Rewrite the following differential equation as an equivalent system of first-order differential equations. Use the variables x1=x, x2=x′,x3=x′′,etc. (so that your equations will have the form x′2=x3, etc.: denote subscripts by appending the subscript to the variable name: x1= x1) Equation to rewrite: x(4) + 17x" - 17' + 17x = -9 cos(2t)

See details below

Step-by-step explanation:

Your equation is . Solve for the fourth derivative to get

Now apply said change of variables: let . Then, substituting on out first equation, we obtain the system:

In general, if you have an nth order ordinary differential equation, you can apply the same idea to obtain a system of differential equations with n unknowns. Therefore, solving systems of differential equations is equivalent to solving higher-order differential equations.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

answer: get jesus in your life

step-by-step explanation: