a cube has an edge of 4 feet. the edge is increasing at the rate of 3 feet per minute. express the volume of the cube as a function of m, the number of minutes elapsed

V = 144m + 64

Step-by-step explanation:

The cube has an edge (a) = 4 feet.

Now, the volume of the cube is given by V = a³ ....... (1)

So, initially, the volume of the cube was 4³ =64 cubic feet.

Now, differentiating equation (1) with respect to m (a variable which measurea number of minutes) we get

{Since the rate of change of length of edge is 3 feet/ minutes}

⇒

Integrating both sides we get,

V = 144m + c {Where c is the constant of integration} ........ (2)

Now, we know that at m = 0, V = 64 cubic feet.

So, from equation (2), we get c = 64

Therefore, V = 144m + 64 .... this is the expression of V in terms of m. (Answer)

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

-22

times both sides by 2, times () by 8, add alile terms, move terms, add alike and caculate divide both sides by 3