Oil from a leaking container radiates outwards in the form of a circular film on the water surfaces. If the area of the circle increases at rate of 900m²/s, how fast is the radius of the circle
increasing when the area is 1400 z m??
[6 marks)
[Ans:3.83m/s]

Step by Step Explanation:

The area a is defined as

Now take derivative of the above expression with respect to time:

Solving for dr/dt, we then get

Note that da/dt = 900 m^2/s and when the area of the oil slick is 1400 m^2, the radius r is r = √(1400/π) = 21.1 m. Therefore,the rate at which the radius is increasing dr/dt is

54.864 meters

step-by-step explanation:

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b