The formula below gives the surface area S of a human body (in square meters) in terms of its weight W (in kilograms) and its height H (in centimeters).
S = 0.007184(W^0.425)(H^0.725)
Compute SW and SH when W = 100 kg and
H = 180 cm.
SW = ?
SH = ?
NOTE: I took the derivative of 0.007184 and multiply it by the derivative (100^.425)(180^.725)
but it still says it is wrong. please help me out.
dS/dW = (.425)(.007184)W^.425-1 (H^.725)
dS/dW =0.0030532W^-.575(H^.725)
dS/dW = 0.0030532H^.725/W^.575
0.0030532(180)^.725/100^.575
dS/dH = (.725)(.007184)W^.425H^.725-1
dS/dH = .0052084 W^.425H^-.275
dS/dH = .0052084 W^.425/H^.275
dS/dH = 0.0052084(100)^.425/180^.275
To compute SW and SH, we need to substitute the given values of W = 100 kg and H = 180 cm into the formula. Let's start with SW.
SW = 0.007184(W^0.425)(H^0.725)
Substituting W = 100 kg, we have:
SW = 0.007184(100^0.425)(H^0.725)
To simplify, let's calculate 100^0.425 using a calculator:
100^0.425 ≈ 5.848
Now, we can substitute this value back into the formula:
SW = 0.007184(5.848)(H^0.725)
Next, we substitute H = 180 cm:
SW = 0.007184(5.848)(180^0.725)
To simplify further, let's calculate 180^0.725:
180^0.725 ≈ 49.41
Substituting this value back into the equation:
SW ≈ 0.007184(5.848)(49.41)
Now, let's calculate the result:
SW ≈ 2.041
Therefore, SW ≈ 2.041 square meters.
Now let's move on to SH.
SH = 0.007184(W^0.425)(H^0.725)
Substituting the given values of W = 100 kg and H = 180 cm:
SH = 0.007184(100^0.425)(180^0.725)
Calculating 100^0.425:
100^0.425 ≈ 5.848
Substituting the value back into the formula:
SH = 0.007184(5.848)(180^0.725)
Calculating 180^0.725:
180^0.725 ≈ 49.41
Substituting this value back into the equation:
SH ≈ 0.007184(5.848)(49.41)
Now, let's calculate the result:
SH ≈ 2.041
Therefore, SH ≈ 2.041 square meters.
It appears that you tried to use the derivative to calculate SW and SH, but the derivatives are used for finding the rate of change or slope of a function, which is not necessary in this case. Simply substituting the given values into the formula will give you the correct values for SW and SH.