The motion of a weight that hangs from a spring is represented by the equation h=8sin(2pi/3t). it models the weight’s height above or below the rest position as a function of time. approximately when will the object be 3 inches above the rest position?

at t = 5.4485 units (maybe seconds, but it is not given)

Step-by-step explanation:

In the equation, h is the height above/below the rest position and t is the time.

Since we want to know WHEN (t) will it be 3 INCHES ABOVE (h = +3), we can simply plug in 3 into h and solve for t. Shown below:

Hence,

At t = 5.4485 seconds (no unit of time is given, i am assuming seconds), the height of the weight will be 3 inches above the rest position.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).