Answer:
The value of
is
.
Step-by-step explanation:
We know that the position function is given by
![s(t)=30t-\frac{g_s}{2} t^2](https://tex.z-dn.net/?f=s%28t%29%3D30t-%5Cfrac%7Bg_s%7D%7B2%7D%20t%5E2)
Velocity is defined as the rate of change of position. Therefore,
![v(t)=\frac{d}{dt}(s(t))](https://tex.z-dn.net/?f=v%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%28s%28t%29%29)
So, the velocity function is
![v(t)=\frac{d}{dt}(s(t))\\\\v(t)=\frac{d}{dt}(30t-\frac{g_s}{2} t^2)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\v(t)=\frac{d}{dt}\left(30t\right)-\frac{d}{dt}\left(\frac{g_s}{2}t^2\right)\\\\v(t)=30-g_st](https://tex.z-dn.net/?f=v%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%28s%28t%29%29%5C%5C%5C%5Cv%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%2830t-%5Cfrac%7Bg_s%7D%7B2%7D%20t%5E2%29%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3ASum%2FDifference%5C%3ARule%7D%3A%5Cquad%20%5Cleft%28f%5Cpm%20g%5Cright%29%27%3Df%5C%3A%27%5Cpm%20g%27%5C%5C%5C%5Cv%28t%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%2830t%5Cright%29-%5Cfrac%7Bd%7D%7Bdt%7D%5Cleft%28%5Cfrac%7Bg_s%7D%7B2%7Dt%5E2%5Cright%29%5C%5C%5C%5Cv%28t%29%3D30-g_st)
When a body reaches a vertical velocity of zero, this is the maximum height of the body and then gravity will take over and accelerate the object downward. Thus,
![v(t)=30-g_st=0\\\\g_s=\frac{30}{t}](https://tex.z-dn.net/?f=v%28t%29%3D30-g_st%3D0%5C%5C%5C%5Cg_s%3D%5Cfrac%7B30%7D%7Bt%7D)
We know that the ball bearing reaches its maximum height 21 seconds after being launched (t = 21 s).
So, the value of
is
.
Answer:
A. -f(1/2 x)
Step-by-step explanation:
Reflextion about the x-axis is
f(x) -> -f(x)
and horizontal dilation is
f(x) -> f(-x/b) where b is the factor of dilation.
so the proper answwer is
A. -f(1/2 x)
Mental math is something that can be done i your head.
for example you can do 1+1 in your head and you dont need a calculator or paper to do it so i would be called mental math
Hope this helps
remember if you ever need anything and you dont want to waste points you can just post it on my pfp or message me the question
From what I think of this question, i think of 9x37 and 8x37 OR 9/37 and 8/37. either way
8x37=296
9x37=333
9/37=0.2432
8/37=0.2162