scientists use the formula d=0.099m^(9/10) to give the drinking rate, d litres per day, for a mammal with mass m kilograms.
A) rewrite the equation using radicals
B) Determine the drinking rate of each mammal.
i) a 35kg dog
ii) a 520kg moose
iii) a 28g mouse
my answers:
A) radicals: 10√m^9
B) i) 10√35^9 = 2.45 L/day
ii) 10√520^9 =
I got 278230 L/day but my textbook answer says 27.54 L/day. I really don't understand why.
iii) 28/100 = 0.028kg
10√0.028^9 = 0.04
I got 0.04 L/day but my textbook answer says 0.003963 L/day. I really don't understand why.
You forgot to multiply by 0.099
ok thanks
A) To rewrite the equation using radicals, you can rewrite the exponent 9/10 as a radical.
The formula d = 0.099m^(9/10) can be rewritten as:
d = 0.099 * √(m^9)
B) Now let's calculate the drinking rate for each mammal:
i) For a 35kg dog:
d = 0.099 * √(35^9)
d = 0.099 * √(52521875)
d = 0.099 * 7244.64
d ≈ 717.62 L/day
ii) For a 520kg moose:
d = 0.099 * √(520^9)
d = 0.099 * √(3252390400)
d = 0.099 * 57002.66
d ≈ 5641.54 L/day
iii) For a 28g mouse:
Convert 28g to kg: 28g / 1000 = 0.028kg
d = 0.099 * √(0.028^9)
d = 0.099 * √(1.186805288e-12)
d = 0.099 * 3.44802197e-7
d ≈ 3.41 x 10^-8 L/day
It appears that the textbook answers differ from your answers due to rounding errors in the calculations.
A) To rewrite the equation using radicals, we can rewrite the exponent as a radical. The exponent 9/10 can be expressed as the tenth root of m^9. Therefore, the equation can be rewritten as d = 0.099 * (m^9)^(1/10).
B) Let's calculate the drinking rate for each mammal:
i) For a 35kg dog:
d = 0.099 * (35^9)^(1/10) = 0.099 * (35)^(9/10) = 0.099 * (3.998883726) = 0.395 L/day (rounded to three decimal places)
ii) For a 520kg moose:
d = 0.099 * (520^9)^(1/10) = 0.099 * (520)^(9/10) = 0.099 * (41.09803163) = 4.069 L/day (rounded to three decimal places)
iii) For a 28g mouse:
First, convert the mass to kilograms: 28g = 0.028kg
d = 0.099 * (0.028)^9/10 = 0.099 * (0.028)^(9/10) = 0.099 * (0.5550434369) = 0.055 L/day (rounded to three decimal places)
The reason your calculated values differ from the textbook answers is likely due to rounding errors. When performing calculations, make sure to use the full precision of the intermediate steps before rounding to get accurate results.