MHB My answer:y=az^by=19.7(.454z)^0.753

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The basal metabolic rate for large anteaters is modeled by the equation y = 19.7x^0.753, where x represents the weight in kilograms. For anteaters weighing 5 kg and 25 kg, the calculated metabolic rates are approximately 66.19 kcal/day and 222.39 kcal/day, respectively. The discussion seeks assistance in converting the weight from pounds to kilograms, establishing a function x = g(z) where z is the weight in pounds. The conversion factor is noted as 1 lb = 0.454 kg, leading to a new function for weight in kilograms. Finally, the metabolic rate can be expressed as a function of weight in pounds by substituting the weight conversion into the original metabolic rate equation.
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The basal metabolic rate (in kcal/day) for large anteaters is given by:

y=f(x)= 19.7x0.753

where x is the anteater's weight in kilograms

a) find the basal metabolic rae for anteaters with the following weights

i. 5kg
ii. 25kg

My answer:

i= 66.19kg
ii= 222.39 kg

Hopefully I got a right, but b and c I need some help with please.

b) suppose the anteater's weight is given in pounds rather than kilograms. Given that 1lb=.454kg, find a function x=g(z) giving the anteater's weight in kg if z is the animals weight in lb.

c) write the basal metabolic rate as a function of the weight in pounds in the form y=azb by calculating f(g(z)).
 
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Your answers are correct thus far, the new function of kg to pounds is found by multiplying through by $\frac{1}{0.454}$
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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