One model for the ideal body weight, W, for men (in kilograms) is W = 50 + 2.3(h-60), where h represents height (in inches).
1. According to this model, what is the ideal weight of a 6-foot male?
2. Rewrite the function in order to express height as a function of weight. Call this function h. Show your work.
3. Verify that the given function and your function from part (b) are inverses, by showing that (W°h)(W) = W and that (h°W)(h) = h.
4. What is the height of a male whose ideal weight is 83 kg?

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isyllus isyllus · Answer 1 · 2018-11-29T15:36:45+01:00

Answer:

1) Height of 6 foot male could be 77.6 kg.

2) Function of h as form of W, [tex]h=\Rightarrow \dfrac{W+88}{2.3}[/tex]

4) Height of a male would be 74.35 inches.

Step-by-step explanation:

Ideal body weight model, W=50 + 2.3(h-60)

where, W is idea weight (in kilogram) and h represents height (in inches)

Part 1) We need to find ideal weight for 6 foot.

First we change 6 foot into inches

1 feet = 12 inch

6 foot = 72 inches

So, h=72 inches

Now we will put h=72 into W=50 + 2.3(h-60)

W=50 + 2.3(72-60)

W=77.6 Kg

Thus, Height of 6 foot male could be 77.6 kg.

Part 2) Rewrite the function as function of W

W=50 + 2.3(h-60)

2.3(h-60)=W-50

[tex]h=\frac{W-50}{2.3}+60\Rightarrow \dfrac{W+88}{2.3}[/tex]

Thus, Function of h as form of W, [tex]h=\Rightarrow \dfrac{W+88}{2.3}[/tex]

Part 3) Verify (Woh)=h and (hoW)=h

(Woh)=[tex]50+2.3(\dfrac{W+88}{2.3}-60)[/tex]

(Woh)=50+(W-50) = W

Similarly,

(hoW)=[tex]\dfrac{50 + 2.3(h-60)-88}{2.3}[/tex]

(hoW)=[tex]\dfrac{50 +2.3h-50}{2.3}\Rightarrow h[/tex]

Thus, Given function inverses to each other.

Part 4) Given [tex]h=\dfrac{W-88}{2.3}[/tex]

We need to find height of male of 83 kg weight. So, we put W=83 into above equation.

[tex]h=\dfrac{83+88}{2.3}\Rightarrow 74.35\ inches.[/tex]

Thus, Height of a male would be 74.35 inches.