Step-by-step explanation:
please mark me as brainlest
Let the length be x
width = x - 8
Perimeter = Length + Length + Width + Width
x + x + x - 8 + x - 8 > 184
4x - 16 > 184
4x > 184 + 16
4x > 200
x > 50
Therefore:
Length > 50
Width > 50 - 8
Width > 42
Ans: Length > 50, Width > 42
3018
Mentally,
503 = 500 + 3
500 times 6 = 3000
3 times 6 = 18
Add them up:
3018
Answer:
Step-by-step explanation:
Given that:
mass m = 100 g = 0.1 kg
Length of the spring = 5 cm = 0.05 m
The set in motion from the equilibrium position u(0) = 0
The set in motion from its equilibrium position with a downward velocity u'(0) = 50 cm/s = 0.5 m/s
The spring constant (k) = ![\dfrac{0.1 \times 9.8}{0.05}](https://tex.z-dn.net/?f=%5Cdfrac%7B0.1%20%5Ctimes%209.8%7D%7B0.05%7D)
The equation of the system is expressed as:
![\dfrac{1}{10} u'' + \dfrac{98}{5} u =0](https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B10%7D%20u%27%27%20%2B%20%5Cdfrac%7B98%7D%7B5%7D%20u%20%3D0)
By estimating the characteristics equation, we have r = ± 14![i](https://tex.z-dn.net/?f=i)
Thus; the general solution is:
![u(t) = c_1cos \ 14t + c_2 sin 14 \ t](https://tex.z-dn.net/?f=u%28t%29%20%3D%20c_1cos%20%20%5C%2014t%20%2B%20c_2%20sin%2014%20%5C%20t)
By applying the initial condition:
u(0) = 0
⇒ 0 =
∴
![\dfrac{du}{dt} = ( - c_1 \ sin 14 t )\times 14 +14c_2 \ cos 14 t](https://tex.z-dn.net/?f=%5Cdfrac%7Bdu%7D%7Bdt%7D%20%3D%20%28%20-%20c_1%20%5C%20sin%2014%20t%20%29%5Ctimes%2014%20%2B14c_2%20%5C%20cos%2014%20t)
u'(0) = 0.5
0.5 = 14 × c₂
c₂ = 0.5/14
c₂ = 1/28
∴
![\mathbf{u(t) = \dfrac{1}{28} sin 14 t}](https://tex.z-dn.net/?f=%5Cmathbf%7Bu%28t%29%20%3D%20%5Cdfrac%7B1%7D%7B28%7D%20sin%2014%20t%7D)
Equating u(t) = 0, we have t = π/14sec as the time when the mass first returns to its equilibrium position.
Answer:
1- the figure doesn't provide enough information from what I'm aware of
2- x= 17.78
3- x=12
4- x=19
Step-by-step explanation: