4 is what percent of 20?
1 answer:
You might be interested in
Answer:
0.48 rad/sec
Step-by-step explanation:
From the diagram:
We can find 'x' using trigonometry :
Tanθ = opposite / Adjacent
Opposite = x ; adjacent = 4
Tanθ = x / 4
x = 4tanθ
Let u = 4 and v = tanθ
If dx/dt = 3ft/s ;
dθ/dt when x = 3ft
Differentiate x with respect to t
dx/dt (4tanθ)
Let d/dθ tanθ = sec^2θ
Sec^2θ = 1 / cos^2θ
dθ/dt = 1/4cos^2θdx/dt
dθ/dt = 1/4cos^2θ(3)
dθ/dt = 3/4cos^2θ
When x = 3ft
Cosθ = Adjacent / Hypotenus
Hypotenus = √(4^2 + 3^2
Hypotenuse = √16 + 9 = √25 = 5
Cosθ = 4/5
dθ/dt = 3/4(4/5)^2
dθ/dt = 3/4(16/25)
dθ/dt = 48/100 = 12/25 = 0.48 rad/sec
