Answer:
15 miles
Step-by-step explanation:
1/2 inch = 3 miles
1 inch = 6 miles
2 inches = 12 miles
2.5 inches = 15 miles
Answer:
1) ![\frac{(-2)^{-5}}{(-2)^{-10}}=-32](https://tex.z-dn.net/?f=%5Cfrac%7B%28-2%29%5E%7B-5%7D%7D%7B%28-2%29%5E%7B-10%7D%7D%3D-32)
2) ![2^{-1}.2^{-4} = \frac{1}{32}](https://tex.z-dn.net/?f=2%5E%7B-1%7D.2%5E%7B-4%7D%20%3D%20%5Cfrac%7B1%7D%7B32%7D)
3) ![(-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}](https://tex.z-dn.net/?f=%28-%5Cfrac%7B1%7D%7B2%7D%20%29%5E3.%28-%5Cfrac%7B1%7D%7B2%7D%20%29%5E2%3D-%5Cfrac%7B1%7D%7B32%7D)
4) ![\frac{2}{2^{-4}} = 32](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B2%5E%7B-4%7D%7D%20%3D%2032)
Step-by-step explanation:
1) ![\frac{(-2)^{-5}}{(-2)^{-10}}](https://tex.z-dn.net/?f=%5Cfrac%7B%28-2%29%5E%7B-5%7D%7D%7B%28-2%29%5E%7B-10%7D%7D)
Solving using exponent rule: ![a^{-m}=\frac{1}{a^m}](https://tex.z-dn.net/?f=a%5E%7B-m%7D%3D%5Cfrac%7B1%7D%7Ba%5Em%7D)
![\frac{(-2)^{-5}}{(-2)^{-10}}\\=(-2)^{-5+10}\\=(-2)^{5}\\=-32](https://tex.z-dn.net/?f=%5Cfrac%7B%28-2%29%5E%7B-5%7D%7D%7B%28-2%29%5E%7B-10%7D%7D%5C%5C%3D%28-2%29%5E%7B-5%2B10%7D%5C%5C%3D%28-2%29%5E%7B5%7D%5C%5C%3D-32)
So, ![\frac{(-2)^{-5}}{(-2)^{-10}}=-32](https://tex.z-dn.net/?f=%5Cfrac%7B%28-2%29%5E%7B-5%7D%7D%7B%28-2%29%5E%7B-10%7D%7D%3D-32)
2) ![2^{-1}.2^{-4}](https://tex.z-dn.net/?f=2%5E%7B-1%7D.2%5E%7B-4%7D)
Using the exponent rule: ![a^m.a^n=a^{m+n}](https://tex.z-dn.net/?f=a%5Em.a%5En%3Da%5E%7Bm%2Bn%7D)
We have:
![2^{-1}.2^{-4}\\=2^{-1-4}\\=2^{-5}](https://tex.z-dn.net/?f=2%5E%7B-1%7D.2%5E%7B-4%7D%5C%5C%3D2%5E%7B-1-4%7D%5C%5C%3D2%5E%7B-5%7D)
We also know that: ![a^{-m}=\frac{1}{a^m}](https://tex.z-dn.net/?f=a%5E%7B-m%7D%3D%5Cfrac%7B1%7D%7Ba%5Em%7D)
Using this rule:
![2^{-5}\\=\frac{1}{2^5}\\=\frac{1}{32}](https://tex.z-dn.net/?f=2%5E%7B-5%7D%5C%5C%3D%5Cfrac%7B1%7D%7B2%5E5%7D%5C%5C%3D%5Cfrac%7B1%7D%7B32%7D)
So, ![2^{-1}.2^{-4} = \frac{1}{32}](https://tex.z-dn.net/?f=2%5E%7B-1%7D.2%5E%7B-4%7D%20%3D%20%5Cfrac%7B1%7D%7B32%7D)
3) ![(-\frac{1}{2} )^3.(-\frac{1}{2} )^2](https://tex.z-dn.net/?f=%28-%5Cfrac%7B1%7D%7B2%7D%20%29%5E3.%28-%5Cfrac%7B1%7D%7B2%7D%20%29%5E2)
Solving:
![(-\frac{1}{2} )^3.(-\frac{1}{2} )^2\\=(-\frac{1}{8} ).(\frac{1}{4} )\\=-\frac{1}{32}](https://tex.z-dn.net/?f=%28-%5Cfrac%7B1%7D%7B2%7D%20%29%5E3.%28-%5Cfrac%7B1%7D%7B2%7D%20%29%5E2%5C%5C%3D%28-%5Cfrac%7B1%7D%7B8%7D%20%29.%28%5Cfrac%7B1%7D%7B4%7D%20%29%5C%5C%3D-%5Cfrac%7B1%7D%7B32%7D)
So, ![(-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}](https://tex.z-dn.net/?f=%28-%5Cfrac%7B1%7D%7B2%7D%20%29%5E3.%28-%5Cfrac%7B1%7D%7B2%7D%20%29%5E2%3D-%5Cfrac%7B1%7D%7B32%7D)
4) ![\frac{2}{2^{-4}}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B2%5E%7B-4%7D%7D)
We know that: ![a^{-m}=\frac{1}{a^m}](https://tex.z-dn.net/?f=a%5E%7B-m%7D%3D%5Cfrac%7B1%7D%7Ba%5Em%7D)
![\frac{2}{2^{-4}}\\=2\times 2^4\\=2(16)\\=32](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B2%5E%7B-4%7D%7D%5C%5C%3D2%5Ctimes%202%5E4%5C%5C%3D2%2816%29%5C%5C%3D32)
So, ![\frac{2}{2^{-4}} = 32](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B2%5E%7B-4%7D%7D%20%3D%2032)
Answer:
The radius of the inflated spherical balloon is 45 millimeters.
Step-by-step explanation:
Volume of the spherical water balloon = 121,500 pi cubic millimeters
Let the radius of the balloon = r
Now, Volume of a Sphere = ![\frac{4}{3} \pi r^{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D)
⇒![\frac{4}{3} \pi r^{3} = 121,500 \pi](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%5Cpi%20r%5E%7B3%7D%20%20%3D%20121%2C500%20%5Cpi)
On solving for the value of r, we get:
![r^{3} = \frac{121,500\times 3}{4} = 91125\\ \implies r = \sqrt[3]{91125}](https://tex.z-dn.net/?f=r%5E%7B3%7D%20%20%3D%20%5Cfrac%7B121%2C500%5Ctimes%203%7D%7B4%7D%20%20%20%3D%2091125%5C%5C%20%5Cimplies%20%20r%20%20%3D%20%5Csqrt%5B3%5D%7B91125%7D)
or, r = 45 millimeter
Hence, the radius of the inflated spherical balloon is 45 millimeters.
73. Area- 55 Perimeter-32
75. Area-30 Perimeter-30