Answer:
Step-by-step explanation:
x= the number
2x+4
3= x
2(3)+4=
6+4= 10
Answer:
x = -5 sin (2t)
Step-by-step explanation:
k is the spring stiffness. The unstretched length of the spring is L.
When the mass is added, the spring stretches to an equilibrium position of L+s, where mg = ks. When the mass is displaced a distance x (where x is positive if the displacement is down and negative if it's up), the spring is stretched a total distance s + x.
There are two forces on the mass: weight and force from the spring. Sum of the forces in the downward direction:
∑F = ma
mg − k(s + x) = ma
mg − ks − kx = ma
Since mg = ks:
-kx = ma
Acceleration is second derivative of position, so:
-kx = m d²x/dt²
Let's find k:
F = kx
400 = 2k
k = 200
We know that m = 50. Substituting:
-200x = 50 d²x/dt²
-4x = d²x/dt²
d²x/dt² + 4x = 0
This is a linear second order differential equation of the form:
x" + ω² x = 0
The solution to this is:
x = A cos (ωt) + B sin (ωt)
Here, ω² = 4, so ω = 2.
x = A cos (2t) + B sin (2t)
We're given initial conditions that x(0) = 0 and x'(0) = -10 (remember that down is positive and up is negative).
Finding x'(t):
x' = -2A sin (2t) + 2B cos (2t)
Plugging in the initial conditions:
0 = A
-10 = 2B
Therefore:
x = -5 sin (2t)
<h3>
Answer: The graph is shown in the attached image below</h3>
-2x means -2*x or "-2 times x" where x is a placeholder for any number you want.
To graph y = -2x, you just need two points. Each point is of the form (x,y)
Let's plug in zero as it is often the easiest to work with.
If x = 0, then -2*x = -2*0 = 0. Notice how I replaced x with 0 and simplified.
Therefore, if x = 0, then y = 0. We have (x,y) = (0,0) as one point on this line. I have marked it as point A in the graph.
Point B is (1, -2) and it is found by plugging x = 1 into the equation to get...
y = -2x
y = -2*1
y = -2
You could find other points, but two points is enough to draw a straight line through them. The slope of this line is -2 = -2/1. The y intercept is 0.
Answer:
4 kilometers.
Step-by-step explanation:
