Rachel, Mario and Sanjit share some money in the ratios 4 : 3 : 9 Mario receives £96. Work out the difference between the amount
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Answer:
Max Value: x = 400
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>
- Antiderivatives
- Integral Property:
- Integration Method: U-Substitution
- [Integration] Reverse Power Rule:
Step-by-step explanation:
<u>Step 1: Define</u>
<u>Step 2: Identify Variables</u>
<em>Using U-Substitution, we set variables in order to integrate.</em>
<u>Step 3: Integrate</u>
- Define:
- Substitute:
- [Integral] Int Property:
- [Integral] U-Sub:
- [Integral] Rewrite:
- [Integral - Evaluate] Reverse Power Rule:
- Simplify:
- Back-Substitute:
- Factor:
<u>Step 4: Identify Domain</u>
We know from a real number line that we cannot have imaginary numbers. Therefore, we cannot have any negatives under the square root.
Our domain for our integrated function would then have to be (-∞, 400]. Anything past 400 would give us an imaginary number.
The number of half-hour sittings needed to watch all the shows by Devon is 11
<u>Solution:</u>
Given, Devon records 4 hours of reality shows on her DVR
she records comedy shows for 3/8 of that amount of time.
Devon watches all the reality and comedy shows in half-hour sittings.
We have to find the number of half-hour sittings needed to watch all the shows
Now, number of half hour sittings is given as
Hence Devon needs 11 sittings