(Solved): The Eighth Gate Arriving at the eighth and penultimate gate, you immediately get to work. "Computer ...

The Eighth Gate Arriving at the eighth and penultimate gate, you immediately get to work. "Computer, translate this gate for me." Your computer replies with the follow: The function $f(t)=a{\left(\sin \left(t^6\right)\right)}^{10}$ models the position of an oscillating particle that has recently been discovered. Assume that $a$ is a constant. What is the function that represents the velocity of this particle? Note: If you want to write a power of a trigonometric function, remember that writing $\sin (x)$ to the fourth power as ${\sin }^4(x)$ is just a shorthand method. To be mathematically correct, you should write that as $(\sin (x){)}^4$ which is what your computer expects and can translate. Velocity Function: Explain, in your own words and with your own work, how you arrived at this result. Be sure to explain using calculus concepts to best support the work of the game design team.