The controlled variable is the one that you keep constant. The responding variable or variables is what happens as a result of the experiment (i.e. it's the output variable).
50. The atomic mass is essentially a tally of all of the atoms in the nucleus, since electrons are essentially negligible in mass.
Answer:
6
Explanation:
The rate of change in this scenario corresponds to the number of inches that Ree grows every year. Basically, Ree's height can be written as a linear equation as follows:
![y=mx+q](https://tex.z-dn.net/?f=y%3Dmx%2Bq)
where
x is the number of years after the first birthday
y is the height in inches
q = 27 is the height of Ree on her first birthday
m = 6 is the inches gained by Ree at each birthday
So the equation can also be rewritten as
y = 6x + 27
Answer:
a) t = 2.0 s, b) x_f = - 24.56 m, Δx = 16.56 m
Explanation:
This is an exercise in kinematics, the relationship of position and time is indicated
x = 5 t³ - 9t² -24 t - 8
a) ask when the velocity is zero
speed is defined by
v =
let's perform the derivative
v = 15 t² - 18t - 24
0 = 15 t² - 18t - 24
let's solve the quadratic equation
t =
t1 = -0.8 s
t2 = 2.0 s
the time has to be positive therefore the correct answer is t = 2.0 s
b) the position and distance traveled for a = 0
acceleration is defined by
a = dv / dt
a = 30 t - 18
a = 0
30 t = 18
t = 18/30
t = 0.6 s
we substitute this time in the expression of the position
x = 5 0.6³ - 9 0.6² - 24 0.6 - 8
x = 1.08 - 3.24 - 14.4 - 8
x = -24.56 m
we see that all the movement is in one dimension so the distance traveled is the change in position between t = 0 and t = 0.6 s
the position for t = 0
x₀ = -8 m
the position for t = 0.6 s
x_f = - 24.56 m
the distance
ΔX = x_f - x₀
Δx = | -24.56 -(-8) |
Δx = 16.56 m
Answer:
a
![t = 3.798 \ s](https://tex.z-dn.net/?f=t%20%3D%203.798%20%5C%20%20s%20)
b
![S = 67.91 \ m](https://tex.z-dn.net/?f=S%20%3D%20%2067.91%20%5C%20m%20)
Explanation:
From the question we are told that
The height of the helicopter is
The height of the bed of the truck is ![h_b = 3 \ ft](https://tex.z-dn.net/?f=h_b%20%20%3D%20%203%20%5C%20ft)
The speed of the truck is ![v = 40 \ miles / hour = \frac{40 * 1609.34}{3600} = 17.88 \ m/s](https://tex.z-dn.net/?f=v%20%20%3D%20%2040%20%5C%20miles%20%2F%20hour%20%3D%20%20%5Cfrac%7B40%20%2A%201609.34%7D%7B3600%7D%20%3D%2017.88%20%5C%20m%2Fs)
Generally the distance between the truck bed and the helicopter is mathematically represented as
![H = h - h_b](https://tex.z-dn.net/?f=H%20%3D%20%20h%20-%20h_b)
=> ![H = 235 -3](https://tex.z-dn.net/?f=H%20%3D%20%20235%20-3)
=> ![H = 232 \ ft](https://tex.z-dn.net/?f=H%20%3D%20%20232%20%5C%20%20ft%20)
Converting to meters
![H = \frac{ 232}{3.281} = 70.7 \ m](https://tex.z-dn.net/?f=H%20%3D%20%20%5Cfrac%7B%20232%7D%7B3.281%7D%20%20%3D%2070.7%20%5C%20%20m%20)
Generally the time at which the helicopter should drop the package is mathematically represented as
![t = \sqrt{\frac{2 * H}{g} }](https://tex.z-dn.net/?f=t%20%3D%20%5Csqrt%7B%5Cfrac%7B2%20%2A%20H%7D%7Bg%7D%20%7D)
![t = \sqrt{\frac{2 * 70.7}{9.8} }](https://tex.z-dn.net/?f=t%20%3D%20%5Csqrt%7B%5Cfrac%7B2%20%2A%2070.7%7D%7B9.8%7D%20%7D)
![t = 3.798 \ s](https://tex.z-dn.net/?f=t%20%3D%203.798%20%5C%20%20s%20)
Generally distance of the helicopter from the drop site at time t = 0 s is
![S = v * t](https://tex.z-dn.net/?f=S%20%3D%20%20v%20%20%2A%20t)
=> ![S = 17.88 * 3.798](https://tex.z-dn.net/?f=S%20%3D%20%2017.88%20%20%20%2A%20%203.798)
=> ![S = 67.91 \ m](https://tex.z-dn.net/?f=S%20%3D%20%2067.91%20%5C%20m%20)