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>
Answer:
Square
Step-by-step explanation:
The length of AB is (a+b)-a = b. The length of BC is b-0 = b. So, adjacent sides are the same length. AB has a constant y-value, so is horizontal. BC has a constant x-value, so is vertical.
A figure with horizontal and vertical sides of the same length is a square.
Simple interest is basically the cost of borrowing money over a period of time. So if you have borrowed $110.00 at 5% for two years, you will multiply the 5% by the two years (presuming that it is 5% annual percentage rate (APR). So, You will multiply the 110 by 10% (or .1) to get $11 dollars of simple interest.
Answer:
52/997
Step-by-step explanation:
i just know and i checked it on khan academy
Answer:
.85 times the cost to make the shirt
Step-by-step explanation:
Let x represent cost to make the shirt.
Today, the shirt is in a 15 percent discount from its normal price.
Discount = 15/100 * x = 0.15x
Current cost = Original cost - discount
Current cost = x - 0.15x = 0.85x
The answer is;
.85 times the cost to make the shirt
