An expression is shown. 590.92 - 219.38 What is the value of the expression?
2 answers:
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Answer:
The equation of the line is y = -1.x + 9
Graph is provided in the attached figure
Step-by-step explanation:
The slope intercept equation of a line in 2D(x,y) coordinates is given by the equation
where m is the slope of the line and c the y-intercept i.e. where the line crosses the y axis at x = 0
Given slope = -1, we can find c and the equation of the line
Since (3,6) is a point on the graph, these coordinates must satisfy the above equation
Substitute for y = 6 and x = 3
In the attached figure you can see that (3,6) is on the line
First check the characteristic solution:
<em>y''</em> + 4<em>y'</em> + 4<em>y</em> = 0
has characteristic equation
<em>r</em> ² + 4<em>r</em> + 4 = (<em>r</em> + 2)² = 0
with a double root at <em>r</em> = -2, so the characteristic solution is
For the particular solution corresponding to , we might first try the <em>ansatz</em>
but and
are already accounted for in the characteristic solution. So we instead use
which has derivatives
Substituting these into the left side of the ODE gives
so that 6<em>A</em> = 12 and 2<em>B</em> = 0, or <em>A</em> = 2 and <em>B</em> = 0.
For the second solution corresponding to , we use
with derivative
Substituting these gives
so that 4<em>C</em> = -8 and 4<em>C</em> + 4<em>D</em> = -12, or <em>C</em> = -2 and <em>D</em> = -1.
Then the general solution to the ODE is
Given the initial conditions <em>y</em> (0) = -2 and <em>y'</em> (0) = 1, we have
and so the particular solution satisfying these conditions is
or