Incorrect.

$($a$)$ What is the value of divvec$(F)?$ Include units.

Enter an exact answer.

Flux $=$

$($b$)$ Assume the heat flows outward symmetrically. Verify that vec$(F)=vec(r),$ where vec$(r)=$xvec$(i)+$yvec$(j)+$zvec$(k)$ and $$ is a

suitable constant, satisfies the given conditions. Find $.$

Enter an exact answer.

$=$

eTextbook and Media

Hint

$($c$)$ Let $T(x,y,z)$ denote the temperature inside the earth. Heat flows according to the equation vec$(F)=-$kgradT,

where $k$ is a constant. Complete the following paragraph by filling in the blanks.

The vector gradT gives the direction of greatest

in temperature. Thus, $-$gradT gives the direction of

greatest

in temperature. The equation vec$(F)=-$kgradT says that heat will flow in the direction of

greatest

in temperature $($i$.$e$.$ from hot regions to cold$),$ and at a rate

the

temperature gradient.

eTextbook and Media

Incorrect.

$($d$)$ If $T$ is in $C,$ then $k=30,000$ watts $\frac{?}{km}C.$ Assuming the earth is a sphere with radius $6400km$ and surface

temperature $20C,$ what is the temperature at the center?

Round your answer to the nearest integer.

$T=$

$C$