Cobalt-60 is a radioactive isotope that decays into nickel-60 at a rate that is proportional to...
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Cobalt-60 is a radioactive isotope that decays into nickel-60 at a rate that is proportional to the current amount of cobalt-60 present. Representing the mass of cobalt-60 at time t as M(t): (i) Write down a differential equation that describes this radioactive decay. Explain any additional symbols used and state the order of the equation. [3 marks] (ii) -2 Given that cobalt-60 has a half-life (i.e. the time taken for half of a sample to decay) of 5.27 years, calculate how long it will take for a 50 gram sample of cobalt-60 to decay to 20 grams. [7 marks] (b) Work out of of 8² f and 1 dx dy dyox 1-cos(x²) 1-4 (c) Evaluate lim- x→0 R -1 0 1 Figure 1: Circular half-annulus (d) The second moment of area of a shape R about the x axis is defined as ² d. Evaluate this integral for the circular half-annulus shown in Figure 1. [7 marks] 2 for the function f(x, y) = ln(x²-3y). X y spatula blade [4 marks] 9 cm [4 marks] x=6y-y² Figure 2: Plan view of a spatula blade. Cobalt-60 is a radioactive isotope that decays into nickel-60 at a rate that is proportional to the current amount of cobalt-60 present. Representing the mass of cobalt-60 at time t as M(t): (i) Write down a differential equation that describes this radioactive decay. Explain any additional symbols used and state the order of the equation. [3 marks] (ii) -2 Given that cobalt-60 has a half-life (i.e. the time taken for half of a sample to decay) of 5.27 years, calculate how long it will take for a 50 gram sample of cobalt-60 to decay to 20 grams. [7 marks] (b) Work out of of 8² f and 1 dx dy dyox 1-cos(x²) 1-4 (c) Evaluate lim- x→0 R -1 0 1 Figure 1: Circular half-annulus (d) The second moment of area of a shape R about the x axis is defined as ² d. Evaluate this integral for the circular half-annulus shown in Figure 1. [7 marks] 2 for the function f(x, y) = ln(x²-3y). X y spatula blade [4 marks] 9 cm [4 marks] x=6y-y² Figure 2: Plan view of a spatula blade.
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step 1 A1 a i The radioactive decay of cobalt60 can be described using a firstorder linear ordinary differential equation The rate of decay is proport... View the full answer
Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
Posted Date:
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