Answer:
n <u>></u> 3
Step-by-step explanation:
n - 5 <u>></u> -2
Add 5 to both sides
n <u>></u> 3
Answer:
The president is using the mode because it is the most obvious answer. The fans are using the iconic mean which is the middle number of the data set. They can be different because different people think of numbers differently.
Step-by-step explanation:
Answer:
a medium smoothie cost $3.25
Step-by-step explanation:
j = 4.95 which is the cost of one jumbo
equation from word problem
2j + m = 4m + 0.15
subtract m from both sides
also subtract 0.15 from both sides
2j - 0.15 = 3m
substitute j
2(4.95) - 0.15 = 3m
9.75 = 3m
m = 3.25 or $3.25
Answer:
18.66 ft/s
Step-by-step explanation:
The distance between you and the elevator is given by:
![h=\sqrt{x^2+y^2}](https://tex.z-dn.net/?f=h%3D%5Csqrt%7Bx%5E2%2By%5E2%7D)
The rate of change for the distance between you and the elevator is given by:
![\frac{dh}{dt}=\frac{dh}{dy}*\frac{dy}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7Bdh%7D%7Bdy%7D%2A%5Cfrac%7Bdy%7D%7Bdt%7D)
![-16=\frac{dh}{dy}*\frac{dy}{dt}](https://tex.z-dn.net/?f=-16%3D%5Cfrac%7Bdh%7D%7Bdy%7D%2A%5Cfrac%7Bdy%7D%7Bdt%7D)
![\frac{dh}{dy}=\frac{d}{dy} (\sqrt{x^2+y^2})\\](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdy%7D%3D%5Cfrac%7Bd%7D%7Bdy%7D%20%28%5Csqrt%7Bx%5E2%2By%5E2%7D%29%5C%5C)
Applying the chain rule:
![u=x^2+y^2\\\frac{dh}{dy}=\frac{d\sqrt u}{du} *\frac{du}{dy}\\\frac{dh}{dy}=\frac{1}{2\sqrt u} *2y\\\frac{dh}{dy}=\frac{y}{\sqrt {(x^2+y^2)}}](https://tex.z-dn.net/?f=u%3Dx%5E2%2By%5E2%5C%5C%5Cfrac%7Bdh%7D%7Bdy%7D%3D%5Cfrac%7Bd%5Csqrt%20u%7D%7Bdu%7D%20%2A%5Cfrac%7Bdu%7D%7Bdy%7D%5C%5C%5Cfrac%7Bdh%7D%7Bdy%7D%3D%5Cfrac%7B1%7D%7B2%5Csqrt%20u%7D%20%2A2y%5C%5C%5Cfrac%7Bdh%7D%7Bdy%7D%3D%5Cfrac%7By%7D%7B%5Csqrt%20%7B%28x%5E2%2By%5E2%29%7D%7D)
Therefore, at x=300 and y = 500, dy/dt is:
![-16=\frac{y}{\sqrt {(x^2+y^2)}}*\frac{dy}{dt}\\-16=\frac{500}{\sqrt {(300^2+500^2)}}*\frac{dy}{dt}\\\frac{dy}{dt}=-18.66\ ft/s](https://tex.z-dn.net/?f=-16%3D%5Cfrac%7By%7D%7B%5Csqrt%20%7B%28x%5E2%2By%5E2%29%7D%7D%2A%5Cfrac%7Bdy%7D%7Bdt%7D%5C%5C-16%3D%5Cfrac%7B500%7D%7B%5Csqrt%20%7B%28300%5E2%2B500%5E2%29%7D%7D%2A%5Cfrac%7Bdy%7D%7Bdt%7D%5C%5C%5Cfrac%7Bdy%7D%7Bdt%7D%3D-18.66%5C%20ft%2Fs)
The elevator is descending at 18.66 ft/s.
Given,
Rate of free fall = 216 km/h
Solution,
km/h to m/s is converted as follows :
![216\ \dfrac{km}{h}=216\times \dfrac{1000\ m}{3600\ s}\\\\=60\ m/s](https://tex.z-dn.net/?f=216%5C%20%5Cdfrac%7Bkm%7D%7Bh%7D%3D216%5Ctimes%20%5Cdfrac%7B1000%5C%20m%7D%7B3600%5C%20s%7D%5C%5C%5C%5C%3D60%5C%20m%2Fs)
So, the rate of fall is 60 m/s.
If t = 20 s
Assume, initial velocity = 0
It will move under the action of gravity.
Using equation of motion,
![h=ut+\dfrac{1}{2}gt^2\\\\h=0+\dfrac{1}{2}\times 10\times 20^2\\\\h=2000\ m](https://tex.z-dn.net/?f=h%3Dut%2B%5Cdfrac%7B1%7D%7B2%7Dgt%5E2%5C%5C%5C%5Ch%3D0%2B%5Cdfrac%7B1%7D%7B2%7D%5Ctimes%2010%5Ctimes%2020%5E2%5C%5C%5C%5Ch%3D2000%5C%20m)
Hence, this is all for the solution.