Q:

(1 point) The length of an insect (L, in mm) is a function of the temperature during development (T , measured in ∘C according to L(T)=8+T10 ) . The volume of the insect (V , in cubic mm) is a function of the length according to V(L)=7L3 . The mass (M in milligrams) depends on volume according to M(V)=1.1V . Find mass as a function of temperature. M(T)= How much would an insect weigh that developed at 22∘C?

Accepted Solution

A:
Answer:[tex]M(T)=1.1(7(8+T^{10})^{3})[/tex] and [tex]M(T)=1.1(7(8+22^{10})^{3})=1.44\time10^{41}[/tex]Step-by-step explanation:We have the next set of functions:[tex]L(T)=8+T^{10}[/tex][tex]V(L)=7L^{3}[/tex][tex]M(V)=1.1V[/tex]We want to know M(T) then:[tex]M(V)=1.1V[/tex] but we know that [tex]V(L)=7L^{3}[/tex]:[tex]M(L)=1.1(7L^{3})[/tex] and we know that [tex]L(T)=8+T^{10}[/tex][tex]M(T)=1.1(7(8+T^{10})^{3})[/tex]Finally using the value of 22º we have[tex]M(T)=1.1(7(8+22^{10})^{3})=1.44\time10^{41}[/tex]