Pythagoras Theorem:

Apply Pythagoras Theorem:
a² + 6² = 11²
a² = 11² - 6²
a²= 85
a = √85
a = 9.22 (nearest hundredth)
Answer: RT = 9.22 cm
Answer:
0.128rad/sec
Step-by-step explanation:
Let x represent the between the man and the point on the path
θ = the angle
dx/dt = 4 ft/s
dθ/dt = rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the searchlight
tan θ = x/20 ft
Cross Multiply
20tan θ = x
dx/dt = 20sec² θ dθ/dt
dθ/dt = 1/20 × cos² θ dx/dt
dθ/dt= 1/20 × cos² θ × 4
dθ/dt = 1/5 × cos² θ
Note : cos θ = 4/5
dθ/dt = 1/5 × (4/5)²
dθ/dt = 16/125
dθ/dt = 0.128rad/sec
In this we know all three zeros and one point from which the graph pass.
So we will let specific cubic polynomial function of the form

As we know zeros are that point where we will get value of function equal to zero. So it is basically in form

SO in given question zeros are (2 , 0) , (3, 0) and (5,0)
So we can say

So required equation is

Now we have one point (0 , -5) from which graph passes.
So we say at x = 0 , f(x) = -5



So required equation of cubic polynomial is

For finding y - intercept we simply plugin x = 0 in given equation.
As we know at x = 0 , value of function is -5.
So y - intercept is -5.