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3 years ago

Help again :) :) will give brainlist :)

Mathematics

1 answer:

-BARSIC- [3]3 years ago

7 0

Answer:

-2.85 < -2.70 < -4 < 0 < 3.4

-2 3/4 < -2 1/6 < -2 1/4 < 3 < 3 1/5

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Use the Newton-Raphson method to find the root of the equation f(x) = In(3x) + 5x2, using an initial guess of x = 0.5 and a stop

xxMikexx [17]

Answer with explanation:

The equation which we have to solve by Newton-Raphson Method is,

f(x)=log (3 x) +5 x²

$f'(x)=\frac{1}{3x}+10 x$

Initial Guess =0.5

Formula to find Iteration by Newton-Raphson method

$x_{n+1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})}\\\\x_{1}=x_{0}-\frac{f(x_{0})}{f'(x_{0})}\\\\ x_{1}=0.5-\frac{\log(1.5)+1.25}{\frac{1}{1.5}+10 \times 0.5}\\\\x_{1}=0.5- \frac{0.1760+1.25}{0.67+5}\\\\x_{1}=0.5-\frac{1.426}{5.67}\\\\x_{1}=0.5-0.25149\\\\x_{1}=0.248$

$x_{2}=0.248-\frac{\log(0.744)+0.30752}{\frac{1}{0.744}+10 \times 0.248}\\\\x_{2}=0.248- \frac{-0.128+0.30752}{1.35+2.48}\\\\x_{2}=0.248-\frac{0.17952}{3.83}\\\\x_{2}=0.248-0.0468\\\\x_{2}=0.2012$

$x_{3}=0.2012-\frac{\log(0.6036)+0.2024072}{\frac{1}{0.6036}+10 \times 0.2012}\\\\x_{3}=0.2012- \frac{-0.2192+0.2025}{1.6567+2.012}\\\\x_{3}=0.2012-\frac{-0.0167}{3.6687}\\\\x_{3}=0.2012+0.0045\\\\x_{3}=0.2057$

$x_{4}=0.2057-\frac{\log(0.6171)+0.21156}{\frac{1}{0.6171}+10 \times 0.2057}\\\\x_{4}=0.2057- \frac{-0.2096+0.21156}{1.6204+2.057}\\\\x_{4}=0.2057-\frac{0.0019}{3.6774}\\\\x_{4}=0.2057-0.0005\\\\x_{4}=0.2052$

So, root of the equation =0.205 (Approx)

Approximate relative error

$=\frac{\text{Actual value}}{\text{Given Value}}\\\\=\frac{0.205}{0.5}\\\\=0.41$

Approximate relative error in terms of Percentage

=0.41 × 100

= 41 %

7 0

3 years ago

15 plus the quotient of 60 and w

Romashka [77]

$15+60:w=15+\dfrac{60}{w}$

6 0

3 years ago

Read 2 more answers

Services provided by public service companies are also known as

sammy [17]

The answer is “housing expenses”

4 0

3 years ago

A circular pizza costs $19.99. What is the cost of 1 square centimetre if the diameter of the pizza is 36 cm?

butalik [34]

Answer:

$1.29

Step-by-step explanation:

=> (26÷20)-0.01

=> 1.3-0.01

=>1.29

1.29 $ is the answer

4 0

2 years ago

Robert collected 330 aluminum cans. If 100 aluminum cans weigh 4 pounds, and the recycling center is paying 25 cents a pound, ho

labwork [276]

First, determine the weight of 330 cans with the given conditions,
(330 cans) x (4 lbs / 100 cans) = 13.2 lbs
Then, the price is determined by multiplying this weight to the price that the recycling center is paying,
(13.2 lbs) x (25 cents / lb) = 330 cents = $3.3
Thus, Robert will be paid $3.3.

4 0

3 years ago