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Leto [7]
3 years ago
9

Use Newton's method to find all solutions of the equation correct to six decimal places. (Enter your answers as a comma-separate

d list.) ln(x) = 1 /x − 3

Mathematics
1 answer:
Nata [24]3 years ago
7 0

Answer:

  x ≈ {0.653059729092, 3.75570086464}

Step-by-step explanation:

A graphing calculator can tell you the roots of ...

  f(x) = ln(x) -1/(x -3)

are near 0.653 and 3.756. These values are sufficiently close that Newton's method iteration can find solutions to full calculator precision in a few iterations.

In the attachment, we use g(x) as the iteration function. Since its value is shown even as its argument is being typed, we can start typing with the graphical solution value, then simply copy the digits of the iterated value as they appear. After about 6 or 8 input digits, the output stops changing, so that is our solution.

Rounded to 6 decimal places, the solutions are {0.653060, 3.755701}.

_____

A similar method can be used on a calculator such as the TI-84. One function can be defined a.s f(x) is above. Another can be defined as g(x) is in the attachment, by making use of the calculator's derivative function. After the first g(0.653) value is found, for example, remaining iterations can be g(Ans) until the result stops changing,

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8 trips

Step-by-step explanation:

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3 years ago
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Of the Students that attended Roosevelt Elementary 6/8 of the school play a sport. Of the students are playing a sport 3/5 of th
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Answer:

\frac{9}{20} students.

Step-by-step explanation:

We have been given that of the students that attended Roosevelt Elementary 6/8 of the school play a sport. Of the students are playing a sport 3/5 of the students are also involved in the drama club.

To find the students are both play a sport and a part of the drama club, we need to find 3/5 part of 6/8 as:

\text{Students who play a sport and a part of the drama club}=\frac{6}{8}\times \frac{3}{5}

\text{Students who play a sport and a part of the drama club}=\frac{3}{4}\times \frac{3}{5}

\text{Students who play a sport and a part of the drama club}=\frac{3\times 3}{4\times 5}

\text{Students who play a sport and a part of the drama club}=\frac{9}{20}

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If the length of a leg of a triangle is 39.2 and the area of the triangle is 63 what is the length of the other leg
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Answer:

The length of the other leg is 3.21\ units

Step-by-step explanation:

I will assume that the triangle is a right triangle

In a right triangle the legs are perpendicular

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In this problem we have

a=39.2\ units

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substitute the values

63=\frac{1}{2}(39.2)(b)

126=(39.2)(b)

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3 years ago
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