First, solve the given system of linear equations.
Second, multiply the first equation by 4 (which was an arbitrary choice). Add your result to the 2nd equation.
You should now have the following:
First equation: No change: <span>2x + 7y = 1
Second equation: 4(</span><span>-3x – 4y = 5) = -12x -16y = 20
Solve this new system of linear equations. Do you (or do you not) obtain the same solution as your earlier one?</span>
Answer:
x=\frac{2y-3}{y}
Step-by-step explanation:
This DE has characteristic equation

with a repeated root at r = 3/2. Then the characteristic solution is

which has derivative

Use the given initial conditions to solve for the constants:


and so the particular solution to the IVP is

Answer:
2.42 feet
Step-by-step explanation:
the bicycle wheel rotates 5 times and travels 37.94 feet, then we know that the circumference of the wheel (the outside of the wheel as it touches the ground 5 times around) is 37.94/5 = 7.588
Then we use the formula for the circumference of a circle: 2(pi)(radius) = circumference
We plug in what we know 2(3.14)(radius) = 7.588 and then solve for the radius
We divide 2 from both sides of the equation (3.14)(radius) = 3.794
We divide pi from both sides (radius) = 1.208
Then the last step, we multiply the radius by 2, because we need the diameter, which is double the radius
1.208 * 2 = 2.416 or 2.42 rounded up
Final answer = 2.42 feet