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DochEvi [55]
2 years ago
11

A boutique prices merchandise by adding 80% to its cost. It later decreases by 25% the price of items that do not sell quickly

Mathematics
1 answer:
Darya [45]2 years ago
8 0
A. Write a function f(x) to represent the price after the 80% markup. 
<span>b. Write a function g(x) to represent the price after the 25% markdown. </span>
<span>c. Use a composition function to find the price of an item after both price adjustments that originally costs the boutique $150. </span>
<span>d. Does the order in which the adjustments are applied make a difference? Explain. 
</span>
answers 

 <span>a) f(x) = 1.8x 

b) f(x) = 0.75(1.8x) 

c) f(150) = 0.75(1.8(150) = $202.50 

d) No, it doesn't matter. The result is the same.
</span>
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How do you solve ? <br>2(x−(3+2x)+9)=3x−8
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Hey there!!

Given equation :

... 2 ( x - ( 3 + 2x ) + 9 ) = 3x - 8

Using the distributive property.

... 2 ( x - 3 - 2x + 9 ) = 3x - 8

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Find the nth taylor polynomial for the function, centered at c. f(x) = ln(x), n = 4, c = 5
masha68 [24]

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Given:

f(x) = ln(x)

n = 4

c = 3

nth Taylor polynomial for the function, centered at c

The Taylor series for f(x) = ln x centered at 5 is:

P_{n}(x)=f(c)+\frac{f^{'} (c)}{1!}(x-c)+  \frac{f^{''} (c)}{2!}(x-c)^{2} +\frac{f^{'''} (c)}{3!}(x-c)^{3}+.....+\frac{f^{n} (c)}{n!}(x-c)^{n}

Since, c = 5 so,

P_{4}(x)=f(5)+\frac{f^{'} (5)}{1!}(x-5)+  \frac{f^{''} (5)}{2!}(x-5)^{2} +\frac{f^{'''} (5)}{3!}(x-5)^{3}+.....+\frac{f^{n} (5)}{n!}(x-5)^{n}

Now

f(5) = ln 5

f'(x) = 1/x ⇒ f'(5) = 1/5

f''(x) = -1/x² ⇒ f''(5) = -1/5² = -1/25

f'''(x) = 2/x³  ⇒ f'''(5) = 2/5³ = 2/125

f''''(x) = -6/x⁴ ⇒ f (5) = -6/5⁴ = -6/625

So Taylor polynomial for n = 4 is:

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Hence,

The nth taylor polynomial for the given function is

P₄(x) = ln5 + 1/5 (x-5) - 1/25*2! (x-5)² + 2/125*3! (x-5)³ - 6/625*4! (x - 5)⁴

Find out more information about nth taylor polynomial here

brainly.com/question/28196765

#SPJ4

3 0
1 year ago
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