Answer:
hi your question options is not available but attached to the answer is a complete question with the question options that you seek answer to
Answer: v = 5v + 4u + 1.5sin(3t),
Step-by-step explanation:
u" - 5u' - 4u = 1.5sin(3t) where u'(1) = 2.5 u(1) = 1
v represents the "velocity function" i.e v = u'(t)
As v = u'(t)
<em>u' = v</em>
since <em>u' = v </em>
v' = u"
v' = 5u' + 4u + 1.5sin(3t) ( given that u" - 5u' - 4u = 1.5sin(3t) )
= 5v + 4u + 1.5sin(3t) ( noting that v = u' )
so v' = 5v + 4u + 1.5sin(3t)
d/dt ![\left[\begin{array}{ccc}u&\\v&\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Du%26%5C%5Cv%26%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}0&1&\\4&5&\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%26%5C%5C4%265%26%5C%5C%5Cend%7Barray%7D%5Cright%5D)
+ ![\left[\begin{array}{ccc}0&\\1.5sin(3t)&\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%26%5C%5C1.5sin%283t%29%26%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Given that u(1) = 1 and u'(1) = 2.5
since v = u'
v(1) = 2.5
note: the initial value for the vector valued function is given as
![\left[\begin{array}{ccc}u(1)&\\v(1)\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Du%281%29%26%5C%5Cv%281%29%5C%5C%5Cend%7Barray%7D%5Cright%5D)
= ![\left[\begin{array}{ccc}1\\2.5\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C2.5%5C%5C%5Cend%7Barray%7D%5Cright%5D)
Thank you! This helped a lot!!! :)
The equation for a parabola is y = ((x - a)^2) + b. There is a shift one to the left (we’ll call that a) and one shift down (we’ll call that b) for the point (-1,-1). Shifts to the left and right are replaced with a and shifts up and down are replaced with b. y = ( x - (-1))^2 - 1. Simplify: y = (( x + 1)^2) - 1
Answer:
B) identity property of addition.
Step-by-step explanation:
Given:
The statement given is:
Here, we observe that 10 is added to a giving the number 10 itself as the answer. So, we know of a property which says that when 0 is added to a number, the result is the number itself. This property is called identity property of addition.
So, the value of 
must be 0 because on adding to 10, we are getting the number 10 only. So, the above statement is an example of identity property of addition.
