Evan takes 15.5 minutes to walk 1 mile.
2 answers:
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Given:
The parent absolute function is
To find:
The new function if the parent function is translated up by 5 units and vertically stretched by a factor of 3.
Solution:
The translation is defined as
.... (1)
Where, k is stretch factor, a is horizontal shift and b is vertical shift.
If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.
If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.
If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.
Parent function is translated up by 5 units. So, b=5
It is vertically stretched by a factor of 3. So, k=3.
There is no horizontal shift. So, a=0.
Now, putting k=3, a=0 and b=5 in (1), we get
Therefore, the correct option is D.
Answer:
Step-by-step explanation:
This is <em>a separable differential equation</em>. Rearranging terms in the equation gives
Integration on both sides gives
where is a constant of integration.
The steps for solving the integral on the right hand side are presented below.
Therefore,
Multiply both sides by
By taking exponents, we obtain
Isolate .
Since when
, we obtain an initial condition
.
We can use it to find the numeric value of the constant .
Substituting for
and
in the equation gives
Therefore, the solution of the given differential equation is