That’s the equation for the radius of a circle, it would equal r2
Answer:
Time machine one = 3.56
Time machine two = 4.56
Step-by-step explanation:
Let machine 2 do the job in x hours
Let machine 1 do the job in x - 1 hours.
The general formula for this problem is
Time = A*B/(A + B)
Givens
Time = 2 hours
B = x hours alone
A = x - 1 hours alone.
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x *( x - 1)
======= = 2
(x + x - 1)
(x^2 - x)/(2x - 1) = 2
x^2 - x = 2(2x - 1)
x^2 - x = 4x - 2
x^2 - 5x + 2 = 0
a = 1
b = - 5
c = 2
This gives 2 roots
x = 4.56
x = 0.43
The second root will not work because when 1 is subtracted from 0.43 the time give will be minus, which won't work.
Time for machine 2 is 4.56
The time for machine 1 is 3.56
Check
(A * B)/(A + B) = 2
A = 4.56
B = 3.56
Time = 4.56*3.56/(4.56 + 3.56)
Time = 16.2336/(8.12)
Time = 1.9992
The rounding error in the check comes from the rounding error in the times.
Check if the equation is exact, which happens for ODEs of the form

if
.
We have


so the ODE is not quite exact, but we can find an integrating factor
so that

<em>is</em> exact, which would require


Notice that

is independent of <em>x</em>, and dividing this by
gives an expression independent of <em>y</em>. If we assume
is a function of <em>x</em> alone, then
, and the partial differential equation above gives

which is separable and we can solve for
easily.




So, multiply the original ODE by <em>x</em> on both sides:

Now


so the modified ODE is exact.
Now we look for a solution of the form
, with differential

The solution <em>F</em> satisfies


Integrating both sides of the first equation with respect to <em>x</em> gives

Differentiating both sides with respect to <em>y</em> gives


So the solution to the ODE is


Answer:
I need more information, meaning his formula.
Step-by-step explanation: