Answer:
Step-by-step explanation:
A butterfly has 1 line of symmetry
Answer:
(a)![L(x)=48x-64](https://tex.z-dn.net/?f=L%28x%29%3D48x-64)
(b)![P_{2}(x)=48x-64+3(x-4)^{2}](https://tex.z-dn.net/?f=P_%7B2%7D%28x%29%3D48x-64%2B3%28x-4%29%5E%7B2%7D)
(c)Using Linear Approximation,L(4.2)=137.6
Using Quadratic Approximation,![P_{2}(4.2)=137.72](https://tex.z-dn.net/?f=P_%7B2%7D%284.2%29%3D137.72)
Step-by-step explanation:
Given: ![f(x) = 16x^{3/2}, a = 4](https://tex.z-dn.net/?f=f%28x%29%20%3D%2016x%5E%7B3%2F2%7D%2C%20%20a%20%3D%204)
(a)Linear Approximation, ![L(x)=f(a)+f'(a)(x-a)](https://tex.z-dn.net/?f=L%28x%29%3Df%28a%29%2Bf%27%28a%29%28x-a%29)
![f(4) = 16*4^{3/2}=128](https://tex.z-dn.net/?f=f%284%29%20%3D%2016%2A4%5E%7B3%2F2%7D%3D128)
![f'(x) = 24\sqrt{x}](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%2024%5Csqrt%7Bx%7D)
![f'(4) = 24\sqrt{4}=24*2=48](https://tex.z-dn.net/?f=f%27%284%29%20%3D%2024%5Csqrt%7B4%7D%3D24%2A2%3D48)
![L(x)=128+48(x-4)](https://tex.z-dn.net/?f=L%28x%29%3D128%2B48%28x-4%29)
![L(x)=128+48x-192\\L(x)=48x-64](https://tex.z-dn.net/?f=L%28x%29%3D128%2B48x-192%5C%5CL%28x%29%3D48x-64)
(b)Quadratic Approximation, ![P_{2}(x)=f(a)+f'(a)(x-a)+\frac{1}{2}f''(a)(x-a)^{2}](https://tex.z-dn.net/?f=P_%7B2%7D%28x%29%3Df%28a%29%2Bf%27%28a%29%28x-a%29%2B%5Cfrac%7B1%7D%7B2%7Df%27%27%28a%29%28x-a%29%5E%7B2%7D)
![f''(x)=12x^{-1/2}\\f''(4)=12*4^{-1/2}=6](https://tex.z-dn.net/?f=f%27%27%28x%29%3D12x%5E%7B-1%2F2%7D%5C%5Cf%27%27%284%29%3D12%2A4%5E%7B-1%2F2%7D%3D6)
![P_{2}(x)=48x-64+3(x-4)^{2}](https://tex.z-dn.net/?f=P_%7B2%7D%28x%29%3D48x-64%2B3%28x-4%29%5E%7B2%7D)
(c)To approximate:
L(x)=48x-64
L(4.2)=48(4.2)-64=137.6
Also, Using Quadratic Approximation
![P_{2}(x)=48x-64+3(x-4)^{2}\\P_{2}(4.2)=48(4.2)-64+3(4.2-4)^{2}=137.72](https://tex.z-dn.net/?f=P_%7B2%7D%28x%29%3D48x-64%2B3%28x-4%29%5E%7B2%7D%5C%5CP_%7B2%7D%284.2%29%3D48%284.2%29-64%2B3%284.2-4%29%5E%7B2%7D%3D137.72)
The part of the cake he pit on each plate is 2/12 or 1/6
Answer:
The Federal government relies the most on income tax.
Step-by-step explanation: