The rate of change of the volume V of water in a tank with respect to time t is directly proportional to the cubed root of the volume. Write a differential equation that describes the relationship. Display keyboard shortcuts for Rich Content Editor

The differential equation becomes -

i.e.

Step-by-step explanation:

Given - The rate of change of the volume V of water in a tank with respect to time t is directly proportional to the cubed root of the volume.

To find - Write a differential equation that describes the relationship.

Proof -

Rate of change of volume V with respect to time t is represented by

Now,

Given that,

The rate of change of the volume V of water in a tank with respect to time t is directly proportional to the cubed root of the volume.

⇒ ∝

Now,

We know that, when we have to remove the Proportionality sign , we just put a constant sign.

Let k be any constant.

So,

The differential equation becomes -

i.e.

3

step-by-step explanation:

in standard form:

a= dictionaries

b= maps

you have to buy 3 dictionaries, so put a 3 next to the a (dictionaries) so that you can multiply them by each other.

a3+b= 60 (the amount of money you have)

we already know the cost of a=15 so replace a with $15

($15 x 3)+b=60

multiply 15 and 3 to get $45 and replace it with $45

45+b=60

and then replace b with 15 to get the total:

45+15=60

that means you have $15 left after buying 3 dictionaries.

15 divided by the cost of a map ($5) equals 3.

so you can buy 3 maps.

sorry if it was confusing!