# A lamb grows with its mass proportional

• Nerdlight
In summary, when a lamb's length changes by 15.8%, its mass increases by 17.3kg. Using the equation m = kx^3, the final mass (mf) can be found by substituting the given values and solving for mf. The final equation for mf is 1.55mi, which can also be written as mf = 1.55mi. This is because mi = kxi^3, and the x value can be any value (initial, final, or middle). The manual may not be helpful because it eliminates mi and solves for mf directly.
Nerdlight
A lamb grows with its mass proportional to the cube of its length. When the lambs length changes by 15.8% its mass increases by 17.3kg. Find the final mass.

Really stumped thanks for any help

mf=kxf3
length change by 15.8%
xi+.158xi=xf
xf=1.158xi

mf=k(1.158x)3
mf=1.55kx3

I couldn't get the right answer because at this point, my book shows kx3 turning into mi and continuing the problem from there. Why?

kx3=mi
mf=1.55mi
mi=mf/1.55

Nerdlight said:
mf=kxf3
The information given is more general than that. It tells you m=kx3. In particular, mi=kxi3 and mf=kxf3.
xf=1.158xi

mf=k(1.158x)3
You dropped the subscript on the x. Based on your equations to this point, it should be mf=k(1.158xi)3

It was a little confusing ill try to make it more clear.
Need to find the value of m at the end of this process.

m = kx3

length change by 15.8%
xi+.158xi = xf
xf = 1.158xi

mass increase of 17.3kg
mf = mi+17.3

mf = kxf3
mf = k(1.158xi)3
mf = 1.55kxi3

The solutions manual does something here I don't understand
mf = 1.55(kxi3)
mf = 1.55mi
mi = mf/1.55

Why does kxi3 = mi
k and xi3 just disappear and mi shows up
I got 109kg from 2 different methods which is incorrect and the manual isn't helping much on this one.

Last edited:
Nerdlight said:
m = kx3

Why does kxi3 = mi

The answer should be staring you in the face. It's because #m=kx^3##.

Lol gotcha, subscripts were throwing me, got to remember that m=kx^3 can take any x value whether its initial/final/middle. Thanks

You have it and you don't know it:

1.55mi-mi=17.3

Except he's been asked to solve for mf, not mi. It's better to eliminate mi rather than mf so you can solve for mf directly.

D H said:
Except he's been asked to solve for mf, not mi. It's better to eliminate mi rather than mf so you can solve for mf directly.
Potatoes, Potahtoes. I thought it would be easier for him to see it that way. I would have done it your way.

Chet

## 1. How does a lamb's mass affect its growth?

A lamb's mass directly affects its growth as it is proportional to its development and overall size. The larger the lamb's mass, the more nutrients and energy it requires to grow and develop.

## 2. What does it mean for a lamb's growth to be proportional to its mass?

When we say that a lamb's growth is proportional to its mass, we mean that as the lamb's mass increases, its growth and development will also increase at the same rate. This is known as a direct proportion.

## 3. How is a lamb's growth affected by its mass?

A lamb's growth is greatly affected by its mass as it determines the amount of food and nutrients it needs to consume to support its growth. A larger lamb with a higher mass will require more food and resources compared to a smaller lamb with a lower mass.

## 4. Can a lamb's growth be stunted by a lower mass?

Yes, a lamb's growth can be stunted if its mass is significantly lower than average. This may be due to inadequate nutrition, illness, or genetic factors. A lower mass can result in slower growth and development, leading to smaller size and potential health issues.

## 5. Is there a specific ratio for a lamb's mass and growth?

There is no specific ratio for a lamb's mass and growth as it can vary depending on several factors such as breed, genetics, and environment. However, in general, a larger mass will result in a faster and more substantial growth rate compared to a smaller mass.

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