Pythagorean triples are integer solutions to the Pythagorean theorem a^2 + b^2 = c^2 I like triplets but triples seems to be the favored term for right triangle the x side is the hypotenuse the side opposite the right angle
hope this helps!
Answer:
![2a^3b^2\sqrt[3]{3a}](https://tex.z-dn.net/?f=2a%5E3b%5E2%5Csqrt%5B3%5D%7B3a%7D)
Step-by-step explanation:
Use the following rules for exponents:
![a^m*a^n=a^{m+n}\\\\\sqrt[3]{x^3}=x](https://tex.z-dn.net/?f=a%5Em%2Aa%5En%3Da%5E%7Bm%2Bn%7D%5C%5C%5C%5C%5Csqrt%5B3%5D%7Bx%5E3%7D%3Dx)
Simplify 24. Find two factors of 24, one of which should be a perfect cube:
![8*3=24\\\\2^3=8](https://tex.z-dn.net/?f=8%2A3%3D24%5C%5C%5C%5C2%5E3%3D8)
Insert:
![\sqrt[3]{2^3*3a^{10}b^6}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2%5E3%2A3a%5E%7B10%7Db%5E6%7D)
Now split the exponents. Split 10 into as many 3's as possible:
![10=3+3+3+1](https://tex.z-dn.net/?f=10%3D3%2B3%2B3%2B1)
Insert as exponents:
![\sqrt[3]{2^3*3*a^3*a^3*a^3*a^1*b^6}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2%5E3%2A3%2Aa%5E3%2Aa%5E3%2Aa%5E3%2Aa%5E1%2Ab%5E6%7D)
Split 6 into as many 3's as possible:
![6=3+3](https://tex.z-dn.net/?f=6%3D3%2B3)
Insert as exponents:
![\sqrt[3]{2^3*3*a^3*a^3*a^3*a^1*b^3*b^3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2%5E3%2A3%2Aa%5E3%2Aa%5E3%2Aa%5E3%2Aa%5E1%2Ab%5E3%2Ab%5E3%7D)
Now simplify. Any terms with an exponent of 3 will be moved out of the radical (rule #2):
![2\sqrt[3]{3*a^3*a^3*a^3*a^1*b^3*b^3}\\\\\\2*a*a*a\sqrt[3]{3*a^1*b^3*b^3}\\\\\\2*a*a*a*b*b\sqrt[3]{3*a^1}](https://tex.z-dn.net/?f=2%5Csqrt%5B3%5D%7B3%2Aa%5E3%2Aa%5E3%2Aa%5E3%2Aa%5E1%2Ab%5E3%2Ab%5E3%7D%5C%5C%5C%5C%5C%5C2%2Aa%2Aa%2Aa%5Csqrt%5B3%5D%7B3%2Aa%5E1%2Ab%5E3%2Ab%5E3%7D%5C%5C%5C%5C%5C%5C2%2Aa%2Aa%2Aa%2Ab%2Ab%5Csqrt%5B3%5D%7B3%2Aa%5E1%7D)
Simplify:
![2a^3b^2\sqrt[3]{3a}](https://tex.z-dn.net/?f=2a%5E3b%5E2%5Csqrt%5B3%5D%7B3a%7D)
:Done
To find this answer, just divide 360 by 5 to find out how many times his heart beats in one minute instead of 5. Doing this will give you a final answer of 72 bpm.
Answer:
<h2>The answer is 8.9 units</h2>
Step-by-step explanation:
The distance between two points can be found by using the formula
![d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\](https://tex.z-dn.net/?f=d%20%3D%20%20%5Csqrt%7B%20%28%7Bx1%20-%20x2%7D%29%5E%7B2%7D%20%2B%20%20%28%7By1%20-%20y2%7D%29%5E%7B2%7D%20%20%7D%20%5C%5C)
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
(-3, 2) and (1, -6)
The distance between them is
![d = \sqrt{ ({ - 3 - 1})^{2} + ({2 + 6})^{2} } \\ = \sqrt{ ({ - 4})^{2} + {8}^{2} } \\ = \sqrt{16 + 64} \\ = \sqrt{80} \: \: \: \: \: \: \: \: \: \: \\ = 4 \sqrt{5} \: \: \: \: \: \: \: \: \: \: \\ = 8.9442719...](https://tex.z-dn.net/?f=d%20%3D%20%20%20%5Csqrt%7B%20%28%7B%20-%203%20-%201%7D%29%5E%7B2%7D%20%20%2B%20%20%28%7B2%20%2B%206%7D%29%5E%7B2%7D%20%7D%20%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B%20%28%7B%20-%204%7D%29%5E%7B2%7D%20%2B%20%20%7B8%7D%5E%7B2%7D%20%20%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B16%20%2B%2064%7D%20%20%5C%5C%20%20%3D%20%20%5Csqrt%7B80%7D%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%5C%20%20%3D%204%20%5Csqrt%7B5%7D%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%5C%20%20%3D%208.9442719...)
We have the final answer as
8.9 units to the nearest tenth
Hope this helps you