Answer:
The inverse will be:
Step-by-step explanation:
In order to find the inverse of the equation, we do a variable change, since we are finding the inverse, :
Now solve for y'.
First add 4 in both sides of the equation and change to the left y'.
= x + 4
Second divide by 9
/9 = (x + 4)/9
= (x + 4)/9
Now you will have to clear y, with the square root.
![[tex]y'^{\frac{2}{2}} = \sqrt{x + 4} / \sqrt{9}](https://tex.z-dn.net/?f=%5Btex%5Dy%27%5E%7B%5Cfrac%7B2%7D%7B2%7D%7D%20%3D%20%5Csqrt%7Bx%20%2B%204%7D%20%20%2F%20%5Csqrt%7B9%7D)
[/tex] =
Simplifying terms
You can check the answer by doing the evaluation of the following equation:
(f o 
) (x)
substitute the equation for y' or inverse function
f(
)
Now substitue the value into f(x)
You will have
=x
Answer:
18 = m
Step-by-step explanation:
2=m/2-7
Add 7 to each side
2+7=m/2 - 7+7
9 = m/2
Multiply each side by 2
9*2 = m/2 * 2
18 = m
Answer:
Step-by-step explanation:
(-5,-3) is a point on the graph.
f⁻¹(-3) = -5
Expanding the left side gives
which gives two solutions,
and
. But if
, then
, but this number isn't real, so
is an extraneous solution. Meanwhile if
, you get
, so this solution is correct.
"Potential solutions" might refer to both possibilities, but there is only one actual (real) solution.
Answer:
Step-by-step explanation:
Since P(t) increases at a rate proportional to the number of people still unaware of the product, we have
Since no one was aware of the product at the beginning of the campaign and 50% of the people were aware of the product after 50 days of advertising
<em>P(0) = 0 and P(50) = 1,500,000
</em>
We have and ordinary differential equation of first order that we can write
The <em>integrating factor </em>is
Multiplying both sides of the equation by the integrating factor
Hence
Integrating both sides
But P(0) = 0, so C = -3,000,000
and P(50) = 1,500,000
so
And the equation that models the number of people (in millions) who become aware of the product by time t is
