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# Proportional relationships

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Assume that male snakes of a particular species are all scaled versions of the same basic shape.

(i) (a) Describe in words the sort of relationship that you might expect there to be between the volume and the length of a snake. What relationship would you expect there to be between the mass and the length of a snake ?.

(b) If the mass (in grams) is denoted by M and the length (in cm) is denoted by L, write down a proportional relationship for M in terms of L.

(c) Rearrange this relationship to find a proportional relationship for L in terms of M Hence, write down a power law relationship for L in terms OF M, Using K as the constant of proportionality.

(iii) (a) A snake sheds its skin periodically; this is a process known as sloughing. Denoting the area of the shed skin as A (in cm^2), find a proportional relationship for A in in terms of M.

(b) The skin area of a particular snake of mass 64g is approximately 270cm^2 Use this information to estimate the constant of proportionality for the power law for A in terms of M ,

Hence, estimate the approximate skin area for a snake of mass 200g.

##### Solution Summary

The main aims of this question are to:
1,Use proportional relationships in relevant contexts.
2,Explain the meaning of, and use correctly, words describing proportional relationships.
3,Write down proportional relationships both in the from of a power equation and as an expression involving the proportion symbol x.
4, Use power regression to test proportional relationships.
5, Manipulate proportional relationships in practical contexts.

##### Solution Preview

Solution.
(i) (a) By observation of its shape, i think the relationship between the volume and its length might be linear, that is, the longer the bigger volume. Similarly, there is a linear ...

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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