I am struggling to get the right answer with these two problems. If anyone can help me even if it is only one of the problems I would greatly appreciate it. I will hand out a best answer!
Question 1:
It has been estimated that 1000 curies of a radioactive substance introduced at a point on the surface of the open sea would spread over an area of 20,000 km2 in 20 days. Assuming that the area covered by the radioactive substance is a linear function of time t and is always circular in shape, express the radius r (in km) of the contamination as a function of t (in days).
Question 2:
A large cone has radius 5 cm and height 12.5 cm. Express the volume of the smaller cone as a function of y.
Question 1:
It has been estimated that 1000 curies of a radioactive substance introduced at a point on the surface of the open sea would spread over an area of 20,000 km2 in 20 days. Assuming that the area covered by the radioactive substance is a linear function of time t and is always circular in shape, express the radius r (in km) of the contamination as a function of t (in days).
Question 2:
A large cone has radius 5 cm and height 12.5 cm. Express the volume of the smaller cone as a function of y.
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If the area is a linear function of time:
A(t) = mt + b
A(0) = 0 ==> b = 0
A(20) = 20000 = m20 ==> m = 1000
A(t) = 1000t
If the area is circular, then A(t) = πR²(t) = 1000t : R ≥ 0
R²(t) =1000t/π
R(t) = ±√(1000t/π) : The negative result is outside the domain and can be discarded.
R(t) = 10√(10t/π)
Question 2 is poorly formed.
What is y? Is the undefined smaller cone similar to the larger cone? Is the radius of the smaller cone a function of the height or is the radius constant? Is y the height?
A(t) = mt + b
A(0) = 0 ==> b = 0
A(20) = 20000 = m20 ==> m = 1000
A(t) = 1000t
If the area is circular, then A(t) = πR²(t) = 1000t : R ≥ 0
R²(t) =1000t/π
R(t) = ±√(1000t/π) : The negative result is outside the domain and can be discarded.
R(t) = 10√(10t/π)
Question 2 is poorly formed.
What is y? Is the undefined smaller cone similar to the larger cone? Is the radius of the smaller cone a function of the height or is the radius constant? Is y the height?