Question

@Michele_Laino

Answer 1

it is none of the above right?

Answer 2

@Michele_Laino

Answer 3

please you have to apply the subsequent rule:
\[\frac{ d (x ^{n}) }{ dx }=n*x ^{(n-1)}, n \in \mathbb{N} \]
nevertheless n can be any real number

Answer 4

for example:
\[\frac{ dx ^{3} }{ dx }=3x ^{2}\]
so \[\frac{ d4x ^{3} }{ dx }=12x^{2}\]
that's the first term of your answer, please continue that calculus

Answer 5

for example the derivative of the second term is:
\[\frac{ d(-3x ^{2}) }{ dx }=-6x\]
now, try to calculate the derivative of the third term of your polynomial, please

Answer 6

9 @Michele_Laino

Answer 7

12x^2-6x+9 right?

Answer 8

which would be none of the above(:

Answer 9

perfect! your answer is right, namely noone of the answers listed

Answer 10

I'm ready!

Answer 11

iis it -24 in^2/hour?

Answer 12

the rate of 1.5 inches/hour is referring to an edge of your cube?

Answer 13

noo how fast its melting

Answer 14

I think the formulae are these:
\[\frac{ dl }{ dt }=-1.5\]
so we can write:
\[l(t)=-1.5*t+l _{0}\]
where l_0 is the initial length
furthermore, we have:
\[A(t)=[l(t)]^{2}\]
so:
\[\frac{ dA }{ dt }=2*l(t)*\frac{ dl }{ dt }=2*(-1.5t+l _{0})*(-1.5)\]

Answer 15

do you know what is the initial length of your cube?

Answer 16

side length of 2 inches?

Answer 17

I think that it must be greater than 2 inches

Answer 18

don't worry I got the solution:
in order to find our rate you havet calculate this
\[\frac{ dS }{ dt }=2*2*(-1.5)=-6\]

we don't needto know what is the initial lenftg of a sidof ur cube, because at the time when the side of o cube has a lenfgth equalss to 2, we can write:
l_0-1.5t=2, without need to know what is l_0

Answer 19

@mondona

Answer 20

and then what do we do?

Answer 21

rate of changing (decreasing) area is 6 inches^2/hour

Answer 22

so it would be negative right?

Answer 23

that's right, because during melting the dimensions of our ice cube are decreasing, so also area does that

Answer 24

6 wouldnt be right..

Answer 25

I think that your problem calls surface the total surface of our cube, whereas my calculus is refferring to the surface of only one face of the cube. So in order to get the right answer, you have to multiply -6 by 6, and you will get:
\[\frac{ dS }{ dt }=6*(-6)=-36\]
inches/hour
since, of course a cube has six faces

Answer 26

so the third option is the right answer!

Answer 27

ohhh thats what i thought i was thinking about that

Answer 28

thank you !

Answer 29

thank you!