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)
Answer:
- table: 14, 16, 18
- equation: P = 2n +12
Step-by-step explanation:
Perimeter values will be ...
rectangles . . . perimeter
1 . . . 14
2 . . . 16
3 . . . 18
__
The perimeter of a figure is twice the sum of the length and width. Here, the length is a constant 6. The width is n, the number of rectangles. So, the perimeter is ...
P = 2(6 +n) = 12 +2n
Your equation is ...
P = 2n +12 . . . . . . . . perimeter P of figure with n rectangles.
_____
<em>Additional comment</em>
You may be expected to write the equation using y and x for the perimeter and the number of rectangles. That would be ...
y = 2x +12 . . . . . . . . . perimeter y of figure with x rectangles
Answer: Great
Step-by-step explanation:
Answer: You will spend 25.94$
Step-by-step explanation:
6.5 yards by 3.99 per yard = 6.5 times 3.99 = 25.935 witch rounds too 25.94$
63$
five hours = 45$
1 hour = 9$
7 hours = 63$
