=5-2sin((2pi(t+1))/(7)). When does the weight first reach its maximum height? Give an exact answer. When t= seconds

Question

A weight is attached to the end of a spring. Its height after  t seconds is given by the equation  h(t)=5-2sin((2pi(t+1))/(7)). When does the weight first reach its maximum height? Give an exact answer. When  t= seconds

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Find Maximum Height: The maximum height is reached when the sine function is at its maximum value, which is 1.Find Value of t: We need to find the value of t for which sin((2pi(t+1))/7) equals 1.Set Sine Function Equal: Set the inside of the sine function equal to pi/2, because sin(pi/2) = 1.Solve for t: (2pi(t+1))/7 = pi/2. Now solve for t.Multiply by 7: Multiply both sides by 7 to get rid of the denominator: 2pi(t+1) = (7pi)/2.Divide by 2pi: Divide both sides by 2pi to solve for (t+1): t+1 = (7pi)/(4pi).Simplify Right Side: Simplify the right side: t+1 = 7/4.Subtract 1: Subtract 1 from both sides to solve for t: t = 7/4 - 1.Convert to Common Denominator: Convert 1 to 4/4 to have a common denominator: t = 7/4 - 4/4.Add Fractions: Add the fractions: t = (7-4)/4.Calculate Result: Calculate the result: t = 3/4.

A weight is attached to the end of a spring. Its height after $t$ seconds is given by the equation $\newline$ $h(t)=5-2 \sin \left(\frac{2 \pi(t+1)}{7}\right) .$ $\newline$ When does the weight first reach its maximum height? Give an exact answer. $\newline$ When $t= \square$ seconds

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