The second-order equation as its equivalent system of first-order equations is
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= ![\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:
=
Learn more about the equivalent system here brainly.com/question/14878855
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Wow ! If I understand what's go0ing on here, then
we have to be careful, and THINK .
I was going to ask you "What does Ф mean ?", and then I realized,
Ф is a new operation that the teacher invented.
The first line on the board is the definition of Ф .
Ф means "<u>Add the two numbers and subtract 4</u>."
Now you have to use this new invention to find the value
of the second line:
Take care of the stuff inside the parentheses first: ( 4 Ф 2 )
<u>Add the two numbers and subtract 4
</u>4 + 2 - 4 = <u>2</u><u>
</u>That's the part inside the parentheses. It's <span><u>2</u> .</span><u>
</u>NOW, we have to do the new operation with the 2 inside,
and the 3 that's outside the parentheses:<u>
</u>3 Ф 2
<u>Add the two numbers and subtract 4</u>
3 + 2 - 4 =<u> 1</u>
And that's the final value of 3 Ф (4 Ф 2) . It's <u>1</u> .
Pretty sneaky.
<u />
2/3 ÷ (-5/6)
When dividing fractions, all you really have to do is multiply the first fraction by the second fraction's reciprocal.
Remember, a reciprocal is the fraction/whole number flipped.
Ex : 4/6 turns into 6/4
So, the reciprocal of -5/6 is -6/5
Therefore, our new equation looks like this :
2/3 × -6/5
Multiply the numerators with the numerators, and the denominators with the denominators :)
Numerators : 2 × -6 = -12
Denominators : 3 × 5 = 15
SO, our answer is -12/15
Simplify this.
-4/5
~Hope I helped!~
Answer:
A or 53 squared
Step-by-step explanation:
Cubic root of 8 is 2
Cubic root of 27 is 3
So the fraction will be -2/3
