Answer:

Domain: All Real Numbers
General Formulas and Concepts:
<u>Algebra I</u>
- Domain is the set of x-values that can be inputted into function f(x)
<u>Calculus</u>
The derivative of a constant is equal to 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Chain Rule: ![\frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Derivative: ![\frac{d}{dx} [ln(u)] = \frac{u'}{u}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bln%28u%29%5D%20%3D%20%5Cfrac%7Bu%27%7D%7Bu%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = ln(2x² + 1)
<u>Step 2: Differentiate</u>
- Derivative ln(u) [Chain Rule/Basic Power]:

- Simplify:

- Multiply:

<u>Step 3: Domain</u>
We know that we would have issues in the denominator when we have a rational expression. However, we can see that the denominator would never equal 0.
Therefore, our domain would be all real numbers.
We can also graph the differential function to analyze the domain.
Ayden bought 4 oranges.
Explanation:
4.20 divided by 6 will give you 0.7
0.7 times 4 gives you 2.8
Answer:
maximum area will be 1058 square yards
maximum height will be 81 feet
Step-by-step explanation:
P = 2L +2W
but in this case it will be P= L+2W and P=92 yards
L+2W = 92
Solve for L , L = 92-2W
The area of rectangle A = L x W
Plug in L and simplify: A = (92-2W)W =92W -2W²
Plot in your calculator and look for maximum so when the width is 23 yards maximum area will be 1058 square yards.
Second problems is the maximum height of the rocket. Maximum will be at the vertex of the upside-down parabola.
To solve this plug 2 in for d in the equation like so:

The fraction
can be simplified to 2.
How I found this:
The greatest common factor of 8 and 4 is 4.
If we divide 8 by 4 you get 2
If you divide 4 by 4 you would get 1
That gives you the simplified fraction:
Which is the same as simply 2
Now we have the expression:
2 - 2
^^^ A number subtracted from itself is always zero
The answer is:
0
Hope this helped!
~Just a girl in love with Shawn Mendes
Let the number be x.
then the number is (x + 6)
the difference between their squares is 192
(x + 6)² - x² = 192
expanding we get;
x² + 12x + 36 - x² = 192
12x + 36 = 192
12x = 192 - 36
12x = 156
x = 13
the numbers are 13 and 19.
hope this helps, God bless!