Answer:
Step-by-step explanation:
<u>Given sides of a rectangle</u>
- Length: l =4 − 7(3x + 4y)
- Width: w = 3x(−2y)
<u>Perimeter of rectangle</u>
<u>Using the given values</u>
- P = 2( 4- 7(3x + 4y) + 3x(-2y)) =
- 2( 4 - 21x - 28y - 6xy) =
- 8 - 42x - 56y - 12xy
Answer:
counted down
Step-by-step explanation:
it was counting up and went down by couting down in 2
Answer: 975
Step-by-step explanation:
Because you multiply 6 times 150 and then you add 75 because that is half of 150 and you only need one more mile
<span>the particle's initial position is at t=0, x = 0 - 0 + 4 = 4m
velocity is rate of change of displacement = dx/dt = d(t^3 - 9t^2 +4)/dt
= 3t^2 - 18t
acceleration is rate of change of velocity = d(3t^2 -18t)/dt
= 6t - 18
</span><span>the particle is stationary when velocity = 0, so 3t^2 - 18t =0
</span>3t*(t - 6) = 0
t = 0 or t = 6s
acceleration = 6t - 18 = 0
t = 3s
at t = 3s, velocity = 3(3^2) -18*3 = -27m/s
displacement = 3^3 - 9*3^2 +4 = -50m
Answer:
y =
+ ![\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B18%7D%28t%5E2%2B%5Cfrac%7B2t%7D%7B6%7D%20%2B%20%5Cfrac%7B2%7D%7B36%7D%2B%5Cfrac%7B2t%7D%7B3%7D%2B%5Cfrac%7B2%7D%7B18%7D%2B%5Cfrac%7B2%7D%7B9%7D%29)
Step-by-step explanation:
y''- 9 y' + 18 y = t²
solution of ordinary differential equation
using characteristics equation
m² - 9 m + 18 = 0
m² - 3 m - 6 m+ 18 = 0
(m-3)(m-6) = 0
m = 3,6
C.F. = ![C_1e^{3t}+C_2e^{6t}](https://tex.z-dn.net/?f=C_1e%5E%7B3t%7D%2BC_2e%5E%7B6t%7D)
now calculating P.I.
![P.I. = \frac{t^2}{D^2 - 9D +18}](https://tex.z-dn.net/?f=P.I.%20%3D%20%5Cfrac%7Bt%5E2%7D%7BD%5E2%20-%209D%20%2B18%7D)
![P.I. = \dfrac{t^2}{(D-3)(D-6)}\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1-\frac{D}{6})^{-1}(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(1+\frac{D}{6}+\frac{D^2}{36}+....)(t^2)\\P.I. =\dfrac{1}{18}(1-\frac{D}{3})^{-1}(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(1+\frac{D}{3}+\frac{D^2}{9}+....)(t^2+\frac{2t}{6} + \frac{2}{36})\\P.I. =\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})](https://tex.z-dn.net/?f=P.I.%20%3D%20%5Cdfrac%7Bt%5E2%7D%7B%28D-3%29%28D-6%29%7D%5C%5CP.I.%20%3D%5Cdfrac%7B1%7D%7B18%7D%281-%5Cfrac%7BD%7D%7B3%7D%29%5E%7B-1%7D%281-%5Cfrac%7BD%7D%7B6%7D%29%5E%7B-1%7D%28t%5E2%29%5C%5CP.I.%20%3D%5Cdfrac%7B1%7D%7B18%7D%281-%5Cfrac%7BD%7D%7B3%7D%29%5E%7B-1%7D%281%2B%5Cfrac%7BD%7D%7B6%7D%2B%5Cfrac%7BD%5E2%7D%7B36%7D%2B....%29%28t%5E2%29%5C%5CP.I.%20%3D%5Cdfrac%7B1%7D%7B18%7D%281-%5Cfrac%7BD%7D%7B3%7D%29%5E%7B-1%7D%28t%5E2%2B%5Cfrac%7B2t%7D%7B6%7D%20%2B%20%5Cfrac%7B2%7D%7B36%7D%29%5C%5CP.I.%20%3D%5Cdfrac%7B1%7D%7B18%7D%281%2B%5Cfrac%7BD%7D%7B3%7D%2B%5Cfrac%7BD%5E2%7D%7B9%7D%2B....%29%28t%5E2%2B%5Cfrac%7B2t%7D%7B6%7D%20%2B%20%5Cfrac%7B2%7D%7B36%7D%29%5C%5CP.I.%20%3D%5Cdfrac%7B1%7D%7B18%7D%28t%5E2%2B%5Cfrac%7B2t%7D%7B6%7D%20%2B%20%5Cfrac%7B2%7D%7B36%7D%2B%5Cfrac%7B2t%7D%7B3%7D%2B%5Cfrac%7B2%7D%7B18%7D%2B%5Cfrac%7B2%7D%7B9%7D%29)
hence the complete solution
y = C.F. + P.I.
y =
+ ![\dfrac{1}{18}(t^2+\frac{2t}{6} + \frac{2}{36}+\frac{2t}{3}+\frac{2}{18}+\frac{2}{9})](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B18%7D%28t%5E2%2B%5Cfrac%7B2t%7D%7B6%7D%20%2B%20%5Cfrac%7B2%7D%7B36%7D%2B%5Cfrac%7B2t%7D%7B3%7D%2B%5Cfrac%7B2%7D%7B18%7D%2B%5Cfrac%7B2%7D%7B9%7D%29)