Answer:
8/5
Step-by-step explanation:
w = k / √x
4 = k / √4
k = 8
w = 8 / √x
w = 8 / √25
w = 8/5
what are the coordinates of point b on ac such that ab=2/5ac
Answer:
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
Step-by-step explanation:
Coordinates of points A and C are (-8, 6) and (2, 5).
If a point B intersects the segment AB in the ratio of 2 : 5
Then coordinates of the point B will be,
x = [tex]\frac{mx_2+nx_1}{m+n}[/tex]
and y = [tex]\frac{my_2+ny_1}{m+n}[/tex]
where [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.
For the coordinates of point B,
x = [tex]\frac{2\times 2+(-8)\times 5}{2+5}[/tex]
= [tex]-\frac{36}{7}[/tex]
y = [tex]\frac{2\times 5+5\times 6}{2+5}[/tex]
= [tex]\frac{40}{7}[/tex]
Therefore, coordinates of pint B will be,
[tex](-\frac{36}{7},\frac{40}{7})[/tex]
in the number 23.45 the digit 5 is in ?
Answer: hundredths place
Step-by-step explanation:
Simplify the expression . 39*x / 13
Answer:
3x
Step-by-step explanation:
39*x / 13
39/13 * x
3*x
3x
Answer:
3x
Step-by-step explanation:
We are given the expression:
39*x /13
We want to simplify this expression. It can be simplified because both the numerator (top number) and denominator (bottom number) can be evenly divided by 13.
(39*x /13) / (13/13)
(39x/13) / 1
3x / 1
When the denominator is 1, we can simply eliminate the denominator and leave the numerator as our answer.
3x
The expression 39*x/13 can be simplified to 3x
Shannon went to an auto repair shop and paid $339.50, which included parts that cost $112 and 3.5 hours of labor. Joni went to an auto repair shop and paid $455, which included parts that cost $310 and 2.5 hours of labor. Which correctly compares the cost of the labor? Shannon paid $7 more per hour for labor. Shannon paid $7 less per hour for labor. Joni paid $85 more per hour for labor. Joni paid $85 less per hour for labor.
for labor. Joni paid $85 less per hour for labor. explanation:
The correct comparison of the cost of labor between Shannon and Joni is that Shannon paid $7 more per hour for labor.
What is the cost?It refers to the total amount of the expenditure done on a product in manufacturing or procuring.
What is labor cost?It refers to the expenditure done on procuring labor for the work.
How to calculate per hour labor cost?In our situation Shannon paid total $339.50 in which the cost of the parts is $112 and 3.5 hours of labor. So,
labor cost Shannon Paid=339.50-112
=$227.50
labor cost per hour=227.50/3.5
=$6.5 per hour
Joni paid total $455 in which the cost of spare parts is $310 and rest is labor
labor cost paid by Joni=455-310
=$145
labor cost per hour=145/2.5
=$58 per hour
So by doing comparing we found that Shannon had paid $6 per hour extra for labor.
Learn more about cost at https://brainly.com/question/1153322
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find the coordinates of the vertices of the triangle after a reflection across the line y = -1 and then across the line x = -2
Answer: A) N'=(-2, 2) M'=(-1, 0) L'=(-5, -2)
Step-by-step explanation:
N = (-2, -4) M = (-3, -2) L = (1, 0)
Reflection over y = -1
N' = (-2, 2) M' = (-3, 0) L' = (1, -2)
Reflection over x = -2
N'' = (-2, 2) M'' = (-1, 0) L'' = (-5, -2)
help plsssssssssssss
Answer:
[tex]z = \frac{x}{y} [/tex]
Step-by-step explanation:
Let x be the price of carton of ice cream
Let y be the number of grams in carton
Let z be price per gram.
[tex]z = \frac{x}{y} [/tex]
Which means price of carton of ice cream divided by the number of grams in carton equals price per gram.
Hope this helps ;) ❤❤❤
What is the next term of the geometric sequence? 1, 2, 4, 8, 16,
Answer: 32
Step-by-step explanation:
The side length of the cube is s. Find the domain of the volume of the cube.
Answer:
-∞<x<∞
Step-by-step explanation:
volume of a cube=s^3
the domain is (-∞,∞) the domain is all the real number of s
What is the image of (-8, 10) when reflected in the y-axis?
Answer:
if you're just reflecting the point over the y-axis it just becomes (8,10)
Answer: (8, 10)
Explanation and Example:
I have a trick that I use. I'm not sure if it will make sense to you but I'll explain it. When the question asks you to reflect over the x-axis, then keep the x in (x,y) the same and just flip the sign for the y. If the question asks you to reflect over the y-axis, then keep y the same and flip the sign for x.
Reflect over x-axis:
(-2, 6) -----> (-2, -6)
Reflect over y-axis:
(-4, -8) -----> (4, -8)
The average weight of a person is 160.5 pounds with a standard deviation of 10.4 pounds. 1. What is the probability a person weighs more than 150.2 pounds
Answer:
0.8390
Step-by-step explanation:
From the question,
Z score = (Value-mean)/standard deviation
Z score = (150.2-160.5)/10.4
Z score = -0.9904.
P(x>Z) = 1- P(x<Z)
From the Z table,
P(x<Z) = 0.16099
Therefore,
P(x>Z) = 1-0.16099
P(x>Z) = 0.8390
Hence the probability that a person weighs more than 150.2 pounds = 0.8390
Which parent function is represented by the graph?
A. The quadratic parent function
B. The absolute value parent function
C. An exponential parent function
D. The linear parent function
Answer:
D. The linear parent function
Step-by-step explanation:
Linear functions are always characterized by a straight line graph with or without an intercept on the vertical or horizontal axis. A linear function usually has an independent variable and a dependent variable. The independent variable is commonly depicted as x while the dependent variable is y.
Thus a linear equation is an equation of the type y=ax where a is a constant term. The equation of a straight line graph his y=mx +c, where;
m= gradient of the straight line graph
x= the independent variable
y= the dependent variable
c= the vertical intercept
Answer:
The linear parent function :)
Step-by-step explanation:
A bag of marbles contains 4 green marbles, 3 blue marbles, 2 red marbles, and 5 yellow marbles. How many total possible outcomes are there when choosing a marble from the bag?
Answer:
its 14/C
Step-by-step explanation:
i got i right on edg U^U
Answer:
16
Step-by-step explanation:
i did edge test yea dont be imma fake :***
magazine provided results from a poll of adults who were asked to identify their favorite pie. Among the respondents, % chose chocolate pie, and the margin of error was given as percentage points. What values do , , n, E, and p represent? If the confidence level is %, what is the value of ?
Complete Question
A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 12 % chose chocolate pie, and the margin of error was given as plus or minus 5 percentage points.What values do [tex]\r p , \ \r q[/tex], n, E, and p represent? If the confidence level is 90%, what is the value of [tex]\alpha[/tex] ?
Answer:
a
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e [tex]\r q = 1- \r p[/tex]
b
[tex]\alpha = 10\%[/tex]
Step-by-step explanation:
Here
[tex]\r p[/tex] is the sample proportion [tex]\r p = 0.12[/tex]
[tex]n[/tex] is the sample size is [tex]n = 500[/tex]
[tex]\r q[/tex] represents the proportion of those that did not chose chocolate pie i.e
[tex]\r q = 1- \r p[/tex]
[tex]\r q = 1- 0.12[/tex]
[tex]\r q = 0.88[/tex]
[tex]E[/tex] is the margin of error is [tex]E = 0.05[/tex]
Generally [tex]\alpha[/tex] is the level of significance and it value is mathematically evaluated as
[tex]\alpha = ( 100 - C )\%[/tex]
Where [tex]C[/tex] is the confidence level which is given in this question as [tex]C = 90 \%[/tex]
So
[tex]\alpha = ( 100 - 90 )\%[/tex]
[tex]\alpha = 10\%[/tex]
Part A Each time you press F9 on your keyboard, you see an alternate life for Jacob, with his status for each age range shown as either alive or dead. If the dead were first to appear for the age range of 75 to 76, for example, this would mean that Jacob died between the ages of 75 and 76, or that he lived to be 75 years old. Press F9 on your keyboard five times and see how long Jacob lives in each of his alternate lives. How long did Jacob live each time? Part B The rest of the potential clients are similar to Jacob, but since they’ve already lived parts of their lives, their status will always be alive for the age ranges that they’ve already lived. For example, Carol is 44 years old, so no matter how many times you press F9 on your keyboard, Carol’s status will always be alive for all the age ranges up to 43–44. Starting with the age range of 44–45, however, there is the possibility that Carol’s status will be dead. Press F9 on your keyboard five more times and see how long Carol lives in each of her alternate lives. Remember that she will always live to be at least 44 years old, since she is already 44 years old. How long did Carol live each time? Part C Now you will find the percent survival of each of your eight clients to the end of his or her policy using the simulation in the spreadsheet. For each potential client, you will see whether he or she would be alive at the end of his or her policy. The cells in the spreadsheet that you should look at to determine this are highlighted in yellow. Next, go to the worksheet labeled Task 2b and record either alive or dead for the first trial. Once you do this, the All column will say yes if all the clients were alive at the end of their policies or no if all the clients were not alive at the end of their policies. Were all the clients alive at the end of their policies in the first trial? Part D Next, go back to the Task 2a worksheet, press F9, and repeat this process until you have recorded 20 trials in the Task 2b worksheet. In the Percent Survived row at the bottom of the table on the Task 2b worksheet, it will show the percentage of times each client survived to the end of his or her policy, and it will also show the percentage of times that all of the clients survived to the end of their respective policies. Check to see whether these percentages are in line with the probabilities that you calculated in questions 1 through 9 in Task 1. Now save your spreadsheet and submit it to your teacher using the drop box. Are your probabilities from the simulation close to the probabilities you originally calculated?
Step-by-step explanation:
brain list me please......
Answer:
Jacob:
Alive 69-70
alive 79-80
alive 62-63
alive 73-74
alive 78-Died 79
Carol:
alive 88-89
alive 67-68
alive 99-100
alive 73-74
alive 94- Died 95
Step-by-step explanation:
This afternoon, Vivek noticed that the temperature was above zero when the temperature was 17 5/8 degrees. Its evening now, and the temperature is -8 1/2 degrees. What does this mean?
Answer:
The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.
Step-by-step explanation:
Convert to a mixed number:
209/8
Divide 209 by 8:
8 | 2 | 0 | 9
8 goes into 20 at most 2 times:
| | 2 | |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
8 goes into 49 at most 6 times:
| | 2 | 6 |
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 |
Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:
| | 2 | 6 | (quotient)
8 | 2 | 0 | 9 |
- | 1 | 6 | |
| | 4 | 9 |
| - | 4 | 8 |
| | | 1 | (remainder)
The quotient of 209/8 is 26 with remainder 1, so:
Answer: 26 1/8° C
According to the histogram below, how many people took the test? 39 9 16 23
The correct answer is D. 23
Explanation:
Histograms similar to other graphs represent numerical information, usually by using bars, as well as ranges. For example, in the case presented the information presented belongs to the scores obtained in a test, which are shown using ranges. Moreover, it is possible to know the total of people that took the test by adding each of the frequencies, as the frequency in the y-axis shows the number of times the range repeated and it is expected each grade registered belongs to 1 person. This means the total of people is equal to 2 (score from 60-69) + 9 (score from 70-79) + 7 (score from 80-89) + 5 (score from 90-99) = 23 people.
Answer:
the answer is 23
Step-by-step explanation:
hopes this helps:)
write and equation to represent the following statement 28 is 12 less thank K. solve for K K =
Answer:
K = 40
Step-by-step explanation:
As they said that 28 is 12 less than K , it means that you've to add them to get the answer. So , 28 + 12 = 40 which is represented by the variable "K"
Hope it helps and pls mark as brainliest : )
Answer:
Equation : 28 = k - 12K = 40Step-by-step explanation:
28 is 12 less than k
Let's create an equation:
[tex]28 = k - 12[/tex]
Now, let's solve:
[tex]28 = k - 12[/tex]
Move variable to L.H.S and change its sign
Similarly, Move constant to R.H.S and change its sign
[tex] - k = - 12 - 28[/tex]
Calculate the difference
[tex] - k = - 40[/tex]
Change the signs on both sides of the equation
[tex]k = 40[/tex]
Hope this helps...
Best regards!!
Solve the equation for X. 2(2x-4)=3(x+4) A -4 B 4 C 20 D 6
Answer:
X=20
Step-by-step explanation:
The answer is C
Explain how the interquartile range of a data set can be used to identify outliers. The interquartile range (IQR) of a data set can be used to identify outliers because data values that are ▼ less than equal to greater than ▼ IQR Upper Q 3 minus 1.5 (IQR )Upper Q 3 plus IQR Upper Q 3 plus 1.5 (IQR )or ▼ less than equal to greater than ▼ IQR Upper Q 1 plus 1.5 (IQR )Upper Q 1 minus IQR Upper Q 1 minus 1.5 (IQR )are considered outliers.
Answer:
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Step-by-step explanation:
To identify outliers the interquartile range of the dataset can be used
Outliers can be identified as data values that are
- greater than Upper Q 3 plus 1.5 (IQR)
- less than Upper Q 1 minus 1.5 (IQR)
Using the interquartile range concept, it is found that:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
----------------------------
The interquartile range of a data-set is composed by values between the 25th percentile(Q1) and the 75th percentile(Q3).It's length is: [tex]IQR = Q3 - Q1[/tex]Values that are more than 1.5IQR from the quartiles are considered outliers, that is:[tex]v < Q1 - 1.5IQR[/tex] or [tex]v > Q3 + 1.5IQR[/tex]
Thus:
The interquartile range (IQR) of a data set can be used to identify outliers because data values that are 1.5IQR less than Q1 and 1.5IQR more than Q3 and considered outliers.
A similar problem is given at https://brainly.com/question/14683936
Zoey wants to use her iPad throughout a 6-hour flight. Upon takeoff, she uses the iPad for 2 hoursand notices that the battery dropped by 25%, from 100% to 75%. How many total hours can Zoeyexpect from the iPad on a full battery charge?
Answer:
8 hours
Step-by-step explanation:
25%= 2 hrs
100%=8 hrs
brainliest plsssssssssssssssssssss
-zylynn
What is a3 if an=64(12)n−1
Answer:
[tex]\huge\boxed{a_3=9,216}[/tex]
Step-by-step explanation:
[tex]a_n=64(12)^{n-1}\\\\\text{substitute}\ n=3:\\\\a_3=64(12)^{3-1}=64(12)^2=64(144)=9,216[/tex]
explain square roots
Answer:A square root of a number is a value that, when multiplied by itself, gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. Note that (−4) × (−4) = 16 too, so −4 is also a square root of 16. The symbol is √ which always means the positive square root. Example: √36 = 6 (because 6 x 6 = 36)
Connor has a collection of dimes and quarters with a total value of $6.30. The number of dimes is 14 more than the number of quarters. How many of each coin does he have?
Answer:
14 Quarters and 28 dimes
Step-by-step explanation: 14 quarters $3.50
28 dimes is $2.80 total is $6.30
Given p(x) = x4 + x3 - 13x2 - 25x - 12
1. What is the remainder when p(x) is divided by X - 4?
2. Describe the relationship between the linear expression and the polynomial?
How do we describe the relationship?
You are given the following information obtained from a random sample of 5 observations. 20 18 17 22 18 At 90% confidence, you want to determine whether or not the mean of the population from which this sample was taken is significantly less than 21. (Assume the population is normally distributed.) a) State the null and the alternative hypotheses. b) Compute the standard error of the mean. c) Determine the test statistic. d) Test to determine whether or not the mean of the population is significantly less than 21.
Answer:
a
The null hypothesis is
[tex]H_o : \mu = 21[/tex]
The Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
b
[tex]\sigma_{\= x} = 0.8944[/tex]
c
[tex]t = -2.236[/tex]
d
Yes the mean population is significantly less than 21.
Step-by-step explanation:
From the question we are given
a set of data
20 18 17 22 18
The confidence level is 90%
The sample size is n = 5
Generally the mean of the sample is mathematically evaluated as
[tex]\= x = \frac{20 + 18 + 17 + 22 + 18}{5}[/tex]
[tex]\= x = 19[/tex]
The standard deviation is evaluated as
[tex]\sigma = \sqrt{ \frac{\sum (x_i - \= x)^2}{n} }[/tex]
[tex]\sigma = \sqrt{ \frac{ ( 20- 19 )^2 + ( 18- 19 )^2 +( 17- 19 )^2 +( 22- 19 )^2 +( 18- 19 )^2 }{5} }[/tex]
[tex]\sigma = 2[/tex]
Now the confidence level is given as 90 % hence the level of significance can be evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha = 10[/tex]%
[tex]\alpha =0.10[/tex]
Now the null hypothesis is
[tex]H_o : \mu = 21[/tex]
the Alternative hypothesis is
[tex]H_a : \mu< 21[/tex]
The standard error of mean is mathematically evaluated as
[tex]\sigma_{\= x} = \frac{\sigma}{ \sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x} = \frac{2}{ \sqrt{5 } }[/tex]
[tex]\sigma_{\= x} = 0.8944[/tex]
The test statistic is evaluated as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 19 - 21 }{ 0.8944 }[/tex]
[tex]t = -2.236[/tex]
The critical value of the level of significance is obtained from the critical value table for z values as
[tex]z_{0.10} = 1.28[/tex]
Looking at the obtained value we see that [tex]z_{0.10}[/tex] is greater than the test statistics value so the null hypothesis is rejected
and click Submit
By visual inspection, determine the best fitting regression model for the
scatterplot.
O A Quadratic
O B. Linear
OC Exponential
OD. No pattern
Answer:
quadratic
Step-by-step explanation:
This graph has a parabola form wich is a propertie for qaudratic functions
Answer:
A
Step-by-step explanation:
An anchor lowered at a constant rate into the ocean takes 5 seconds to move -17.5 meters. What is the rate of the anchor in meters per second?
Answer:
-3.5 meters per second
Step-by-step explanation:
Take the distance and divide by the time
-17.5 meters/ 5 seconds
-3.5 meters per second
Answer:
-3.5 m/s
Step-by-step explanation:
Rate of the anchor = [tex]\frac{distance}{time}[/tex]
[tex]\frac{-17.5}{5}[/tex]
-3.5 meters per second.
A rectangular waterbed is 7 ft long 5 ft wide and 1 ft tall
How many gallons of water are needed to fill the waterbed?
Assume i gallon is 013 cu ft. Round to the nearest whole galon
Hey there! I'm happy to help!
We want to find the volume of this rectangular waterbed. This means the amount of space it takes up. To find the volume of a rectangular prism, you just multiply together the three side lengths.
7×5×1=35 cubic feet
Now, we need to see how many gallons fit into 35 cubic feet. We see that one gallon is equal to 0.13 cubic feet. So, we can set up a proportion to find how many gallons are needed. We will use g to represent our missing number of gallons.
[tex]\frac{gallons}{cubic feet} = \frac{1}{0.13} =\frac{g}{35}[/tex]
In a proportion, the products of the diagonal numbers are equal. This means that 35, which is 1 multiplied by 35, is equal to 0.13g, which is from multiplying 0.13 by the g.
0.13g=35
We divide both sides by 0.13/
g≈269.23
When rounded to the nearest whole gallon, we will need 269 gallons of water to fill the waterbed.
I hope that this helps! Have a wonderful day! :D
Answer:
Step-by-step explanation:
Since the waterbed is rectangular, its volume would be determined by applying the formula for determining the volume of a cuboid which is expressed as
Volume = length × width × height
Therefore,
Volume of waterbed = 7 × 5 × 1 = 35 cubic feet
1 US gallon = 0.133680556 cubic feet
Therefore, converting 35cubic feet to gallons, it becomes
35/0.133680556 = 261.81818094772 gallons
Rounding up to whole gallon, it becomes 262 gallons
The total cost of a sweater and a jacket was $71.55 If the price of the sweater was $3.19 less than the jacket, what was the price of the sweater? Express your answer as a simplified fraction or a decimal rounded to two places.
Answer: $34.18
Step-by-step explanation:
Let the cost of the Jacket = $x and
The cost of the sweater. = $y
Now total price. = $71.55.
So, $x + $y. = $71.55 -- 1
From the second statements, the price of the sweater was $3.19 less than the price of the jacket. Transforming that into equation
y = ( x - $3.19 )
Now substitute for y in the equation (1) above.
x + ( x - 3.19 ) = 71.55
Now solve the equation
x + x - 3.19 = 71.55
2x - 3.19. = 71.55
2x = 71.55 + 3.19
2x. = 74.74
x = 74.74/2
= $37.37. cost of the jacket
Now to determine the cost of the sweater,
$71.55 - $37.37 = $34.18
The cost of the sweater = $34.18.
Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The negative root of ex = 4 − x2
Answer:
x = -1.964636
Step-by-step explanation:
Given equation;
eˣ = 4 - x²
This can be re-written as;
eˣ - 4 + x² = 0
Let
f(x) = eˣ - 4 + x² -----------(i)
To use Newton's method, we need to get the first derivative of the above equation as follows;
f¹(x) = eˣ - 0 + 2x
f¹(x) = eˣ + 2x -----------(ii)
The graph of f(x) has been attached to this response.
As shown in the graph, the curve intersects the x-axis twice - around x = -2 and x = 1. These are the approximate roots of the equation.
Since the question requires that we use the negative root, then we start using the Newton's law with a guess of x₀ = -2 at n=0
From Newton's method,
[tex]x_{n+1} = x_n + \frac{f(x_{n})}{f^1(x_{n})}[/tex]
=> When n=0, the equation becomes;
[tex]x_{1} = x_0 - \frac{f(x_{0})}{f^1(x_{0})}[/tex]
[tex]x_{1} = -2 - \frac{f(-2)}{f^1(-2)}[/tex]
Where f(-2) and f¹(-2) are found by plugging x = -2 into equations (i) and (ii) as follows;
f(-2) = e⁻² - 4 + (-2)²
f(-2) = e⁻² = 0.13533528323
And;
f¹(2) = e⁻² + 2(-2)
f¹(2) = e⁻² - 4 = -3.8646647167
Therefore
[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]
[tex]x_{1} = -2 - \frac{0.13533528323}{-3.8646647167}[/tex]
[tex]x_{1} = -2 - -0.03501863503[/tex]
[tex]x_{1} = -2 + 0.03501863503[/tex]
[tex]x_{1} = -1.9649813649[/tex]
[tex]x_{1} = -1.96498136[/tex] [to 8 decimal places]
=> When n=1, the equation becomes;
[tex]x_{2} = x_1 - \frac{f(x_{1})}{f^1(x_{1})}[/tex]
[tex]x_{2} = -1.96498136 - \frac{f(-1.9649813)}{f^1(-1.9649813)}[/tex]
Following the same procedure as above we have
[tex]x_{2} = -1.96463563[/tex]
=> When n=2, the equation becomes;
[tex]x_{3} = x_2 - \frac{f(x_{2})}{f^1(x_{2})}[/tex]
[tex]x_{3} = -1.96463563- \frac{f( -1.96463563)}{f^1( -1.96463563)}[/tex]
Following the same procedure as above we have
[tex]x_{3} = -1.96463560[/tex]
From the values of [tex]x_2[/tex] and [tex]x_3[/tex], it can be seen that there is no change in the first 6 decimal places, therefore, it is safe to say that the value of the negative root of the equation is approximately -1.964636 to 6 decimal places.
Newton's method of approximation is one of the several ways of estimating values.
The approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]
The equation is given as:
[tex]\mathbf{e^x = 4 - x^2}[/tex]
Equate to 0
[tex]\mathbf{4 - x^2 = 0}[/tex]
So, we have:
[tex]\mathbf{x^2 = 4}[/tex]
Take square roots of both sides
[tex]\mathbf{ x= \pm 2}[/tex]
So, the negative root is:
[tex]\mathbf{x = -2}[/tex]
[tex]\mathbf{e^x = 4 - x^2}[/tex] becomes [tex]\mathbf{f(x) = e^x - 4 + x^2 }[/tex]
Differentiate
[tex]\mathbf{f'(x) = e^x +2x }[/tex]
Using Newton's method of approximation, we have:
[tex]\mathbf{x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}}[/tex]
When x = -2, we have:
[tex]\mathbf{f'(-2) = e^{(-2)} +2(-2) = -3.86466471676}[/tex]
[tex]\mathbf{f(-2) = e^{-2} - 4 + (-2)^2 = 0.13533528323}[/tex]
So, we have:
[tex]\mathbf{x_{1} = -2 - \frac{0.13533528323}{-3.86466471676}}[/tex]
[tex]\mathbf{x_{1} = -2 + \frac{0.13533528323}{3.86466471676}}[/tex]
[tex]\mathbf{x_{1} = -1.96498136}[/tex]
Repeat the above process for repeated x values.
We have:
[tex]\mathbf{x_{2} = -1.96463563}[/tex]
[tex]\mathbf{x_{3} = -1.96463560}[/tex]
Up till the 6th decimal places,
[tex]\mathbf{x_2 = x_3}[/tex]
Hence, the approximated value of [tex]\mathbf{e^x = 4 - x^2}[/tex] to 6 decimal places is [tex]\mathbf{ -1.964636}[/tex]
Read more about Newton approximation at:
https://brainly.com/question/14279052