What does part a mean i dont understand
Using Laplace transform we have:L(x')+7L(x) = 5L(cos(2t))sL(x)-x(0) + 7L(x) = 5s/(s^2+4)(s+7)L(x)- 4 = 5s/(s^2+4)(s+7)L(x) = (5s - 4s^2 -16)/(s^2+4)
=> L(x) = -(4s^2 - 5s +16)/(s^2+4)(s+7)
now the boring part, using partial fractions we separate 1/(s^2+4)(s+7) that is:(7-s)/[53(s^2+4)] + 1/53(s+7). So:
L(x)= (1/53)[(-28s^2+4s^3-4s^2+35s-5s^2+5s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]L(x)= (1/53)[(4s^3 -37s^2 +40s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]
denoting T:= L^(-1)and x= (4/53) T(s^3/(s^2+4)) - (37/53)T(s^2/(s^2+4)) +(40/53) T(s^2+4)-(4/53) T(s^2/s+7) +(5/53)T(s/s+7) - (16/53) T(1/s+7)
<u>Answer</u><u>:
</u>
Required integer is -12.
Step-by-step explanation:
Given:
Required number is integer.
Required integer is less than zero
greater than -13.
When number is substracted from -11, result is positive.
To Find:
The integer=?
Solution:
Lets assume required integer = x
As Required integer is less than zero and greater than -13 ,
-13 < x < 0 ------(1)
Also when number is subtracted from -11, result is positive.
=> -11 – x > 0
=> -11 > x -------(2)
So form 1 and 2
-13 < x < -11 that is x is an integer which is less than -11 and greater than -13. There is only one integer between -13 and -11 that is -12.
Hence required integer is -12.
The answer is -14 . i think
Here's a graph of those terms.
