The answer to your question is 706,000.
The answer is b. 25.12
because we are finding the amount of rope to go around the circle, we are looking for the circumfrence of the circle, and the formula for the circumfrence of the circle is diameter(pi). because the radius of the circle is 4 inches, the diameter iss 8 inches because the diameter is 2(radius) and using multiplication, we can find the the circumfrence to be 25.12 inches
This is a linear differential equation of first order. Solve this by integrating the coefficient of the y term and then raising e to the integrated coefficient to find the integrating factor, i.e. the integrating factor for this problem is e^(6x).
<span>Multiplying both sides of the equation by the integrating factor: </span>
<span>(y')e^(6x) + 6ye^(6x) = e^(12x) </span>
<span>The left side is the derivative of ye^(6x), hence </span>
<span>d/dx[ye^(6x)] = e^(12x) </span>
<span>Integrating </span>
<span>ye^(6x) = (1/12)e^(12x) + c where c is a constant </span>
<span>y = (1/12)e^(6x) + ce^(-6x) </span>
<span>Use the initial condition y(0)=-8 to find c: </span>
<span>-8 = (1/12) + c </span>
<span>c=-97/12 </span>
<span>Hence </span>
<span>y = (1/12)e^(6x) - (97/12)e^(-6x)</span>
4/5 divided by 1/10 = 4/5 x 10/1 = 40/5 = 8
In the pattern, the values are increasing by 22 each time so for the 117th term you take 57 + 22 = 79
So, 117= 79
