Answer:
Verified


Step-by-step explanation:
Question:-
- We are given the following non-homogeneous ODE as follows:

- A general solution to the above ODE is also given as:

- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.
Solution:-
- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.

- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:

- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.
- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

- Therefore, the complete solution to the given ODE can be expressed as:

- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

- Therefore, the complete solution to the given ODE can be expressed as:

Y=140 because U have to go 35 divided by 2 and 8 times 17.5
Answer:
Option b
Step-by-step explanation:
To write the searched equation we must modify the function f (x) = | x | in the following way:
1. Do y = f(x + 4)
This operation horizontally shifts the function f(x) = | x | by a factor of 4 units to the left on the x axis.
y = | x +4 |
2. Do 
This operation horizontally expands the function f (x) = | x | in a factor of 4 units. 
3. Do 
This operation vertically shifts the function f (x) = | x | by a factor of 4 units down on the y-axis.

4. After these transformations the function f(x) = | x | it looks like:

Therefore the correct option is option b. You can verify that your vertex is at point (-4, -4) by making f (-4)

Answer:
A....... x+y=216 and 2/3x+4/9y=118
Step-by-step explanation:
Answer:
The height of the vase is 
Step-by-step explanation:
we know that
The volume of a cone is equal to

we have



substitute and solve for h




