For a period of time as an alligator grows, its mass is proportional to the cube of its length. When the alligator's length changes by 15.8%, its mass increases by 17.3kg. Find its mass at the end of this process.
mass=k*length^3
mass+17.3=k(length*1.158)^3
k*length^3=k(length^3 ( 1.55)-17.3
.55K*length^3=17.3
mass*.55=17.3
massfinalthen=17.3/.55 + 17.3
To solve this problem, we need to set up an equation using the information provided. Let's break down the information into smaller steps:
Step 1: Let's assume the initial length of the alligator is "L" and its corresponding mass is "M."
Step 2: According to the problem, the length changes by 15.8%, which can be expressed as 0.158L (15.8% = 0.158).
Step 3: Therefore, the new length is L + 0.158L = 1.158L.
Step 4: For the mass, we know that it is proportional to the cube of the length. Mathematically, we can express this as:
M ∝ L^3
Step 5: Using this proportionality, we can write the equation as:
M1/M = (L1/L)^3
where M1 is the new mass, L1 is the new length, and M and L are the initial mass and length, respectively.
Step 6: From the given information, we know that when the length changes by 15.8%, the mass increases by 17.3kg. We can set up the equation as:
(M1 - M)/M = 17.3 kg / M
Step 7: Substituting M1 = M + 17.3kg and L1 = 1.158L into the equation (from Steps 3 to 6), we get:
(M + 17.3kg - M)/M = 17.3kg / M = (1.158L / L)^3
Step 8: Solve the equation:
17.3kg / M = 1.158^3
Step 9: Solve for M, the initial mass:
M = 17.3kg / (1.158^3)
Calculating this value, we find:
M ≈ 10.363 kg
Therefore, the mass of the alligator at the end of the process is approximately 10.363 kg.