Question

The approximate number of Calories, C, that an animal needs each day is given by C=72m³/⁶, where m is the animal's mass in kilograms. Find the number of Calories that a 16-kilogram dog needs each day.

Answer 1

A 16-kilogram dog requires approximately 288 Calories each day, calculated using the given formula C = 72m³/⁶ by substituting m with 16 and following the mathematical operations.

Step-by-step explanation:

The question asks us to find out how many Calories a 16-kilogram dog needs each day using the formula C = 72m³/⁶, where C represents Calories and m is the animal's mass in kilograms. To solve this, we'll substitute the value of the dog's mass (m = 16 kg) into the formula:

C = 72 × 16³/⁶

First, calculate the mass to the power of ³/⁶, which means taking the cubic root of the mass (because 3 is the numerator) and then raising that result to the sixth power (as indicated by the denominator 6):

16³ = 4096

Now, take the 6th root of 4096:

4096⁶ = 4

Finally, multiply this by 72 to find the total Calories:

C = 72 × 4

C = 288 Calories

So, a 16-kilogram dog needs approximately 288 Calories each day.