If a triangle has side lengths 5 cm, 18 cm, and 12 cm, is it a right triangle?
1 answer:
Answer:
No, it's not a right triangle.
Step-by-step explanation:
1. The Pythagorean Theorem states that the area of the square whose side is the hypotenuse (longest side of a right triangle) is equal to the sum of the area of the squares from the two other sides.
2. The longest side in this "triangle" has 18 centimeters, and the other 2 sides are 5 and 12 centimeters.
3. Let's apply the Pythagorean Theorem to see if 5^2 + 12^2 = 18^2
4. Okay, so the sum of the area of the squares from the two other sides is not equal to the hypotenuse squared, therefore, it's not a right triangle.
(Plus, it's not even a triangle because 7 < x < 17, and the third "side", 18, is not between 7 and 17.)
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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.