1 pt= 437.1765 mL
0.5 pt= 0.5x437.1765= 218.58825 mL
Ratio = 218.58825/750= 0.2915 % =29.15%
Product means the result you get after multiplying. So you have to multiply the two numbers. 379*8 = 3032
Answer:
1500 meters
Step-by-step explanation:
Answer:
Step-by-step explanation:
The answer to that number pattern is 40,41,50,51
The ball's acceleration is the rate of change of its velocity, and its velocity is the rate of change of its height. So if
is the ball's height at time
, then
![h''(t)=-9.8\dfrac{\rm m}{\mathrm s^2}](https://tex.z-dn.net/?f=h%27%27%28t%29%3D-9.8%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D)
The ball is dropped from
, and since it's being dropped there is no additional velocity added to it, so
.
Integrating both sides of the ODE gives
![\displaystyle\int h''(t)\,\mathrm dt=h'(t)=\left(-9.8\dfrac{\rm m}{\mathrm s^2}\right)t+C_1](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%20h%27%27%28t%29%5C%2C%5Cmathrm%20dt%3Dh%27%28t%29%3D%5Cleft%28-9.8%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%2BC_1)
and since
, we have
.
Integrating again gives
![\displaystyle\int h'(t)\,\mathrm dt=h(t)=\dfrac12\left(-9.8\dfrac{\rm m}{\mathrm s^2}\right)t^2+C_2](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint%20h%27%28t%29%5C%2C%5Cmathrm%20dt%3Dh%28t%29%3D%5Cdfrac12%5Cleft%28-9.8%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%5E2%2BC_2)
and since
, we get ![100\,\mathrm m=C_2](https://tex.z-dn.net/?f=100%5C%2C%5Cmathrm%20m%3DC_2)
So the ball's height at any time is governed by
![h(t)=100\,\mathrm m+\left(-4.9\dfrac{\rm m}{\mathrm s^2}\right)t^2](https://tex.z-dn.net/?f=h%28t%29%3D100%5C%2C%5Cmathrm%20m%2B%5Cleft%28-4.9%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%5E2)
The ball hits the ground when
:
![100\,\mathrm m+\left(-4.9\dfrac{\rm m}{\mathrm s^2}\right)t^2=100\implies t=\approx4.5\,\mathrm s](https://tex.z-dn.net/?f=100%5C%2C%5Cmathrm%20m%2B%5Cleft%28-4.9%5Cdfrac%7B%5Crm%20m%7D%7B%5Cmathrm%20s%5E2%7D%5Cright%29t%5E2%3D100%5Cimplies%20t%3D%5Capprox4.5%5C%2C%5Cmathrm%20s)