There is a 24.71% chance of getting a blue golf ball
Answer:
b. ![\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20225y%5E2%20%2B%20150xy%20%2B%20100x%5E2%20%3D%20225y%5E2%20%2B%20150xy%20%2B%20100x%5E2)
a. ![\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5B8x%20%2B%2012y%5D%5E2%20%2B%20%5B6x%20%2B%209y%5D%5E2%20%3D%20%5B10x%20%2B%2015y%5D%5E2)
Step-by-step explanation:
b. ![\displaystyle 225y^2 + 150xy + 100x^2 = 225y^2 + 150xy + 100x^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20225y%5E2%20%2B%20150xy%20%2B%20100x%5E2%20%3D%20225y%5E2%20%2B%20150xy%20%2B%20100x%5E2)
a. ![\displaystyle [8x + 12y]^2 + [6x + 9y]^2 = [10x + 15y]^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5B8x%20%2B%2012y%5D%5E2%20%2B%20%5B6x%20%2B%209y%5D%5E2%20%3D%20%5B10x%20%2B%2015y%5D%5E2)
The two expressions are identical on each side of the equivalence symbol, therefore they are an identity.
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Answer : The length of the wire is, 8533 cm
Step-by-step explanation :
As the iron sphere is beaten and drawn into a wire. That means, their volume will be equal.
Volume of iron sphere = Volume of cylindrical wire
The formula will be:
![\frac{4}{3}\pi r_1^3=\pi r_2^2h](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r_1%5E3%3D%5Cpi%20r_2%5E2h)
where,
= radius of sphere = ![\frac{Diamtere}{2}=\frac{8cm}{2}=4cm](https://tex.z-dn.net/?f=%5Cfrac%7BDiamtere%7D%7B2%7D%3D%5Cfrac%7B8cm%7D%7B2%7D%3D4cm)
= radius of cylindrical wire = ![\frac{Diamtere}{2}=\frac{2mm}{2}=1mm=0.1cm](https://tex.z-dn.net/?f=%5Cfrac%7BDiamtere%7D%7B2%7D%3D%5Cfrac%7B2mm%7D%7B2%7D%3D1mm%3D0.1cm)
h = height of cylindrical wire or length of wire
Now put all the given values in the above formula, we get:
![\frac{4}{3}\pi r_1^3=\pi r_2^2h](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r_1%5E3%3D%5Cpi%20r_2%5E2h)
![\frac{4}{3}\times r_1^3=r_2^2h](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Ctimes%20r_1%5E3%3Dr_2%5E2h)
![\frac{4}{3}\times (4)^3=(0.1)^2h](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%5Ctimes%20%284%29%5E3%3D%280.1%29%5E2h)
![h=8533.33cm\approx 8533cm](https://tex.z-dn.net/?f=h%3D8533.33cm%5Capprox%208533cm)
Therefore, the length of the wire is, 8533 cm