<h2>Steps:</h2>
So firstly, this function is asking us to divide f(x) by g(x) so let's set that up as such:

Next, remember that <u>dividing by a number is the same as multiplying by its reciprocal.</u> To find the reciprocal of a number, flip the numerator and denominator around. With this info, flip the second fraction to it's reciprocal and change the sign to multiplication:

Next, we are going to factor x² - x - 6. Firstly, what two terms have a product of -6x² and a sum of -x? That would be -3x and 2x. Replace -x with 2x - 3x:

Next, factor x² + 2x and -3x - 6 separately. Make sure that they have the same quantity on the inside of the parentheses:

Now you can rewrite it as:

Next, multiply:

Next, divide:

And lastly, simplify:
- A good tip:


<h2>Answer:</h2>
<u>The correct option is C. x² + 4x + 4.</u>
Answer:
V = 20.2969 mm^3 @ t = 10
r = 1.692 mm @ t = 10
Step-by-step explanation:
The solution to the first order ordinary differential equation:

Using Euler's method

Where initial droplet volume is:

Hence, the iterative solution will be as next:
- i = 1, ti = 0, Vi = 65.45

- i = 2, ti = 0.5, Vi = 63.88

- i = 3, ti = 1, Vi = 62.33

We compute the next iterations in MATLAB (see attachment)
Volume @ t = 10 is = 20.2969
The droplet radius at t=10 mins

The average change of droplet radius with time is:
Δr/Δt = 
The value of the evaporation rate is close the value of k = 0.08 mm/min
Hence, the results are accurate and consistent!
Answer:
a=5, b=-2
Step-by-step explanation:
If you simplify the equation, you get:
3ax +6 -4x -4b - 11x - 14 = 0 =>
3ax - 15x -4b -8 = 0
group together x's and constants:
(3a-15)x -8 -4b = 0
To make this 0 for all x, we have to find an a such that 3a-15 = 0 and b such that -8-4b = 0. this leads to a=5, b=-2
It’s 76 meters hoped it helped!