height of the ball is given as a function of time
it is given by equation
![h = -16t^2 + 96 t](https://tex.z-dn.net/?f=h%20%3D%20-16t%5E2%20%2B%2096%20t)
here in order to find the maximum height we will use the concept of calculus where the maximum value of function will exist when its derivative becomes zero.
so here we can say
![\frac{dh}{dt} = 0](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%20%3D%200)
![-32 t + 96 = 0](https://tex.z-dn.net/?f=-32%20t%20%2B%2096%20%3D%200)
![t = 3 s](https://tex.z-dn.net/?f=t%20%3D%203%20s)
now we will put t = 3 in the given equation
![h = -16*(3)^2 + 96*(3)](https://tex.z-dn.net/?f=h%20%3D%20-16%2A%283%29%5E2%20%2B%2096%2A%283%29)
![h = 144 ft](https://tex.z-dn.net/?f=h%20%3D%20144%20ft)
So the maximum height will be h = 144 ft.
Explanation:
binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically "0" and "1".
Answer:
200N
Explanation:
mass(m) = 10 kg
acceleration(a) = 20 m/s^2
Force = mass * acceleration
= 10*20
= 200 N
Force = 200N
Answer:
R' = R/4
Explanation:
The resistance of a metal rod is R. It is given by the relation as follows :
![R=\rho\dfrac{l}{A}](https://tex.z-dn.net/?f=R%3D%5Crho%5Cdfrac%7Bl%7D%7BA%7D)
Where
l is the length and A is the area of cross-section
![A=\pi r^2=\pi (\dfrac{d}{2})^2](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E2%3D%5Cpi%20%28%5Cdfrac%7Bd%7D%7B2%7D%29%5E2)
If both its length and its diameter are quadrupled, it means,
l' = 4l
and d'= 4d
It means,
![A'=\pi (\dfrac{4d}{2})^2](https://tex.z-dn.net/?f=A%27%3D%5Cpi%20%28%5Cdfrac%7B4d%7D%7B2%7D%29%5E2)
Let new resistance be R'. So,
![R'=\rho\dfrac{l'}{A'}\\\\R'=\rho\dfrac{4l}{\pi (\dfrac{4d}{2})^2}\\\\=\rho \dfrac{4l}{\pi \dfrac{16d^2}{2}}\\\\=\dfrac{4}{16}\times \dfrac{\rho l}{\pi \dfrac{d^2}{2}}\\\\=\dfrac{1}{4}\times \dfrac{\rho l}{\pi \dfrac{d^2}{2}}\\\\R'=\dfrac{R}{4}](https://tex.z-dn.net/?f=R%27%3D%5Crho%5Cdfrac%7Bl%27%7D%7BA%27%7D%5C%5C%5C%5CR%27%3D%5Crho%5Cdfrac%7B4l%7D%7B%5Cpi%20%28%5Cdfrac%7B4d%7D%7B2%7D%29%5E2%7D%5C%5C%5C%5C%3D%5Crho%20%5Cdfrac%7B4l%7D%7B%5Cpi%20%5Cdfrac%7B16d%5E2%7D%7B2%7D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B4%7D%7B16%7D%5Ctimes%20%5Cdfrac%7B%5Crho%20l%7D%7B%5Cpi%20%5Cdfrac%7Bd%5E2%7D%7B2%7D%7D%5C%5C%5C%5C%3D%5Cdfrac%7B1%7D%7B4%7D%5Ctimes%20%5Cdfrac%7B%5Crho%20l%7D%7B%5Cpi%20%5Cdfrac%7Bd%5E2%7D%7B2%7D%7D%5C%5C%5C%5CR%27%3D%5Cdfrac%7BR%7D%7B4%7D)
So, the correct option is (B) "R/4".
Answer:
c) mutation and natural selection both cause changes in a population
Explanation:
Hope it help
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