Answer:
D trust me look
Step-by-step explanation:
Hope This Helped
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.
First, you want to solve for the equation for this problem, would be:
0.05N + 0.10D = 20.50
While N = The amount of nickels, and D = The amount of dimes.
Since N = 164, and D = 123. It would add up to 287 coins. 164 + 123 = 287.
Now that you have the number for those two variables, solve the equation for when N = 164, and D = 123.
0.05N + 0.10D = 20.50
<span>0.05(164) + 0.10(123) = 20.50
</span><span>8.2 + 12.3 = 20.50
</span>20.50 = 20.50
So, there is 164 nickels, and 123 dimes for your answer.
<em>I hope this helps! </em>
<em>~ Notorious Sovereign</em>
Answer:
1/7
Step-by-step explanation:
There are seven people in all on person will arrive at a different time than others. Every single one of them arrives at different times so it's 1/7
Answer: The required equation for points P is 
Step-by-step explanation: We are give two points A(0, 1, 2) and B(6, 4, 2).
To find the equation for points P such that the distance of P from both A and B are equal.
We know that the distance between two points R(a, b, c) and S(d, e, f) is given by

Let the point P be represented by (x, y, z).
According to the given information, we have
![PA=PB\\\\\Rightarrow \sqrt{(x-0)^2+(y-1)^2+(z-2)^2}=\sqrt{(x-6)^2+(y-4)^2+(z-2)^2}\\\\\Rightarrow x^2+y^2-2y+1+z^2-4z+4=x^2-12x+36+y^2-8y+16+z^2-4z+4~~~~~~~[\textup{Squaring both sides}]\\\\\Rightarrow -2y+1=-12x-8y+52\\\\\Rightarrow 12x+6y=51\\\\\Rightarrow 4x+2y=17.](https://tex.z-dn.net/?f=PA%3DPB%5C%5C%5C%5C%5CRightarrow%20%5Csqrt%7B%28x-0%29%5E2%2B%28y-1%29%5E2%2B%28z-2%29%5E2%7D%3D%5Csqrt%7B%28x-6%29%5E2%2B%28y-4%29%5E2%2B%28z-2%29%5E2%7D%5C%5C%5C%5C%5CRightarrow%20x%5E2%2By%5E2-2y%2B1%2Bz%5E2-4z%2B4%3Dx%5E2-12x%2B36%2By%5E2-8y%2B16%2Bz%5E2-4z%2B4~~~~~~~%5B%5Ctextup%7BSquaring%20both%20sides%7D%5D%5C%5C%5C%5C%5CRightarrow%20-2y%2B1%3D-12x-8y%2B52%5C%5C%5C%5C%5CRightarrow%2012x%2B6y%3D51%5C%5C%5C%5C%5CRightarrow%204x%2B2y%3D17.)
Thus, the required equation for points P is 