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)
Answer:
15
Step-by-step explanation:
1 dime = 10
1 quarter=25
x=number of coins - dimes
y= number of coins - quarters
x (10)+y(25)=10.25
x+y=50
x= 50-y
x(10)+y(25)=1025
(50-y)(10)+25y =1025
500-10y+25y=1025
500+15y=1025
15y= 1025 - 500
15y=525
y=525/15
y=35
x= 50-35=15
54 muffins because if you take both your given fraction find the nearest common denominator which is 3 4/12 divide the 4 and 12 to get 3 than divide by 0.10 than divided by a whole 10 which got me 3.03 etc.
Round it see how many times it can go into 10 3 times than multiply it by 18.
50 pairs of whole numbers
2/3 is equivalent to 16/24
and 5/8 is equivalent to 15/24 miles
15/24+16/24= 31/24
31/24 simplifies to 1 6/24
Which simplifies down to 1 1/6
Miles ran 1 and 1/6 miles
