140-180÷1-5. -40÷-4= 10. 140=10(1)+b. b= 130. y= 10x+130
Answer:55.227
Step-by-step explanation:
Given data
mass
=13lb
spring stretches by
=4.5in=0.375 ft
g=![32ft/s^2](https://tex.z-dn.net/?f=32ft%2Fs%5E2)
Now Spring constant K
mg=kx
k=![\frac{13\times 32}{y}=58.667lb/ft](https://tex.z-dn.net/?f=%5Cfrac%7B13%5Ctimes%2032%7D%7By%7D%3D58.667lb%2Fft)
For critical damping ![\zeta =1](https://tex.z-dn.net/?f=%5Czeta%20%3D1)
![2\times \zeta \times \omega_n =\frac{c}{m}](https://tex.z-dn.net/?f=2%5Ctimes%20%5Czeta%20%5Ctimes%20%5Comega_n%20%3D%5Cfrac%7Bc%7D%7Bm%7D)
and ![\omega_n=\sqrt {\frac{k}{m}}](https://tex.z-dn.net/?f=%5Comega_n%3D%5Csqrt%20%7B%5Cfrac%7Bk%7D%7Bm%7D%7D)
![\omega _n=2.1241rad/s](https://tex.z-dn.net/?f=%5Comega%20_n%3D2.1241rad%2Fs)
substituting values
![2\times 1 \times 2.124 =\frac{c}{m}](https://tex.z-dn.net/?f=2%5Ctimes%201%20%5Ctimes%202.124%20%3D%5Cfrac%7Bc%7D%7Bm%7D)
c=55.227 lb.sec/ft
-1.25 or -1 1/4 that’s because the dot is in between a half and a whole number so one half divided by two is 1/4
Answer:
(5, -18)
Step-by-step explanation:
the original formula for the circle is (x – h)2 + (y – k)2 = r2 the center is (h, k)
so,
(x - 5)2 + (y + 18)2 = 36
h= 5, k=-18
Hello!!
![\left \{ {{x = 3 cos t} \atop {y = 3 sin t}} \right. \\\left \{ {{y^2 = (3 cos t)^2} \atop {x^2= (3 sin t)^2}} \right. \\\left \{ {{y^2 = 3^2 cos^2 t} \atop {x^2= 3^2 sin^2 t}} \right.](https://tex.z-dn.net/?f=%5Cleft%20%5C%7B%20%7B%7Bx%20%3D%203%20cos%20t%7D%20%5Catop%20%7By%20%3D%203%20sin%20t%7D%7D%20%5Cright.%20%5C%5C%5Cleft%20%5C%7B%20%7B%7By%5E2%20%3D%20%283%20cos%20t%29%5E2%7D%20%5Catop%20%7Bx%5E2%3D%20%283%20sin%20t%29%5E2%7D%7D%20%5Cright.%20%5C%5C%5Cleft%20%5C%7B%20%7B%7By%5E2%20%3D%203%5E2%20cos%5E2%20t%7D%20%5Catop%20%7Bx%5E2%3D%203%5E2%20sin%5E2%20t%7D%7D%20%5Cright.)
Now add them,
![x^2 + y^2 = 3^2cos^2t + 3^2sin^2t \\x^2 + y^2 = 3^2 * (cos^2t + sin^2t) ---> (REMEMBER: cos^2t + sin^2t = 1) \\x^2 + y^2 = 3^2 * 1 \\x^2 + y^2 = 3^2](https://tex.z-dn.net/?f=x%5E2%20%2B%20y%5E2%20%3D%203%5E2cos%5E2t%20%2B%203%5E2sin%5E2t%20%5C%5Cx%5E2%20%2B%20y%5E2%20%3D%203%5E2%20%2A%20%28cos%5E2t%20%2B%20sin%5E2t%29%20---%3E%20%28REMEMBER%3A%20cos%5E2t%20%2B%20sin%5E2t%20%3D%201%29%20%5C%5Cx%5E2%20%2B%20y%5E2%20%3D%203%5E2%20%2A%201%20%5C%5Cx%5E2%20%2B%20y%5E2%20%3D%203%5E2)
Therefore, the center is at the origin
(0,0), and the radius is
3. We eliminated the parameter!
Good luck :)