x = 27 + 3 √ 129/ 4, 27 − 3 √ 129/ 4
Please note: the entire equation mentioned is divided by 4, not only the last term.
x approximates to 15.26836251, − 1.76836251
That concludes my response. I hope this is helpful. You will still need to work on finding y and z, which can be quite challenging:)
The behavior of the spring can be described using either a sine or cosine function. The spring's maximum displacement is 6 inches, occurring at t=0, which we will define as the positive peak. Therefore, we can express the function as:
6sin(at+B). The spring's period is 4 minutes, which means the time factor in the equation must complete a cycle (2π) in 4 minutes. This gives us the equation 4min*a=2π, leading to a=π/2. Generally, a=2π/T where a is the coefficient and T is the period. For B, since sin(π/2)=1, we determine B=π/2 because at t=0, the equation becomes 6sin(B)=6. Therefore, we substitute to form f(t)=6sin(πt/2+π/2)=6cos(πt/2)
due to trigonometric relations.
<span><span>Center coordinates: (x0, y0, z0)</span></span> and radius r.
<span>The equation of the sphere is:</span>
<span>(x - x0)^2 + (y - y0)^2 + (z - z0)^2 = r^2</span>
