This is not a function but the domain is x and the range is going to y so the first is the domain and the second box it the range
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)
1 and 2 are 1/4 and 90 degrees
3. 360 degrees and 4/4
4. 180 degrees and 2/4
Answer:
6x² - x - 12
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor.
(2x - 3)(3x + 4)
= 2x(3x + 4) - 3 (3x + 4) ← distribute both parenthesis
= 6x² + 8x - 9x - 12 ← collect like terms
= 6x² - x - 12 ← in expanded form
Answer:
- 4/3
Step-by-step explanation:
