simplest reason is that Infinity is not a number, it is an idea.
So 1∞ is a bit like saying 1beauty or 1tall.
Maybe we could say that 1∞= 0, ... but that is a problem too, because if we divide 1 into infinite pieces and they end up 0 each, what happened to the 1?
In fact 1∞ is known to be undefined.
But We Can Approach It!
So instead of trying to work it out for infinity (because we can't get a sensible answer), let's try larger and larger values of x:
graph 1/x
x 1x
11.00000
20.50000
40.25000
100.10000
1000.01000
1,0000.00100
10,0000.00010
Now we can see that as x gets larger, 1x tends towards 0
Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.
a)
[tex]\frac{dy}{dt}\ \alpha\ y(1-y)[/tex]
[tex]\frac{dy}{dt}=ky(1-y)[/tex]
where k is the constant of proportionality, dy/dt = rate at which the rumor spreads
ipuy6tygy
step-by-step explanation:
e
step-by-step explanation:
an equation by definition has to have two or more variables (x and 2 in this case)
simplest reason is that Infinity is not a number, it is an idea.
So 1∞ is a bit like saying 1beauty or 1tall.
Maybe we could say that 1∞= 0, ... but that is a problem too, because if we divide 1 into infinite pieces and they end up 0 each, what happened to the 1?
In fact 1∞ is known to be undefined.
But We Can Approach It!
So instead of trying to work it out for infinity (because we can't get a sensible answer), let's try larger and larger values of x:
graph 1/x
x 1x
11.00000
20.50000
40.25000
100.10000
1000.01000
1,0000.00100
10,0000.00010
Now we can see that as x gets larger, 1x tends towards 0
We are now faced with an interesting situation:
Step-by-step explanation:
The answer is shown below
Step-by-step explanation:
Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.
a)
[tex]\frac{dy}{dt}\ \alpha\ y(1-y)[/tex]
[tex]\frac{dy}{dt}=ky(1-y)[/tex]
where k is the constant of proportionality, dy/dt = rate at which the rumor spreads
b)
[tex]\frac{dy}{dt}=ky(1-y)\\\frac{dy}{y(1-y)}=kdt\\\int\limits {\frac{dy}{y(1-y)}} \, =\int\limit {kdt}\\\int\limits {\frac{dy}{y}} +\int\limits {\frac{dy}{1-y}} =\int\limit {kdt}\\\\ln(y)-ln(1-y)=kt+c\\ln(\frac{y}{1-y}) =kt+c\\taking \ exponential \ of\ both \ sides\\\frac{y}{1-y} =e^{kt+c}\\\frac{y}{1-y} =e^{kt}e^c\\let\ A=e^c\\\frac{y}{1-y} =Ae^{kt}\\y=(1-y)Ae^{kt}\\y=\frac{Ae^{kt}}{1+Ae^{kt}} \\at \ t=0,y=10\%\\0.1=\frac{Ae^{k*0}}{1+Ae^{k*0}} \\0.1=\frac{A}{1+A} \\A=\frac{1}{9} \\[/tex]
[tex]y=\frac{\frac{1}{9} e^{kt}}{1+\frac{1}{9} e^{kt}}\\y=\frac{1}{1+9e^{-kt}}[/tex]
At t = 2, y = 40% = 0.4
c) At y = 75% = 0.75
[tex]y=\frac{1}{1+9e^{-0.8959t}}\\0.75=\frac{1}{1+9e^{-0.8959t}}\\t=3.68\ days[/tex]
The slopes shows that the direction of the field is from -2 to +2, with three point charges, q₁, q₂ and q₃ at -2, 0 and +2 respectively.
Explanation:
Given;
The slope, dy/dx = 2x(y-6) - 4
2x(y-6) - 4 = 2xy - 12x - 4, divide through by 'x'
dy/dx = 2y -12 - 4/x
The slopes of the linear elements on the lines, x =0, y = 5, y = 6, y = 7.
At x = 0, and y = 5
dy/dx = 2y -12 - 4/x
dy/dx = 2(5) - 12 = -2
At x = 0, and y = 6
dy/dx = 2y -12 - 4/x
dy/dx = 2(6) - 12 = 0
At x = 0, and y = 7
= 2y -12 - 4/x
dy/dx = 2(7) - 12 = 2
Therefore, the slopes shows that the direction of the field is from -2 to +2, with three point charges, q₁, q₂ and q₃ at -2, 0 and +2 respectively.