Answer:
If a and b are two positive rational numbers such that ab is not a perfect square of a rational number, then ab is an irrational number lying between a and b.
So an irrational number between 3 and 4 is=3×4=3×4=3×2=23
B!
hope this helps, it just seems like the best answe.
Answer:
slope = 12/5 or 2.4
Step-by-step explanation:
(-2,-7), (3,5)
(5 - (-7) / 3 - (-2)) = (12 / 5)
slope = 12/5 or 2.4
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the following Sum to Product Identities:
<u>Proof LHS → RHS</u>
![\text{Sum to Product:}\qquad \dfrac{\cos 10\bigg[2\cos \bigg(\dfrac{15+25}{2}\bigg)\sin \bigg(\dfrac{15-25}{2}\bigg)\bigg]}{\cos 20\bigg[-2\sin \bigg(\dfrac{15+5}{2}\bigg)\sin \bigg(\dfrac{15-5}{2}\bigg)\bigg]}](https://tex.z-dn.net/?f=%5Ctext%7BSum%20to%20Product%3A%7D%5Cqquad%20%5Cdfrac%7B%5Ccos%2010%5Cbigg%5B2%5Ccos%20%5Cbigg%28%5Cdfrac%7B15%2B25%7D%7B2%7D%5Cbigg%29%5Csin%20%5Cbigg%28%5Cdfrac%7B15-25%7D%7B2%7D%5Cbigg%29%5Cbigg%5D%7D%7B%5Ccos%2020%5Cbigg%5B-2%5Csin%20%5Cbigg%28%5Cdfrac%7B15%2B5%7D%7B2%7D%5Cbigg%29%5Csin%20%5Cbigg%28%5Cdfrac%7B15-5%7D%7B2%7D%5Cbigg%29%5Cbigg%5D%7D)
![\text{Simplify:}\qquad \qquad \dfrac{\cos 10[2\cos 20\sin (-5)]}{\cos 20[-2\sin 10\sin 5]}\\\\\\.\qquad \qquad \qquad =\dfrac{-2\cos10 \cos 20 \sin 5}{-2\sin 10 \cos 20 \sin 5}\\\\\\.\qquad \qquad \qquad =\dfrac{\cos 10}{\sin 10}\\\\\\.\qquad \qquad \qquad =\cot 10](https://tex.z-dn.net/?f=%5Ctext%7BSimplify%3A%7D%5Cqquad%20%5Cqquad%20%5Cdfrac%7B%5Ccos%2010%5B2%5Ccos%2020%5Csin%20%28-5%29%5D%7D%7B%5Ccos%2020%5B-2%5Csin%2010%5Csin%205%5D%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D%5Cdfrac%7B-2%5Ccos10%20%5Ccos%2020%20%5Csin%205%7D%7B-2%5Csin%2010%20%5Ccos%2020%20%5Csin%205%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D%5Cdfrac%7B%5Ccos%2010%7D%7B%5Csin%2010%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D%5Ccot%2010)
LHS = RHS: cot 10 = cot 10 
