Answer:
The resulting function is 
.
Step-by-step explanation:
Let 
a real function, we define the following function operations:
Horizontal translation
(1)
If 
, then horizontal translation is to the left, otherwise it is to the right.
Vertical translation
(2)
If 
, then vertical translation is upwards, otherwise it is downwards.
Knowing that 
and 
is the result of translating four units downwards and five units to the left. Then, we find that:
The resulting function is .
I always do post production in school
Step-by-step explanation:
Solve for a
k + a = v + w
a = v + w - k
Solution → { a = v + w - k }
Answer:
Step-by-step explanation:
We have a separable equation, first let's rewrite the equation as:
But:
So:
Multiplying both sides by dx and dividing both sides by 3a+y:
Integrating both sides:
Evaluating the integrals:
Where C1 is an arbitrary constant.
Solving for y:
So:
Finally, let's evaluate the initial condition in order to find C1:
Solving for C1:
Therefore:
