Answer:
![h \approx 12.7\,cm](https://tex.z-dn.net/?f=h%20%5Capprox%2012.7%5C%2Ccm)
Step-by-step explanation:
The side of the square base is:
![l = \sqrt{64\,cm^{2}}](https://tex.z-dn.net/?f=l%20%3D%20%5Csqrt%7B64%5C%2Ccm%5E%7B2%7D%7D)
![l = 8\,cm](https://tex.z-dn.net/?f=l%20%3D%208%5C%2Ccm)
The formula for the surface area of the pyramid is:
![A_{s} = \frac{1}{2}\cdot (3\cdot l)\cdot \sqrt{0.25\cdot l^{2}+h^{2}} + l^{2}](https://tex.z-dn.net/?f=A_%7Bs%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%283%5Ccdot%20l%29%5Ccdot%20%5Csqrt%7B0.25%5Ccdot%20l%5E%7B2%7D%2Bh%5E%7B2%7D%7D%20%2B%20l%5E%7B2%7D)
The height is cleared in the previous expression:
![A_{s} - l^{2} = \frac{3}{2}\cdot l\cdot \sqrt{0.25\cdot l^{2}+h^{2}}](https://tex.z-dn.net/?f=A_%7Bs%7D%20-%20l%5E%7B2%7D%20%3D%20%5Cfrac%7B3%7D%7B2%7D%5Ccdot%20l%5Ccdot%20%5Csqrt%7B0.25%5Ccdot%20l%5E%7B2%7D%2Bh%5E%7B2%7D%7D)
![\frac{2}{3}\cdot \frac{A_{s}-l^{2}}{l} = \sqrt{0.25\cdot l^{2} + h^{2}}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B3%7D%5Ccdot%20%5Cfrac%7BA_%7Bs%7D-l%5E%7B2%7D%7D%7Bl%7D%20%3D%20%5Csqrt%7B0.25%5Ccdot%20l%5E%7B2%7D%20%2B%20h%5E%7B2%7D%7D)
![\frac{4}{9}\cdot \left(\frac{A_{s}-l^{2}}{l} \right)^{2} = \frac{1}{4} \cdot l^{2} + h^{2}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B9%7D%5Ccdot%20%5Cleft%28%5Cfrac%7BA_%7Bs%7D-l%5E%7B2%7D%7D%7Bl%7D%20%5Cright%29%5E%7B2%7D%20%3D%20%5Cfrac%7B1%7D%7B4%7D%20%5Ccdot%20l%5E%7B2%7D%20%2B%20h%5E%7B2%7D)
![h = \sqrt{\frac{4}{9}\cdot \left(\frac{A_{s}-l^{2}}{l} \right)^{2} - \frac{1}{4}\cdot l^{2}}](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%7B%5Cfrac%7B4%7D%7B9%7D%5Ccdot%20%5Cleft%28%5Cfrac%7BA_%7Bs%7D-l%5E%7B2%7D%7D%7Bl%7D%20%5Cright%29%5E%7B2%7D%20-%20%5Cfrac%7B1%7D%7B4%7D%5Ccdot%20l%5E%7B2%7D%7D)
![h = \sqrt{\frac{4}{9}\cdot \left[\frac{224\,cm^{2}-(8\,cm)^{2}}{8\,cm}\right]^{2}-\frac{1}{4}\cdot (8\,cm)^{2} }](https://tex.z-dn.net/?f=h%20%3D%20%5Csqrt%7B%5Cfrac%7B4%7D%7B9%7D%5Ccdot%20%5Cleft%5B%5Cfrac%7B224%5C%2Ccm%5E%7B2%7D-%288%5C%2Ccm%29%5E%7B2%7D%7D%7B8%5C%2Ccm%7D%5Cright%5D%5E%7B2%7D-%5Cfrac%7B1%7D%7B4%7D%5Ccdot%20%288%5C%2Ccm%29%5E%7B2%7D%20%7D)
![h \approx 12.7\,cm](https://tex.z-dn.net/?f=h%20%5Capprox%2012.7%5C%2Ccm)
Answer:
Area
Step-by-step explanation:
When covering the surface of a solid, we measure or calculate the area.
1) Use the distributive property to eliminate parentheses.
.. 3(6x) -3(5) -7(3x) -7(10) = 0
.. 18x -15 -21x -70 = 0 . . . . . . finish multiplying terms
.. -3x -85 = 0 . . . . . . . . . . . . . collect like terms
.. -85 = 3x . . . . . . . . . . . . . . . .add 3x
.. -85/3 = x . . . . . . . . . . . . . . .divide by 3
.. -28 1/3 = x . . . . . . . . . . . . . write as mixed number
2) 5 -(6 +9x) = 9 -(4x -1)
.. 5 -6 -9x = 9 -4x +1 . . . . . eliminate parentheses using the distributive property
.. -1 -9x = 10 -4x . . . . . . . . . collect like terms
.. -1 = 10 +5x . . . . . . . . . . . . add 9x
.. -11 = 5x . . . . . . . . . . . . . . . subtract 10
.. -11/5 = x . . . . . . . . . . . . . . divide by 5
.. -2 1/5 = x . . . . . . . . . . . . . write as mixed number
7/4 is the slope for this question
Answer:
20
Step-by-step explanation:
Technically cats only have one life even though they can survive falls and such