1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47
So 16 integers.
Answer:
1 5/7 hours.
Step-by-step explanation:
1/3+1/4 = 7/12
1/7/12= 1.714 hrs
The answer is: " 100 cultures " .
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Take the number of the day we are at (from the beginning; in this case, "9" (for "Day 9").
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Then add "1" to that number (in this case, " 9 + 1 = 10" .
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Then, take that value (in this case, "10"); and "square" that value ; (in this case; " 10² = 10 * 10 = 100 . This is the answer.
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The answer is: " 100 cultures " .
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<u>Note</u><u>:</u> We get this steps by noticing the trend from the information provided.
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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.
Hello from MrBillDoesMath!
Answer:
See Discussion section below
Discussion:
2x^2 + 5x + 3 = (2x+3)(x+1) which is Choice 3
3x^2+10x+4 =-1/3 (-3 x + sqrt(13) - 5) (3 x + sqrt(13) + 5)
I don't think any of the provided choices are right!
8x^2+10x-3 = (2x+3)(4x-1) which is Choice 2
6x^2-7x-4 = -1/24 (-12 x + sqrt(145) + 7) (12 x + sqrt(145) - 7)
I don't think any of the provided choices are right!
2x^2+x-28 = (2x-7)(x+4) which is Choice 2
Thank you,
MrB