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Tresset [83]
3 years ago
8

How do I do question 10 PLEASE HELP ASAP THANKS

Mathematics
1 answer:
sashaice [31]3 years ago
5 0

Answer:

hope this helps you

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1. Approximate the given quantity using a Taylor polynomial with n3.
Jet001 [13]

Answer:

See the explanation for the answer.

Step-by-step explanation:

Given function:

f(x) = x^{1/4}

The n-th order Taylor polynomial for function f with its center at a is:

p_{n}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(n)}a}{n!} (x-a)^{n}

As n = 3  So,

p_{3}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(3)}a}{3!} (x-a)^{3}

p_{3}(x) = f(a) + f'(a) (x-a)+\frac{f''(a)}{2!} (x-a)^{2} +...+\frac{f^{(3)}a}{6} (x-a)^{3}

p_{3}(x) = a^{1/4} + \frac{1}{4a^{ 3/4} }  (x-a)+ (\frac{1}{2})(-\frac{3}{16a^{7/4} } ) (x-a)^{2} +  (\frac{1}{6})(\frac{21}{64a^{11/4} } ) (x-a)^{3}

p_{3}(x) = 81^{1/4} + \frac{1}{4(81)^{ 3/4} }  (x-81)+ (\frac{1}{2})(-\frac{3}{16(81)^{7/4} } ) (x-81)^{2} +  (\frac{1}{6})(\frac{21}{64(81)^{11/4} } ) (x-81)^{3}

p_{3} (x) = 3 + 0.0092592593 (x - 81) + 1/2 ( - 0.000085733882) (x - 81)² + 1/6  

                                                                                  (0.0000018522752) (x-81)³

p_{3} (x)  =  0.0092592593 x - 0.000042866941 (x - 81)² + 0.00000030871254

                                                                                                       (x-81)³ + 2.25

Hence approximation at given quantity i.e.

x = 94

Putting x = 94

p_{3} (94)  =  0.0092592593 (94) - 0.000042866941 (94 - 81)² +          

                                                                 0.00000030871254 (94-81)³ + 2.25

         = 0.87037 03742 - 0.000042866941 (13)² + 0.00000030871254(13)³ +    

                                                                                                                       2.25

         = 0.87037 03742 - 0.000042866941 (169) +  

                                                                      0.00000030871254(2197) + 2.25

         = 0.87037 03742 - 0.007244513029 + 0.0006782414503 + 2.25

p_{3} (94)  = 3.113804102621

Compute the absolute error in the approximation assuming the exact value is given by a calculator.

Compute \sqrt[4]{94} as 94^{1/4} using calculator

Exact value:

E_{a}(94) = 3.113737258478

Compute absolute error:

Err = | 3.113804102621 - 3.113737258478 |

Err (94)  = 0.000066844143

If you round off the values then you get error as:

|3.11380 - 3.113737| = 0.000063

Err (94)  = 0.000063

If you round off the values up to 4 decimal places then you get error as:

|3.1138 - 3.1137| = 0.0001

Err (94)  = 0.0001

4 0
3 years ago
X-12=1-2x+5 what does x equal
notka56 [123]

X= - x/2+9 if that is what you are asking

or -2x+18

8 0
3 years ago
Read 2 more answers
stadium has 49,000 seats. Seats sell for ​$42 in Section​ A, ​$36 in Section​ B, and ​$30 in Section C. The number of seats in S
REY [17]
Congrats on getting that far!

From here, simplify the equation by dividing each term by the greatest common factor: 6.

36B + 30C = 822600 becomes 6B + 5C = 137100

Now you have stackable simultaneous equations that you can easily work with:

6B + 5C = 137100

B + C = 24500

Multiply the terms in the second equation by either 6 or 5 so that you can subtract the second equation from the first equation and cancel out the B or C, respectively.

Example:

6B + 5C = 137100

minus 5B + 5C = 122500

equals B = 14600

Then plug your answer into the B + C = 24500 equation to find C.

Finally plug B and C into the A + C + B = 49000 equation to get A.
5 0
3 years ago
HELP ME PLEASE !!!!!!!!!!!
Scrat [10]
The angle that you need to choose is 2 I think
4 0
3 years ago
What is the approximate area of the part of the square that is not shaded?
bezimeni [28]
The answer is approximately 69.53.

7 0
3 years ago
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