Answer:
A. 450
Step-by-step explanation:
180 is 40% of the original
450*0.4=180
298*0.4=119.2
240*0.4=96
72*0.4=28.8
so A. 450 is correct
Answer:
i got 45
Step-by-step explanation:
Answer:
Step-by-step explanation:
Limit refers to the value that the function approaches as the input approaches some value.
We say
, if f(x) approaches L as x approaches 'a'.
(a)
![\displaystyle \lim_{x\rightarrow 5}\left ( \frac{f(x)-8}{x-5} \right )=4\\\frac{\displaystyle \lim_{x\rightarrow 5}f(x)-\displaystyle \lim_{x\rightarrow 5}8}{\displaystyle \lim_{x\rightarrow 5}x-\displaystyle \lim_{x\rightarrow 5}5}=4\\](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7D%5Cleft%20%28%20%5Cfrac%7Bf%28x%29-8%7D%7Bx-5%7D%20%5Cright%20%29%3D4%5C%5C%5Cfrac%7B%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29-%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7D8%7D%7B%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Dx-%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7D5%7D%3D4%5C%5C)
![\frac{\displaystyle \lim_{x\rightarrow 5}f(x)-8}{\displaystyle \lim_{x\rightarrow 5}x-5}=4\\\displaystyle \lim_{x\rightarrow 5}f(x)-8=4\left ( \displaystyle \lim_{x\rightarrow 5}x-5 \right )\\\displaystyle \lim_{x\rightarrow 5}f(x)-8=4\displaystyle \lim_{x\rightarrow 5}x-4(5)\\\displaystyle \lim_{x\rightarrow 5}f(x)-8=4(5)-4(5)\\](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29-8%7D%7B%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Dx-5%7D%3D4%5C%5C%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29-8%3D4%5Cleft%20%28%20%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Dx-5%20%5Cright%20%29%5C%5C%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29-8%3D4%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Dx-4%285%29%5C%5C%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29-8%3D4%285%29-4%285%29%5C%5C)
![\displaystyle \lim_{x\rightarrow 5}f(x)-8=20-20=0\\\displaystyle \lim_{x\rightarrow 5}f(x)=8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29-8%3D20-20%3D0%5C%5C%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29%3D8)
(b)
![\displaystyle \lim_{x\rightarrow 5}\left ( \frac{f(x)-8}{x-5} \right )=7\\\frac{\displaystyle \lim_{x\rightarrow 5}f(x)-\displaystyle \lim_{x\rightarrow 5}8}{\displaystyle \lim_{x\rightarrow 5}x-\displaystyle \lim_{x\rightarrow 5}5}=7\\\frac{\displaystyle \lim_{x\rightarrow 5}f(x)-8}{\displaystyle \lim_{x\rightarrow 5}x-5}=7\\](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7D%5Cleft%20%28%20%5Cfrac%7Bf%28x%29-8%7D%7Bx-5%7D%20%5Cright%20%29%3D7%5C%5C%5Cfrac%7B%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29-%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7D8%7D%7B%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Dx-%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7D5%7D%3D7%5C%5C%5Cfrac%7B%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29-8%7D%7B%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Dx-5%7D%3D7%5C%5C)
![\displaystyle \lim_{x\rightarrow 5}f(x)-8=7\left ( \displaystyle \lim_{x\rightarrow 5}x-5 \right )\\\displaystyle \lim_{x\rightarrow 5}f(x)-8=7\displaystyle \lim_{x\rightarrow 5}x-7(5)\\\displaystyle \lim_{x\rightarrow 5}f(x)-8=7(5)-7(5)\\\displaystyle \lim_{x\rightarrow 5}f(x)-8=35-35=0\\\displaystyle \lim_{x\rightarrow 5}f(x)=8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29-8%3D7%5Cleft%20%28%20%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Dx-5%20%5Cright%20%29%5C%5C%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29-8%3D7%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Dx-7%285%29%5C%5C%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29-8%3D7%285%29-7%285%29%5C%5C%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29-8%3D35-35%3D0%5C%5C%5Cdisplaystyle%20%5Clim_%7Bx%5Crightarrow%205%7Df%28x%29%3D8)
Area of shaded region = Area of larger circle - Area of smaller circle.
We know, Area of a Circle = πr²
So, A = πr₁² - πr₂²
A = π (r₁² - r₂²)
A = π(10.2² - 5.4²)
A = 3.14 (104.04 - 29.16)
A = 3.14 (74.88)
A = 235.12
In short, Your Answer would be 235.12 cm²
Hope this helps!