The second-order equation as its equivalent system of first-order equations is
= ![\left[\begin{array}{ccc}7.5\\\\9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7.5%5C%5C%5C%5C9%5Cend%7Barray%7D%5Cright%5D)
An equivalent system that has the identical answer is known as an equivalent structure. Given a gadget of two equations, we can produce an equal system by way of replacing one equation by means of the sum of the 2 equations, or by way of changing an equation by means of a couple of of itself.
Systems of linear equations are equivalent if and handiest in the event that they have an equal set of solutions. In other phrases, two systems are equal if and only if each answer of one in all of them is likewise a solution of the opposite.
In the structures sciences, a machine equivalent system is the conduct of a parameter or thing of a machine in a way just like a parameter or component of a distinctive system. Similarity means that mathematically the parameters and additives will be indistinguishable from each different.
Taking v = u, we have:
u" + 4u' + 6u = 4sin(3t)
--> v' + 4v + 6u = 4sin(3t)
So the system of equations is:
u' = 0u + 1v
v' = -6u - 4v + 4sin(3t)
So we can write it as:
u(1) = 7.5
v(1) = u'(1) = 9
So the initial condition matrix is:
= ![\left[\begin{array}{ccc}7.5\\\\9\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7.5%5C%5C%5C%5C9%5Cend%7Barray%7D%5Cright%5D)
Learn more about the equivalent system here brainly.com/question/14878855
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Answer:
its 5
Step-by-step explanation:
it's in between them
Answer:
a) 94 degrees lower
b) -17 degrees
Step-by-step explanation:
you should draw a number line to visualize what i'm saying..
basically any number that has a greater value but is negative is obviously lower than a smaller negative value
for example: take -563 that is a lot less than -31 because its farther down the number line
okay to find the answer to question a) you need to obviously find the difference between -29 and 65 to do that you need to count the space in between -29 and 65 on a number line.
There's actually a much easier method just use your common sense and some math: so you can say the distance from 0 to 65 is … 65 and the distance from -29 to 0 is 29 so to find the total distance you add them up and you get your answer! (94)
for b) its even easier you just take the number -29 and add 12 from it to get closer to 0 so to do that you need to subtract 12 to get a smaller number but bigger value on the number line (if you draw this one out it will make sense). And the answer is... -17! I hope this made sense :)