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:
3.7
This means that the answer is past the 3 point on the number line and 3 tick marks before the 4 point.
So x + y = 45, and 4x + 5y = 195. Get y by itself. Subtract x from both sides in the first equation to get y = 45 -x, and subtract 4x from the second equation to get 5y = 195 - 4x. Divide by 5 to both sides to get y = 39 - 4/5x. 39 - 4/5x = 45 - x. Add x to both sides to get 39 - 1/5x = 45. Subtract 39 from both sides to get -1/5x = 6. Divide by -1/5 to get x = -30, or 30. In the first equation, do 30 + y = 45. Subtract 30 from both sides to get y = 15. Check. 4(30) + 15(5) = 195, or 120 + 75 = 195.
Answer:
10=10
Step-by-step explanation:
y-3x+15=10
y=3x-15+10
y=3x-5
subtitute y=3x-5 in the above equation:
3x-5-3x+15=10 (3x will be eliminated with -3x)
-5+15=10
10=10
(i hope this is the way you want the answer but at least I think it is correct)
Answer: 105
Step-by-step explanation: 25 frames is 1 second. The video already played 3 and 2/5 seconds before the player started to count 0, so you can write 3 and 2/5 seconds as an improper fraction. =(5*3)+2 / 5 = 17/5 seconds. Multiply by 25 frame. 17/5 *25 =85 frames. So according to the video counter,after 17/5 seconds,it should count 85 frames.However,at 0 seconds,it indicated a count of 190 frames. then to get the number of frames that were already in count you would subtract 85 frames from the 190 frames.
190-85=105 frames
(Not 100% sure so apologies if I'm wrong)
