Arunner sprints around a circular track of radius 100 m at a constant speed of 7 mys. the runner’s friend is standing at a distance 200 m from the center of the track. how fast is the distance between the friends changing when the distance between them is 200 m?

Step-by-step explanation:

Let B represents the position of runner, A represents the position of the friend and C represents the position of centre of the circular track. ( shown  below ),

We need to find :

By the cosine law,

Differentiating with respect to t ( time ),

Now, by arc length formula,

Radius( say r ) × angle = arc length ( say l )

Differentiating w. r. t. t,

Here,

,

Now, again

We know that,

From equation (1), (2) and (3),

Hence, the distance between the friends changing with the rate of meter per sec.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

any options?

step-by-step explanation: