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)
5 and 6 is 65 and 3 and 2 is 25 so I would say add 65 and 25
Answer:
sold 120 chocolate bars
sold 140 peanut butter bars
Step-by-step explanation:
x = peanut butter bars
y = chocolate bars
x + y = 260, total lbs
0.25x + 0.30y = 71, money
solve double variable equation
multiply -4 on both sides for 2nd equation
-x + -1.2y = -284
add both equations together
-0.2y = -24
y = 120
x = 260 - 120
x = 140
sold 120 chocolate bars
sold 140 peanut butter bars
Answer:
i will only answer 11 and 4
Step-by-step explanation:
4: 23 i know its not the whole thing
11:45 its not the full thing
Please be more specific. What do you want to know?
4^x is an exponential function with base 4 and exponent x; its graph is entirely above the horizontal axis, and the curve representing 4^x continues to rise as x increases. Its y-intercept is (0,4^0), or (0,1).
