Answer:
False
Step-by-step explanation:
The cube root is 5
Assuming the sum of the opposite angle would be 180. We can easily calculate for x and ultimately solve for the angle of B. We do as follows
B + D = 180
3x-12 + x = 180
4x - 12 = 180
4x = 192
x = 48 degrees
Therefore angle B would have a measurement of 132 degrees. Hope this helps.
<em>A</em><em>N</em><em>S</em><em>W</em><em>E</em><em>R</em><em>:</em>
<h2><u>4</u><u>2</u><u>:</u><u>5</u><u>4</u></h2>
<em>EXPLANATION</em><em>:</em>
<h2><u>H</u><u>O</u><u>P</u><u>E</u><u> </u><u>I</u><u>T</u><u> </u><u>H</u><u>E</u><u>L</u><u>P</u><u>S</u></h2><h3><u>#</u><u>C</u><u>A</u><u>R</u><u>R</u><u>Y</u><u>O</u><u>N</u><u>L</u><u>E</u><u>A</u><u>R</u><u>N</u><u>I</u><u>N</u><u>G</u></h3>
14.5 is the answer to the equation
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)