Answer:
The value of x at this instant is 3.
Step-by-step explanation:
Let
, we get an additional equation by implicit differentiation:
(1)
From the first equation we find that:
(2)
By applying (2) in (1), we get the resulting expression:
(3)

If we know that
and
, then the first derivative of x in time is:

From (1) we determine the value of x at this instant:




The value of x at this instant is 3.
<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:
9
Step-by-step explanation:
n=3, a=729
For any odd integer, n ; a will have only one real nth root which will be a positive integer.
Similarly, for any integer, n, that is > 1 ; related by the expression ;
p^n = a ; the nth root of a = p
Therefore,
If n = 3 ; a = 729
p^3 = 729
To obtain the value of p ; take the cube of both sides
(p^3)*1/3 = 729^1/3
p = 9
Hence, the real nth root of 729 is +9 when n = 3
You have to find the cos of angle A, so use the Pythagorean equation and trig laws to find the other side of the triangle created by angle A. 3^2 + x^2 = 5^2. x=4. This means cos(A) = 4/5). Make both cos (A) and cos (B) have equal denominators, and add. 148/185 + 60/185 = 208/185. This answer is correct, though it doesn’t appear to be any of the answers you wrote, so either those answers are wrong or you wrote something incorrectly in the problem.
Since it's a linear equation and there's a constant rate (given in the problem), we can choose our x - axis to be the time and the y - axis to be height. We choose it that way because you are going up in the elevator. The more time in the elevator, the higher you go.
Finding this equation uses the point slope formula, y - y₁ = m(x - x₁). It can be done with slope-intercept, y = mx + b too.).
First we need to get the slope of the line. Choose any two points, but be consistent and choose two y points as well as the matching x ones. Here, we use x₁ = 2, x₂ = 4, y₁ = 45, y₂ = 75. Slope, m, is y₂ - y₁ / x₂ - x₁.
m = 75 - 45 / 4 - 2
= 30 /2
= 15
Next, we use the slope of 15 and either of the points to find the linear equation. Choose the same (2, 45) x-y pair above, but any point will work.
y - 45 = 15 (x - 2)
y - 45 = 15x - 30
y = 15x + 15
So the linear equation representing this table us y = 15x + 15.