The slope formula is y2-y1/ x2-x1 so after plugging it in it would be 2-3/5-4 and you will get your answer.
Answer:
the answer to the questions are x, 4 and y=7
Answer:
8
im pretty sure :))
Step-by-step explanation:
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Answer:
(c) 2.034 s; (d) 8.944 cm
Step-by-step explanation:
Velocity and acceleration
s = 8cos(t) + 4sin(t)
v = -8sin(t) + 4cos(t)
a = -8cos(t) + 4sin(t)
(c) Time to first equilibrium position
The equilibrium position is where the mass hangs before it is pulled downward, that is, at s = 0.
Set s = 0 and solve for t.
![\begin{array}{rcl}0 & = & 8\cos t + 4\sin t\\-8\cos t & = & 4\sin t\\-8 & = & 4\dfrac{\sin t}{\cos t}\\\\-2 & = & \tan t\\t & = & \arctan(-2)\\& = & -1.107 \pm n\pi\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7D0%20%26%20%3D%20%26%208%5Ccos%20t%20%2B%204%5Csin%20t%5C%5C-8%5Ccos%20t%20%26%20%3D%20%26%204%5Csin%20t%5C%5C-8%20%26%20%3D%20%26%204%5Cdfrac%7B%5Csin%20t%7D%7B%5Ccos%20t%7D%5C%5C%5C%5C-2%20%26%20%3D%20%26%20%5Ctan%20t%5C%5Ct%20%26%20%3D%20%26%20%5Carctan%28-2%29%5C%5C%26%20%3D%20%26%20-1.107%20%5Cpm%20n%5Cpi%5C%5C%5Cend%7Barray%7D)
If n = 1,
t = -1.107 + π = 2.034 s
(d) Distance from equilibrium position
The mass will reach its maximum distance when v = 0, that is, when it is at the peak or trough of its oscillation.
Set v = 0 and solve for t.
![\end{array}\begin{array}{rcl}0 & = &- 8\sin t + 4\cos t\\8\sin t & = & 4\cos t\\\dfrac{\sin t}{\cos t} & = & \dfrac{1}{2}\\\\\tan t & = & 0.5\\t & = & \arctan(0.5)\\& = & 0.4636 \pm n\pi\\\end{array}](https://tex.z-dn.net/?f=%5Cend%7Barray%7D%5Cbegin%7Barray%7D%7Brcl%7D0%20%26%20%3D%20%26-%208%5Csin%20t%20%2B%204%5Ccos%20t%5C%5C8%5Csin%20t%20%26%20%3D%20%26%204%5Ccos%20t%5C%5C%5Cdfrac%7B%5Csin%20t%7D%7B%5Ccos%20t%7D%20%26%20%3D%20%26%20%5Cdfrac%7B1%7D%7B2%7D%5C%5C%5C%5C%5Ctan%20t%20%26%20%3D%20%26%200.5%5C%5Ct%20%26%20%3D%20%26%20%5Carctan%280.5%29%5C%5C%26%20%3D%20%26%200.4636%20%5Cpm%20n%5Cpi%5C%5C%5Cend%7Barray%7D)
If n = 0,
t = 0.4636
Then
s = 8cos(0.4636) + 4sin(0.4636) = 8×0.8944 + 4×0.4472 = 7.156 + 1.789 = 8.944 cm
The figure below shows the graphs of s and v vs t. They indicate that the mass first reaches its equilibrium position at 2.034 s, and the amplitude of its vibration is 8.944 cm.