To solve this problem, we will need the standard kinematics equation
![distance=v_0t+\frac{1}{2}at^2](https://tex.z-dn.net/?f=distance%3Dv_0t%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2)
where
v0=initial velocity (positive upwards) m/s
t=time in seconds
a=acceleration due to gravity (positive upwards) = -9.81 m/ ²
Substituting values,
distance = 0 (when it falls back on earth)
v0=42 m/s
a=-9.81 (negative means towards earth, downwards)
![distance=v_0t+\frac{1}{2}at^2](https://tex.z-dn.net/?f=distance%3Dv_0t%2B%5Cfrac%7B1%7D%7B2%7Dat%5E2)
![0=42t+\frac{1}{2}(9.81)t^2](https://tex.z-dn.net/?f=0%3D42t%2B%5Cfrac%7B1%7D%7B2%7D%289.81%29t%5E2)
factor and solve
![t(42+\frac{1}{2}(-9.81)t)=0](https://tex.z-dn.net/?f=t%2842%2B%5Cfrac%7B1%7D%7B2%7D%28-9.81%29t%29%3D0)
=>
t=0 (beginning of launch), or
42-(1/2)*9.81t=0 => t=2*42/9.81=8.563 s.
Time to return = 8.6 seconds (to the nearest tenth of a second)
Answer:
74 gallons
Step-by-step explanation:
Volume of water to be added (in ft3) = π(2.0)
= 9.8175 ft3 (5 s.f)
Volume of water to be added (in gal) = 9.8175 (7.5)
= 74 gallons
Answer:
(4x-5)(x-2)
Step-by-step explanation:
factors of 10: 1,10, &2,5
factors of 4: 1,4 &2,2
(4x-5)(×-2)
$42.29
Multiply $35.24 by .2 and add that to the original bill.
Answer:
2.0
Step-by-step explanation:
Couldn't really understnd what you wrote but I'll assume it's the standard deviation of a fair, 7-sided die
The standard deviation is just the square root of the variance (which is just the second moment minus the first moment squared)
The first moment (AKA the average is..)
![\frac{1+2+3+4+5+6+7}{7}=4](https://tex.z-dn.net/?f=%5Cfrac%7B1%2B2%2B3%2B4%2B5%2B6%2B7%7D%7B7%7D%3D4)
The second moment is..
![\frac{1^2+2^2+3^2+4^2+5^2+6^2+7^2}{7}=20](https://tex.z-dn.net/?f=%5Cfrac%7B1%5E2%2B2%5E2%2B3%5E2%2B4%5E2%2B5%5E2%2B6%5E2%2B7%5E2%7D%7B7%7D%3D20)
![\sqrt{20-4^2}=2](https://tex.z-dn.net/?f=%5Csqrt%7B20-4%5E2%7D%3D2)