Question

a given temperature the heat loss of an organism is y = 33x 3
where y is the heat loss in watts and x is the length of the
organism in metres. What is the rate of change of heat loss when
the organism is 0.8 m in length?

Answer 1

Answer:

63.36  W/m

Step-by-step explanation:

The heat loss of an organism is given by :

$y=33x^3$ ...(1)

Where

y is heat loss in watts and x is the length of the organism in metres.

We need to find the rate of change of heat loss when  the organism is 0.8 m in length.

Differentiate equation (1) wrt x.

$\dfrac{dy}{dx}=\dfrac{d}{dx}(33x^3)\\\\=33\times 3x^2\\\\=99x^2$

Put x = 0.8 m in above equation.

$\dfrac{dy}{dx}=99\times (0.8)^2\\\\=63.36\ W/m$

So, the  rate of change of heat loss when  the organism is 0.8 m in length is 63.36  W/m