The correct answer is B.30 inches
Answer:
Option a.
![\lim_{x \to \frac{\pi}{2}}(3e)^{xcosx}=1](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%283e%29%5E%7Bxcosx%7D%3D1)
Step-by-step explanation:
You have the following limit:
![\lim_{x \to \frac{\pi}{2}{(3e)^{xcosx}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7B%283e%29%5E%7Bxcosx%7D)
The method of direct substitution consists of substituting the value of
in the function and simplifying the expression obtained.
We then use this method to solve the limit by doing ![x=\frac{\pi}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B%5Cpi%7D%7B2%7D)
Therefore:
![\lim_{x \to \frac{\pi}{2}}{(3e)^{xcosx} = \lim_{x\to \frac{\pi}{2}}{(3e)^{\frac{\pi}{2}cos(\frac{\pi}{2})}](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%7B%283e%29%5E%7Bxcosx%7D%20%3D%20%5Clim_%7Bx%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%7B%283e%29%5E%7B%5Cfrac%7B%5Cpi%7D%7B2%7Dcos%28%5Cfrac%7B%5Cpi%7D%7B2%7D%29%7D)
![cos(\frac{\pi}{2})=0\\](https://tex.z-dn.net/?f=cos%28%5Cfrac%7B%5Cpi%7D%7B2%7D%29%3D0%5C%5C)
By definition, any number raised to exponent 0 is equal to 1
So
![\lim_{x\to \frac{\pi}{2}}{(3e)^{\frac{\pi}{2}cos(\frac{\pi}{2})} = \lim_{x\to \frac{\pi}{2}}{(3e)^{\frac{\pi}{2}(0)}\\\\](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%7B%283e%29%5E%7B%5Cfrac%7B%5Cpi%7D%7B2%7Dcos%28%5Cfrac%7B%5Cpi%7D%7B2%7D%29%7D%20%3D%20%5Clim_%7Bx%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%7B%283e%29%5E%7B%5Cfrac%7B%5Cpi%7D%7B2%7D%280%29%7D%5C%5C%5C%5C)
![\lim_{x\to \frac{\pi}{2}}{(3e)^{0}} = 1](https://tex.z-dn.net/?f=%5Clim_%7Bx%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%7B%283e%29%5E%7B0%7D%7D%20%3D%201)
Finally
![\lim_{x \to \frac{\pi}{2}}(3e)^{xcosx}=1](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5Cfrac%7B%5Cpi%7D%7B2%7D%7D%283e%29%5E%7Bxcosx%7D%3D1)
If two similar triangles have sides in the ratio a : b, then their areas are in the ratio a² : b².
We have the ratio:
![54:18=\dfrac{54}{18}=3:1](https://tex.z-dn.net/?f=54%3A18%3D%5Cdfrac%7B54%7D%7B18%7D%3D3%3A1)
Area of the smaler triangle = x
Area of the larger triangle = 567 cm²
Therefore we have the equation:
![567:x=3^2:1^2\\\\\dfrac{567}{x}=\dfrac{9}{1}\qquad|\text{cross multiply}\\\\9x=567\qquad|\text{divide both sides by 9}\\\\x=63](https://tex.z-dn.net/?f=567%3Ax%3D3%5E2%3A1%5E2%5C%5C%5C%5C%5Cdfrac%7B567%7D%7Bx%7D%3D%5Cdfrac%7B9%7D%7B1%7D%5Cqquad%7C%5Ctext%7Bcross%20multiply%7D%5C%5C%5C%5C9x%3D567%5Cqquad%7C%5Ctext%7Bdivide%20both%20sides%20by%209%7D%5C%5C%5C%5Cx%3D63)
<h3>Answer: C. 63 cm²</h3>
C. $360
$224x4=896 (total profit)
$896 (total) - $536 (first month profit) = $360 (second month profit)