Answer:
The differential equation becomes -
![\frac{dV}{dt} = k\sqrt[3]{V}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20k%5Csqrt%5B3%5D%7BV%7D)
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.
⇒ ∝ ![\sqrt[3]{V}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7BV%7D)
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.
It is horizontal I believe because if you were to flip it horizontally then it would be symmetrical
Let x be the number of months.
The first plan is 15 dollars sign up fee and 38 dollars per month. So the equation is 38x + 15.
The second plan is 78 dollars as sign up fee and 31 dollars per month. So the equation is 31x + 78.
We need find when x has the same value in both equations, so we do their equality:
38x + 15 = 31x + 78
Let's subtract 15 from both sides
38x + 15 = 31x + 78
38x + 15 - 15 = 31x + 78 - 15
38x = 31x + 63
Now let's subtract 31x from both sides to have the variables on a side and the numbers on side:
38x = 31x + 63
38x - 31x = 31x - 31x + 63
7x = 63
Divide both sides by 7 to have the variable x on a side and its value on the other:
(7x)/7 = 63/7
x = 9
So at month 9, the 2 plans will cost the same.
Let's check our answers, and let y be the cost:
y = 38x + 15 = 38*9 + 15 = 357
y = 31x + 78 = 31*9 + 78 = 357
Our answer has been approved.
Hope this helps! :D
Answer:
Step-by-step explanation:answer is b
Answer:
22⁰
Step-by-step explanation:
By angle sum property :
x + 127 + 31 = 180⁰
x = 180 - 158
x = 22⁰
