Which of the following sets of lengths can sean use to make a right triangle?
group of answer choices

{5 cm, 15 cm, 18 cm}

{6 cm, 12 cm, 16 cm}

{5 cm, 13 cm, 15 cm}

{8 cm, 15 cm, 17 cm}

If we know your Pythagorean Triples we can immediately recognize that the last choice is a right triangle:

8² + 15² = 17²

If you don't know your Pythagorean Triples, it's worth learning the first few off the list because teachers use them in problems all the time.  But for now let's just exhaustively check the Pythagorean Theorem for each triangle.  We don't have to multiply everything out; we can analyze the common factors.  If two have a common factor that the third one doesn't have, there's no way for the Pythagorean Theorem to add up.

Clearly 5²+15² is a multiple of 5 but 18² isn't so that one isn't a right triangle.

6²+12² is a multiple of 6, 16² isn't a multiple of 6, not an RT.

15²-5² is a multiple of 5, 13² isn't, no joy.

8²+15² = 64 + 225 = 289 = 17² -- that's a real right triangle, a valid Pythagorean Triple.

General Formulas and Concepts:

Algebra I

FunctionsFunction NotationGraphing

Calculus

Integrals

Integration Rule [Reverse Power Rule]:                                                              

Integration Rule [Fundamental Theorem of Calculus 1]:                                    

Integration Property [Multiplied Constant]:                                                        

Integration Property [Addition/Subtraction]:                                                      

Shell Method:                                                                                                        

[Shell Method] 2πx is the circumference[Shell Method] 2πxf(x) is the surface area[Shell Method] 2πxf(x)dx is volume

Step-by-step explanation:

Step 1: Define

y = x²

y = 0

x = 5

Step 2: Identify

Find other information from graph.

See Attachment.

Bounds of Integration: [0, 5]

Step 3: Find Volume

Substitute in variables [Shell Method]:                                                         [Integrand] Multiply:                                                                                       [Integral] Integrate [Integration Rule - Reverse Power Rule]:                     Evaluate [Integration Rule - FTC 1]:                                                             Multiply:                                                                                                        

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Applications of Integration

Book: College Calculus 10e