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3 years ago

Through: (-3,-5), perp. to y=-1/3x+2

1 answer:

7 0

Y = -1/3x + 2.....the slope here is -1/3. A perpendicular line will have a negative reciprocal slope. To find the negative reciprocal, flip the slope and change the sign. So the slope is -1/3.....flip it and it becomes - 3/1....change the sign and it becomes 3/1 or just 3. So ur perpendicular line will have a slope of 3.

y = mx + b
slope(m) = 3
(-3,-5)....x = -3 and y = -5
now sub into the formula and find b, the y int
-5 = 3(-3) + b
-5 = -9 + b
-5 + 9 = b
4 = b
so ur perpendicular equation is : y = 3x + 4 <===

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Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

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For real roots the solution is given by:

$y(t)=c_1e^{r_1t} +c_2e^{r_2t}$

For real repeated roots the solution is given by:

$y(t)=c_1e^{rt} +c_2te^{rt}$

For complex roots the solution is given by:

$y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)$

Where:

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So, the roots are given by:

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Therefore, the solution is:

$x(t)=c_1cos(t)+c_2sin(t)$

As you can see, is the same solution provided by the problem.

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$x'(t)=-c_1sin(t)+c_2cos(t)$

Evaluating the initial conditions:

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And

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Now we have found the value of the constants, the solution of the second-order IVP is:

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