Assuming the repetitive part is 152, i.e. the original repeating decimal is
A=3.152152152....
then
1000A=3152.152152152152....
subtract A
1000A-A=3152.152152....-3.152152152....
999A=3149
A=3149/999=3+152/999=3 152/999
Therefore
3.152152152.... = 3149/999 or 3 152/999
4-2 is 2
and 5-3 is 2
when you add or subtract fractions, you don't change the denominator (bottom number in fraction)
so the answer is 2 2/8
Answer:
a
Step-by-step explanation:
to determine cost u need to have a equation to show cost per room.and total cost of rooms
Answer:
![V=V_p-V_cV=27.712 cm^3 - 4.019 cm^3V=23.693 cm^3V=23.6 cm^3](https://tex.z-dn.net/?f=V%3DV_p-V_cV%3D27.712%20cm%5E3%20-%204.019%20cm%5E3V%3D23.693%20cm%5E3V%3D23.6%20cm%5E3)
Step-by-step explanation:
Given that:
Diameter of the cylinder: d=1.6 cm
Apothem of the hexagon: a=2 cm
Assuming the thickness of the steel hex nut: t=2 cm
Volume of metal in the hex nut: V=?
![V=V_p-V_c](https://tex.z-dn.net/?f=V%3DV_p-V_c)
![\texttt {Volume of the prism}: V_p\\\\\texttt {Volume of the cylinder}: V_c](https://tex.z-dn.net/?f=%5Ctexttt%20%7BVolume%20of%20the%20prism%7D%3A%20V_p%5C%5C%5C%5C%5Ctexttt%20%7BVolume%20of%20the%20cylinder%7D%3A%20V_c)
Prism:
![V_p=Ab h](https://tex.z-dn.net/?f=V_p%3DAb%20h)
Ab=n L a / 2
Number of the sides: n=6
Side of the hexagon: L
Height of the prism: h=t=2 cm
Central angle in the hexagon: A=360°/n
A=360°/6
A=60°
![\tan \frac{A}{2} =\frac{L}{2} / a](https://tex.z-dn.net/?f=%5Ctan%20%5Cfrac%7BA%7D%7B2%7D%20%3D%5Cfrac%7BL%7D%7B2%7D%20%2F%20a)
![\tan \frac{60}{2} =\frac{L}{2} / 2cm](https://tex.z-dn.net/?f=%5Ctan%20%5Cfrac%7B60%7D%7B2%7D%20%3D%5Cfrac%7BL%7D%7B2%7D%20%2F%202cm)
![\tan 30 =\frac{L}{2} / 2cm](https://tex.z-dn.net/?f=%5Ctan%2030%20%3D%5Cfrac%7BL%7D%7B2%7D%20%2F%202cm)
![\frac{\sqrt{3} }{3} =\frac{\frac{L}{2} }{2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B3%7D%20%3D%5Cfrac%7B%5Cfrac%7BL%7D%7B2%7D%20%7D%7B2%7D)
![2\frac{\sqrt{3} }{3} =\frac{L}{2}](https://tex.z-dn.net/?f=2%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B3%7D%20%3D%5Cfrac%7BL%7D%7B2%7D)
![L=4\frac{\sqrt{3} }{3}](https://tex.z-dn.net/?f=L%3D4%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B3%7D)
![Ab=n *L *\frac{a}{2}](https://tex.z-dn.net/?f=Ab%3Dn%20%2AL%20%2A%5Cfrac%7Ba%7D%7B2%7D)
![Ab=6(4\frac{\sqrt{3} }{3} )(2cm)/2](https://tex.z-dn.net/?f=Ab%3D6%284%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B3%7D%20%29%282cm%29%2F2)
![=24\frac{\sqrt{3} }{3} cm^2\\\\=8\sqrt{3} cm^2](https://tex.z-dn.net/?f=%3D24%5Cfrac%7B%5Csqrt%7B3%7D%20%7D%7B3%7D%20cm%5E2%5C%5C%5C%5C%3D8%5Csqrt%7B3%7D%20cm%5E2)
![V_p=Ab h](https://tex.z-dn.net/?f=V_p%3DAb%20h)
![=(8\sqrt{3} )cm^2(2cm)\\\\=16\sqrt{3} cm^3\\\\=16(1.732)cm^3\\\\=27.712cm^3](https://tex.z-dn.net/?f=%3D%288%5Csqrt%7B3%7D%20%29cm%5E2%282cm%29%5C%5C%5C%5C%3D16%5Csqrt%7B3%7D%20cm%5E3%5C%5C%5C%5C%3D16%281.732%29cm%5E3%5C%5C%5C%5C%3D27.712cm%5E3)
Cylinder:
![V_c=\pi\frac{d^2}{4} L](https://tex.z-dn.net/?f=V_c%3D%5Cpi%5Cfrac%7Bd%5E2%7D%7B4%7D%20L)
π=3.14
d=1.6 cm
Height of the cylinder: h=t=2 cm
![V_c=3.14\times\frac{1.6^2}{4} \times2\\\\=3.14\times\frac{2.56}{4} \times 2\\\\=2.0096\times2\\\\=4.019cm^3](https://tex.z-dn.net/?f=V_c%3D3.14%5Ctimes%5Cfrac%7B1.6%5E2%7D%7B4%7D%20%5Ctimes2%5C%5C%5C%5C%3D3.14%5Ctimes%5Cfrac%7B2.56%7D%7B4%7D%20%5Ctimes%202%5C%5C%5C%5C%3D2.0096%5Ctimes2%5C%5C%5C%5C%3D4.019cm%5E3)
![V=V_p-V_cV=27.712 cm^3 - 4.019 cm^3V=23.693 cm^3V=23.6 cm^3](https://tex.z-dn.net/?f=V%3DV_p-V_cV%3D27.712%20cm%5E3%20-%204.019%20cm%5E3V%3D23.693%20cm%5E3V%3D23.6%20cm%5E3)