Twenty six times thirty seven is 962
Given : (8 + i)(2 + 7i)
⇒ (8 × 2) + (8 × 7i) + (i × 2) + (i × 7i)
⇒ 16 + 56i + 2i + 7i²
We know that i² = -1
⇒ 16 + 58i + 7(-1)
⇒ 16 + 58i - 7
⇒ 9 + 58i
Answer:
Step-by-step explanation:
1.
![Hypotenuse = 32\\Adjacent = 25\\Angle\:\alpha \:=?\\Using \: SOHCAHTOA ;\\Cos \:\alpha = \frac{adj}{hyp} \\Cos \:\alpha = \frac{25}{32}\\\\\alpha = Cos^-^1\frac{25}{32} \\\alpha =38.62\\\\\alpha = 39](https://tex.z-dn.net/?f=Hypotenuse%20%3D%2032%5C%5CAdjacent%20%3D%2025%5C%5CAngle%5C%3A%5Calpha%20%5C%3A%3D%3F%5C%5CUsing%20%5C%3A%20SOHCAHTOA%20%3B%5C%5CCos%20%5C%3A%5Calpha%20%3D%20%5Cfrac%7Badj%7D%7Bhyp%7D%20%5C%5CCos%20%5C%3A%5Calpha%20%3D%20%5Cfrac%7B25%7D%7B32%7D%5C%5C%5C%5C%5Calpha%20%3D%20Cos%5E-%5E1%5Cfrac%7B25%7D%7B32%7D%20%5C%5C%5Calpha%20%3D38.62%5C%5C%5C%5C%5Calpha%20%3D%2039)
2.
![Opposite = 8\\Adjacent = 16\\\alpha =?\\Using SOHCAHTOA\\Tan\:\alpha = \frac{opp}{adj} \\Tan\:\alpha = \frac{8}{16} \\Tan \:\alpha =1/2\\\alpha = Tan^-^11/2\\\\\alpha =26.56\\\alpha =27](https://tex.z-dn.net/?f=Opposite%20%3D%208%5C%5CAdjacent%20%3D%2016%5C%5C%5Calpha%20%3D%3F%5C%5CUsing%20SOHCAHTOA%5C%5CTan%5C%3A%5Calpha%20%3D%20%5Cfrac%7Bopp%7D%7Badj%7D%20%5C%5CTan%5C%3A%5Calpha%20%3D%20%5Cfrac%7B8%7D%7B16%7D%20%5C%5CTan%20%5C%3A%5Calpha%20%3D1%2F2%5C%5C%5Calpha%20%3D%20Tan%5E-%5E11%2F2%5C%5C%5C%5C%5Calpha%20%3D26.56%5C%5C%5Calpha%20%3D27)
3.
![Hypotenuse = 41\\Opposite = 19\\\alpha = ?\\Using\: SOHCAHTOA\\Sin\:\alpha = \frac{opp}{hyp} \\Sin \:\alpha =\frac{19}{41}\\\\\alpha =Sin^-^1 (19/41)\\\\\alpha =27.6\\ \alpha =28](https://tex.z-dn.net/?f=Hypotenuse%20%3D%2041%5C%5COpposite%20%3D%2019%5C%5C%5Calpha%20%3D%20%3F%5C%5CUsing%5C%3A%20SOHCAHTOA%5C%5CSin%5C%3A%5Calpha%20%3D%20%5Cfrac%7Bopp%7D%7Bhyp%7D%20%5C%5CSin%20%5C%3A%5Calpha%20%3D%5Cfrac%7B19%7D%7B41%7D%5C%5C%5C%5C%5Calpha%20%3DSin%5E-%5E1%20%2819%2F41%29%5C%5C%5C%5C%5Calpha%20%3D27.6%5C%5C%20%5Calpha%20%3D28)
there are 6 numbers on a number cube
1,2,3,4,5,6
there are 2 numbers greater than 4 ( 5 & 6)
so there is a 2/6 chance
2/6 reduces to 1/3