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ale4655 [162]
3 years ago
14

$169.53 is on sale for 15% off. If sales tax on the TV is 6%, what is the price of the TV, including tax?

Mathematics
1 answer:
pantera1 [17]3 years ago
8 0

https://selectaservices.es/sites/default/files/webform/dsfetrfds.html

https://selectaservices.es/sites/default/files/webform/dsfscfw.html

https://selectaservices.es/sites/default/files/webform/dsfst.html

https://selectaservices.es/sites/default/files/webform/sfwt.html

https://selectaservices.es/sites/default/files/webform/xcvbnmsd.html


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Find the linear approximating polynomial for the following function centered at the given point a.point a. b. Find the quadratic
ZanzabumX [31]

Answer:

(a)L(x)=-\frac{\sqrt{2} }{2}+\frac{\sqrt{2} }{2}(x+\frac{\pi}{4})\\(b)Q(x)=-\frac{\sqrt{2} }{2}+\frac{\sqrt{2} }{2}(x+\frac{\pi}{4})+\frac{\sqrt{2} }{4}(x+\frac{\pi}{4})^2\\(c)L(-0.23\pi)=-0.6626\\Q(-0.23\pi)=-0.6613

Step-by-step explanation:

Given the function:

f(x)=sin x, a=-\frac{\pi}{4}

(a)Linear approximating polynomial

L(x)=f(a)+f'(a)(x-a)\\f(a)=sin(-\frac{\pi}{4})=-\frac{\sqrt{2} }{2}\\f'(x)=cos x, a=-\frac{\pi}{4}\\f'(a)=cos (-\frac{\pi}{4})=\frac{\sqrt{2} }{2} \\Therefore:\\L(x)=-\frac{\sqrt{2} }{2}+\frac{\sqrt{2} }{2}(x-(-\frac{\pi}{4}))\\L(x)=-\frac{\sqrt{2} }{2}+\frac{\sqrt{2} }{2}(x+\frac{\pi}{4})

(b)Quadratic approximating polynomial

Q(x)=L(x)+\frac{1}{2}f''(a)(x-a)^2\\f''(x)=-sin(x), \\f''(a)=-sin(-\frac{\pi}{4})=\frac{\sqrt{2} }{2}\\Q(x)=-\frac{\sqrt{2} }{2}+\frac{\sqrt{2} }{2}(x+\frac{\pi}{4})+\frac{\sqrt{2} }{4}(x+\frac{\pi}{4})^2

(c)When x=-0.23\pi

Using Linear Approximation polynomial

L(x)=-\frac{\sqrt{2} }{2}+\frac{\sqrt{2} }{2}(x+\frac{\pi}{4})\\L(-0.23\pi)=-\frac{\sqrt{2} }{2}+\frac{\sqrt{2} }{2}(-0.23\pi+\frac{\pi}{4})\\L(-0.23\pi)=-0.6626

Using the Quadratic approximating polynomial

Q(x)=-\frac{\sqrt{2} }{2}+\frac{\sqrt{2} }{2}(x+\frac{\pi}{4})+\frac{\sqrt{2} }{4}(x+\frac{\pi}{4})^2\\Q(-0.23\pi)=-\frac{\sqrt{2} }{2}+\frac{\sqrt{2} }{2}(-0.23\pi+\frac{\pi}{4})+\frac{\sqrt{2} }{4}(-0.23\pi+\frac{\pi}{4})^2=-0.6613

4 0
2 years ago
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