All categories

2 years ago

PLEASE HELP!

Mathematics

1 answer:

emmainna [20.7K]2 years ago

5 0

Use the given recursion and starting value of $x_0 = 2.4$ to find $x_1$ :

$x_1 = \dfrac{x_0 + \frac6{x_0}}2 = \dfrac{2.4 + \frac{6}{2.4}}2 = 2.45$

Do the same for $x_2$ and $x_3$ :

$x_2 = \dfrac{x_1 + \frac6{x_1}}2 = \dfrac{2.45 + \frac6{2.45}}2 \approx 2.44949$

$x_3 = \dfrac{x_2+\frac6{x_2}}2 \approx \dfrac{2.44949 + \frac6{2.44949}}2 \approx \boxed{2.44949}$

(That's not a mistake. This just tells you that the 2nd and 3rd iterates are very close together and have at least the same first 5 digits after the decimal.)

You might be interested in

Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added toge

WARRIOR [948]

You can use the fact that when coefficient of x variable are of equal magnitude but opposite sign, then adding them will make the coefficient 0, thus, making the x variable eliminated.

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is given by

Option A: –10 times the first equation and 3 times the second equation

<h3>How does elimination works?</h3>

This method is actually called method of elimination to solve a system of linear equations.

We make one specific variable's coefficients of equal magnitude so that we can subtract or add the equations and eliminate that variable to make it easy to get the value of the other variable which will then help in getting the value of the first variable (if working in dual variable system).

If we have equations:

$a_1x + b_1y = c_1\\a_2x + b_2y = c_2$

then, if we want to eliminate variable x, then we have to multiply equation 1 with

$- \dfrac{a_2}{a_1}$

which will make coefficient of x in first equation as

$a_1 \times - \dfrac{a_2}{a_1} = -a_1$

Then adding both equation will eliminate the variable x.

We could've skipped that -ve sign and at then end, instead of adding, we could've subtracted the equations.

<h3>What is magnitude and sign?</h3>

5 has 5 as magnitude, and sign isn't present which means its of positive (+) sign.

-5 has 5 as magnitude and sign is negative(-).

For this case, we're multiplying both the equations but the core concept or aim is same, ie, making the coefficients of equal magnitude but with opposite sign.

<h3>Using the above facts to get the numbers to multiply the equations of the given system</h3>

The given system of equations is

$\dfrac{1}{5}x + \dfrac{3}{4}y = 9\\\\\dfrac{2}{3}x - \dfrac{5}{6}y = 8$

Let two numbers be p,and q who multiply equation first and second respectively to make coefficient of x of equal magnitude but opposite sign.

We have

$\text{Coefficient of x in first equation}= a_1 = \dfrac{1}{5}\\\\\text{Coefficient of x in second equation} = a_2 = \dfrac{2}{3}$

Multiplying with p and q will give us

$p\times a_1 = \dfrac{p}{5}\\\\q \times a_2 = \dfrac{2q}{3}$

We need both resultant coefficient to add up to 0, or

$p/5 + 2q/3 = 0\\p = -10q/3\\q = -3p/10$

Now in options, we see first equation is either getting multiplied with -10, 10, or -3,3

If we put q = 3, we get p = -10q/3= -10

If we put q = -3, we get p = 10

If we put q = 5, we get p = -50/3

Thus only first choice is matching the correct pairs.

Thus,

The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is given by

Option A: –10 times the first equation and 3 times the second equation

Learn more about method of elimination here:

brainly.com/question/20385690

7 0

2 years ago

Read 2 more answers

Find the quotient of 85 & .25

KatRina [158]

42.5, just need to multiply

6 0

3 years ago

Luke's Auto Wash earned $10 from servicing 2 customers. How many

laiz [17]

5 more because 10 divided by 2 is 5 and when u add 5 by 5 you get 10 and when you also add another 5 you get 15 so yeah

4 0

2 years ago

Spencer wants to burn 450 calories while biking. Biking burns about 10 calories per minute. When Spencer goes biking, he usually

Lady bird [3.3K]

Answer:

60 minutes including the 15 minute rest.

Step-by-step explanation:

450/10 is 45. Therefore, biking for 45 minutes will loose 450 calories, 10 calories per minute. Maybe half way during the 45 minutes Spencer will take the 15 minute rest. This brings the biking trip 60 minutes.

8 0

3 years ago

2. Consider the function, f(x)=x^3+x^2-9x-9

Sedaia [141]

The intercepts of the graph are:

x-axis interception: $\left(-1,\:0\right),\:\left(-3,\:0\right),\:\left(3,\:0\right)$ .

y-axis interception: $\left(0,\:-9\right)$ .

See the graph of the function $f(x)=x^3+x^2-9x-9$ in the attached image.

<h3>Constructing a graph</h3>

For constructing a graph we have the following steps:

Determine the range of values for x of your graph.

For this exercise, for example, we can define a range -4<x<4. In others words, the values of x will be in this interval.

Determine the points

Replace these x-values in the given equation. For example:

When x=-4, we will have: $\left(-4\right)^3+\left(-4\right)^2-9\left(-4\right)-9=-21$ . Do this for the all x-values of your ranges.

See the results for this step in the attached table.

Draw the graph

Mark the points <u>x</u> and<u> y</u> that you found in the last step. After that, connect the dots to draw the graph.

The attached image shows the graph for the given function.

<h3>Find the x- and y-intercepts</h3>

The intercepts are points that crosses the axes of your plot. From your graph is possible to see:

x-axis interception points (y=f(x)=0) are: $\left(-1,\:0\right),\:\left(-3,\:0\right),\:\left(3,\:0\right)$ .

y-axis interception point (x=0) is: $\left(0,\:-9\right)$ .

Learn more about intercepts of the graph here:

brainly.com/question/4504979

5 0

2 years ago