For the ODE

multiply both sides by <em>t</em> so that the left side can be condensed into the derivative of a product:


Integrate both sides with respect to <em>t</em> :

Divide both sides by
to solve for <em>y</em> :

Now use the initial condition to solve for <em>C</em> :



So the particular solution to the IVP is

or

We can determine this to be a Geometric Sequence with:
a = 2
r = 1/2
an = ?
We must first find an. We know that an = 1/256, therefore we can use this formula to discover an:
an = a * r^n-1
1/256 = 2 * 1/2^n-1
<span>1/256 / 2 = 1/2^n-1
</span>1/512 = 1/2^n-1
<span>log(1/512) = log(1/2^n-1)
</span>9 = n - 1
10 = n
Therefore, we know an = 10
Now we input it into this equation and solve:
Sn = a(1-r^n/1-<span>r)
</span>Sn = 2(1-1/2^10/1-1/2<span>)
</span>Sn = 2(1023/1024 / 1 / 2)
Sn = 2(1023/1024 * 2 / 1)
<span>Sn = 2(2046/1024)
</span><span>Sn = 2(1023/512)
</span>Sn = 1023/256
Sn = 3.992
Geez, that took awhile... xD
The customer drawing a 30% discount card then the next customer 20% discount card has a probability of 5/40 for the 30% which = 12.5% and 20% is 15/40 which = 37.5% add them together then divide by 2 for a total of 25%.
The customer drawing a 10% card has a 20/40 which = 50% then a customer drawing a 20% card is 15/40 = 37.5% add them together then divide by 2 = 43.75%
The customer drawing a 10% card has a 20/40 which is 50%. Then another customer drawing another 10% is another 50% add them together and divide by 2 = 50%
The customer drawing a 20% card has a 5/40 which is 12.5% and another customer drawing a 20% card again is 12.5%. Add together and divide by 2 = 12.5%. So your answer is the 1st three.
Answer: y= -13/25x
Step-by-step:
Using (50,-26) and -13/25
You put it in the equation y=mx+b which would be -26 = -13/25 (50) +b
Then you simplify to find b which would be 0
so the answer would be y = -13/25x
Hope this helps :^