Step-by-step explanation:
The general equation is y = mx + c...
The given equation is 2x + y = 6
Firstly, move everything on the left except the y to the right.i.e.
y = 6 - 2x
Secondly, rearrange the values on the right to look just like the general equation.
y = -2x + 6
The equation is now in proper general form because it matches the format laid down.
When an spherical balloon volume is increasing at the rate of
then the diameter of the balloon is increasing ![\frac{3}{2\pi }ft /min](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%5Cpi%20%7Dft%20%2Fmin)
How can we find the rate of change of balloon's diameter ?
The volume of a spherical balloon is ![v=\frac{4}{3} \pi r^3](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E3)
In form of diameter we can write as
![v=\frac{4}{3} \pi (\frac{D}{2} )^3\\=\frac{1}{6} \pi D^3](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20%28%5Cfrac%7BD%7D%7B2%7D%20%29%5E3%5C%5C%3D%5Cfrac%7B1%7D%7B6%7D%20%5Cpi%20D%5E3)
Now we will differentiate both sides wrt to
we get
![\frac{dv}{dt} =\frac{1}{6} \pi 3D^2 \frac{dD}{dt} \\\frac{dD}{dt} =\frac{2}{\pi D^2} \frac{dv}{dt} \\\\when r=1\\D=2ft](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D%5Cfrac%7B1%7D%7B6%7D%20%5Cpi%203D%5E2%20%5Cfrac%7BdD%7D%7Bdt%7D%20%5C%5C%5Cfrac%7BdD%7D%7Bdt%7D%20%3D%5Cfrac%7B2%7D%7B%5Cpi%20D%5E2%7D%20%5Cfrac%7Bdv%7D%7Bdt%7D%20%5C%5C%5C%5Cwhen%20r%3D1%5C%5CD%3D2ft)
Given in the question ![\frac{dv}{dt} =3ft^3/min](https://tex.z-dn.net/?f=%5Cfrac%7Bdv%7D%7Bdt%7D%20%3D3ft%5E3%2Fmin)
thus when we substitute the values we get
![\frac{dD}{dt} =\frac{2}{\pi *2^2} (3)\\\frac{dD}{dt}=\frac{3}{2\pi } ft/min](https://tex.z-dn.net/?f=%5Cfrac%7BdD%7D%7Bdt%7D%20%3D%5Cfrac%7B2%7D%7B%5Cpi%20%2A2%5E2%7D%20%283%29%5C%5C%5Cfrac%7BdD%7D%7Bdt%7D%3D%5Cfrac%7B3%7D%7B2%5Cpi%20%7D%20%20ft%2Fmin)
Learn more about the differentiation here:
brainly.com/question/28046488
#SPJ4
It is difficult because prime numbers are numbers with no factors. There's not many. A lot of one digit numbers are prime and odd numbers but after 2, all of the even whole numbers are composite and some odds past 100 (and some before 100) are, also
The median may stay the same.
The range will always change.
I dont think the last 2 will always change.