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polet [3.4K]
3 years ago
5

Use Newton's method with initial approximation x1 = 1 to find x2, the second approximation to the root of the equation x4 − x −

3 = 0. (Round your answer to four decimal places.) x2 =?
Mathematics
1 answer:
drek231 [11]3 years ago
8 0

Answer:

x_{2} = 0.0000

Step-by-step explanation:

The formula for the Newton's method is:

x_{i+1} = x_{i} + \frac{f(x_{i})}{f'(x_{i})}

Where f' (x_{i}) is the first derivative of the function evaluated in x_{i}.

x_{i+1} = x_{i} + \frac{x_{i}^{4}-x_{i}-3}{4\cdot x_{i}^{3}-1}

Lastly, the value of x_{2} is determined by replacing x_{1} with its numerical value:

x_{2} = x_{1} + \frac{x_{1}^{4}-x_{1}-3}{4\cdot x_{1}^{3}-1}

x_{2} = 1.0000 + \frac{1.0000^{4}-1.0000-3}{4\cdot (1.0000)^{3}-1}

x_{2} = 0.0000

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Use the compound interest formulas A=P e^rt to solve the problem given. round answers to the nearest cent.
goblinko [34]

Answer:

a) $20,771.76

b) $20,817.67

c) $20,484.80

d) $20,864.52

Step-by-step explanation:

<u>Compound Interest Formula</u>

\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}

where:

  • A = final amount
  • P = principal amount
  • r = interest rate (in decimal form)
  • n = number of times interest applied per time period
  • t = number of time periods elapsed

<u>Part (a): semiannually</u>

Given:

  • P = $15,000
  • r = 5.5% = 0.055
  • n = 2
  • t = 6 years

Substitute the given values into the formula and solve for A:

\implies \sf A=15000\left(1+\frac{0.055}{2}\right)^{2 \times 6}

\implies \sf A=15000\left(1.0275}{2}\right)^{12}

\implies \sf A=20771.76

<u>Part (b): quarterly</u>

Given:

  • P = $15,000
  • r = 5.5% = 0.055
  • n = 4
  • t = 6 years

Substitute the given values into the formula and solve for A:

\implies \sf A=15000\left(1+\frac{0.055}{4}\right)^{4 \times 6}

\implies \sf A=15000\left(1.01375}\right)^{24}

\implies \sf A=20817.67

<u>Part (c): monthly</u>

Given:

  • P = $15,000
  • r = 5.5% = 0.055
  • n = 12
  • t = 6 years

Substitute the given values into the formula and solve for A:

\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{12 \times 6}

\implies \sf A=15000\left(1+\frac{0.055}{12}\right)^{72}

\implies \sf A=20484.80

<u>Continuous Compounding Formula</u>

\large \text{$ \sf A=Pe^{rt} $}

where:

  • A = Final amount
  • P = Principal amount
  • e = Euler's number (constant)
  • r = annual interest rate (in decimal form)
  • t = time (in years)

<u>Part (d): continuous</u>

Given:

  • P = $15,000
  • r = 5.5% = 0.055
  • t = 6 years

Substitute the given values into the formula and solve for A:

\implies \sf A=15000e^{0.055 \times 6}

\implies \sf A=20864.52

Learn more about compound interest here:

brainly.com/question/27747709

brainly.com/question/28004698

4 0
2 years ago
Factor completely <img src="https://tex.z-dn.net/?f=3x%5E3-3x%5E2-18x" id="TexFormula1" title="3x^3-3x^2-18x" alt="3x^3-3x^2-18x
Sever21 [200]

Answer:

The answer is 3x(x - 3)(x + 2)

Step-by-step explanation:

3x³ - 3x² - 18x

<u>Factor out 3x from the expression</u>

We have

3x ( x² - x - 6)

<u>Solve</u><u> the terms in the bracket</u>

We have

3x ( x² + 2x - 3x - 6)

<u>Factor out x the expression in the bracket</u>

We have

3x ( x ( x + 2) - 3( x + 2) )

<u>Factor out x + 2 from the expression in the bracket</u>

We have the final answer as

<h3>3x ( x - 3) (x + 2)</h3>

Hope this helps you.

5 0
3 years ago
Please help me with number 9-10
Finger [1]
(10). 423,,,,,,,,,,4.10=40.. Hopefully that's help u
7 0
3 years ago
18n squared + 57n -10
aniked [119]
Most people use the decomposition method but i dont know how to do that so i use the Joes method a method similar to decomp. but easier.
canadian way

Find gcf: None
complet trinomial: 18n^2+57-10
find the product=10(18)
                       =-180
find the sum     =57
-3 and 60 goes into both meaning if you multiply 3 and60 you get -180 and if you add them you get 57.

so (n-3)(n+60)
divide by a in this case it 18
so (n<u>-3</u>)(n+<u>60</u>)
       18     18
do not divide. treat it like a fraction so you reduce it to lowest terms
(n<u>-3</u>)(n<u>-3)
</u>   18   10
<u /> at this point its reduced to lowest terms so now you take the deniminator and move it beside the "n"

=(18n-3)(10n-3)

therefore your answer is (18n-3)(10n-3)
I hoped this helped :)
3 0
4 years ago
4/7w = 16 hurry please
Novay_Z [31]

Answer:

4

7

w

=

16

Multiply both sides of the equation by

7

4

.

7

4

⋅

4

7

⋅

w

=

7

4

⋅

16

Simplify  

7

4

⋅

4

7

⋅

w

.

Step-by-step explanation:

5 0
3 years ago
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