343 = 7 x 7 x 7
the answer is 7,7, and well 7
Answer:
.0075 (hope this help; let me know if not)
Step-by-step explanation:
The operation is + and the signs of the numbers are opposite so we have to subtract. The bigger number has positive sign in front if so we do 1.2-1.125=1.200-1.125
I'm going to line up
1.200
-1.125
---------
If you have 200 and you take about 125... 75 should beleft
so
1.200
-1.125
---------
0.075
v = √16 · √d
d = 300 ft
v = √16 · √300
v = √16 · √100 · √3
v = 4 · 10 · √3
<em>v = 40√3 ft/sec </em> <== simplified radical form
That's about 69.3 feet per sec, or 47.2 miles per hour.
Answer:
a)
, b)
, c)
,
.
Step-by-step explanation:
The volume and the surface area of the sphere are, respectively:
![V = \frac{4}{3}\pi \cdot r^{3}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B4%7D%7B3%7D%5Cpi%20%5Ccdot%20r%5E%7B3%7D)
![A_{s} = 4\pi \cdot r^{2}](https://tex.z-dn.net/?f=A_%7Bs%7D%20%3D%204%5Cpi%20%5Ccdot%20r%5E%7B2%7D)
a) The volume of the sphere is:
![V = \frac{4}{3}\pi \cdot (20\,in)^{3}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B4%7D%7B3%7D%5Cpi%20%5Ccdot%20%2820%5C%2Cin%29%5E%7B3%7D)
![V = 33510.322\,in^{3}](https://tex.z-dn.net/?f=V%20%3D%2033510.322%5C%2Cin%5E%7B3%7D)
b) The surface area of the sphere is:
![A_{s} = 4\pi \cdot (20\,in)^{2}](https://tex.z-dn.net/?f=A_%7Bs%7D%20%3D%204%5Cpi%20%5Ccdot%20%2820%5C%2Cin%29%5E%7B2%7D)
![A_{s} = 5026.548\,in^{2}](https://tex.z-dn.net/?f=A_%7Bs%7D%20%3D%205026.548%5C%2Cin%5E%7B2%7D)
c) The total differentials for volume and surface area of the sphere are, respectively:
![\Delta V = 4\pi\cdot r^{2}\,\Delta r](https://tex.z-dn.net/?f=%5CDelta%20V%20%3D%204%5Cpi%5Ccdot%20r%5E%7B2%7D%5C%2C%5CDelta%20r)
![\Delta V = 4\pi \cdot (20\,in)^{2}\cdot (0.03\,in)](https://tex.z-dn.net/?f=%5CDelta%20V%20%3D%204%5Cpi%20%5Ccdot%20%2820%5C%2Cin%29%5E%7B2%7D%5Ccdot%20%280.03%5C%2Cin%29)
![\Delta V = 150.796\,in^{3}](https://tex.z-dn.net/?f=%5CDelta%20V%20%3D%20150.796%5C%2Cin%5E%7B3%7D)
![\Delta A_{s} = 8\pi\cdot r \,\Delta r](https://tex.z-dn.net/?f=%5CDelta%20A_%7Bs%7D%20%3D%208%5Cpi%5Ccdot%20r%20%5C%2C%5CDelta%20r)
![\Delta A_{s} = 8\pi \cdot (20\,in)\cdot (0.03\,in)](https://tex.z-dn.net/?f=%5CDelta%20A_%7Bs%7D%20%3D%208%5Cpi%20%5Ccdot%20%2820%5C%2Cin%29%5Ccdot%20%280.03%5C%2Cin%29)
![\Delta A_{s} = 15.080\,in^{2}](https://tex.z-dn.net/?f=%5CDelta%20A_%7Bs%7D%20%3D%2015.080%5C%2Cin%5E%7B2%7D)
Relative errors are presented hereafter:
![\%V = \frac{\Delta V}{V}\times 100\%](https://tex.z-dn.net/?f=%5C%25V%20%3D%20%5Cfrac%7B%5CDelta%20V%7D%7BV%7D%5Ctimes%20100%5C%25)
![\%V = \frac{150.796 \,in^{3}}{33510.322\,in^{3}}\times 100\,\%](https://tex.z-dn.net/?f=%5C%25V%20%3D%20%5Cfrac%7B150.796%20%5C%2Cin%5E%7B3%7D%7D%7B33510.322%5C%2Cin%5E%7B3%7D%7D%5Ctimes%20100%5C%2C%5C%25)
![\% V = 0.450\,\%](https://tex.z-dn.net/?f=%5C%25%20V%20%3D%200.450%5C%2C%5C%25)
![\% A_{s} = \frac{\Delta A_{s}}{A_{s}}\times 100\,\%](https://tex.z-dn.net/?f=%5C%25%20A_%7Bs%7D%20%3D%20%5Cfrac%7B%5CDelta%20A_%7Bs%7D%7D%7BA_%7Bs%7D%7D%5Ctimes%20100%5C%2C%5C%25)
![\% A_{s} = \frac{15.080\,in^{2}}{5026.548\,in^{2}}\times 100\,\%](https://tex.z-dn.net/?f=%5C%25%20A_%7Bs%7D%20%3D%20%5Cfrac%7B15.080%5C%2Cin%5E%7B2%7D%7D%7B5026.548%5C%2Cin%5E%7B2%7D%7D%5Ctimes%20100%5C%2C%5C%25)
![\%A_{s} = 0.300\,\%](https://tex.z-dn.net/?f=%5C%25A_%7Bs%7D%20%3D%200.300%5C%2C%5C%25)