Answer:
General Formulas and Concepts:
<u>Calculus</u>
Limits
- Limit Rule [Variable Direct Substitution]:
Differentiation
- Derivatives
- Derivative Notation
The definition of a derivative is the slope of the tangent line:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>
<em />
<u>Step 2: Differentiate</u>
- [Function] Substitute in <em>x</em>:
- Substitute in functions [Definition of a Derivative]:
- Simplify:
- Evaluate limit [Limit Rule - Variable Direct Substitution]:
- Simplify:
∴ the derivative of the given function will be equal to 4 divided by x².
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Learn more about derivatives: brainly.com/question/25804880
Learn more about calculus: brainly.com/question/23558817
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Answer:
22 1/2 hours
Step-by-step explanation:
There are several ways you can get there. One way is to use table values to form a sum of 60:
cars = 32×2 - 8×(1/2) = 64 -4 = 60
Then the corresponding hours are ...
hours = 12×2 - 3×(1/2) = 24 -1.5 = 22.5
It will take 22.5 hours to wax 60 cars.
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Another way to get there is to use proportions:
hours/cars = 3/8 = ??/60
Multiply by 60 to find ??
(60)(3/8) = ?? = 180/8 = 22.5 . . . . hours
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We can do these things because we have determined the relationship between hours and cars is proportional: 8/3 = 16/6 = 32/12. If it weren't proportional, some other strategy would be needed to answer the question.
Answer:
Print it
Step-by-step explanation:
Answer:
x is 33
Step-by-step explanation:
All 3 of these angles added together create a straight line, and such lines always measure 180°, so if we create an equation with the 3 angles being added together, set it equal to 180, and solve, we'll find the answer:
104+x+(x+10)=180
104+x+x+10=180 (use the distributive property to remove parenthesis)
104+10+x+x=180 (rearrange terms)
114+2x=180 (combine like terms)
2x=180-114 (subtract 114 from both sides)
2x=66
x=33 (divide 2 from both sides)
The two combinations of two-digit numbers we could have would be 79 and 97. The only one of those that would round to 100 is 97. If we added another digit to the number, it would be over 100. The very smallest three digit number we could have with these two numbers in it would be 179; that would not round to 100. That means 97 must be our number.