Answers
Answer:
k = 6 and k = -4
Step-by-step explanation:
To determine two integral values of k (integer values of k) for which the roots of the quadratic equation kx² - 5x - 1 = 0 will be rational, we can use the Rational Root Theorem.
The Rational Root Theorem states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -1) and q must be a factor of the leading coefficient (in this case, k).
Possible p-values:
Factors of the constant term: ±1Possible q-values:
Factors of the leading coefficient: ±1, ±kTherefore, all the possible values of p/q are:
[tex]\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 1}{\pm k}=\pm 1, \pm \dfrac{1}{k}[/tex]
To find the integral values of k, we need to check the possible combinations of factors. Substitute each possible rational root into the function:
[tex]\begin{aligned} x=1 \implies k(1)^2-5(1)-1 &= 0 \\k-6 &= 0 \\k&=6\end{aligned}[/tex]
[tex]\begin{aligned} x=-1 \implies k(-1)^2-5(-1)-1 &= 0 \\k+4 &= 0 \\k&=-4\end{aligned}[/tex]
[tex]\begin{aligned} x=\dfrac{1}{k} \implies k\left(\dfrac{1}{k} \right)^2-5\left(\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}-\dfrac{5}{k}-1 &= 0 \\-\dfrac{4}{k}&=1\\k&=-4\end{aligned}[/tex]
[tex]\begin{aligned} x=-\dfrac{1}{k} \implies k\left(-\dfrac{1}{k} \right)^2-5\left(-\dfrac{1}{k} \right)-1 &= 0 \\\dfrac{1}{k}+\dfrac{5}{k}-1 &= 0 \\\dfrac{6}{k}&=1\\k&=6\end{aligned}[/tex]
Therefore, the two integral values of k for which the roots of the equation kx² - 5x - 1 = 0 will be rational are k = 6 and k = -4.
Note:
If k = 6, the roots are 1 and -1/6.
If k = -4, the roots are -1 and -1/4.
Related Questions
Find the perioa
equation.
llowing
y = 2 cos(5x + 3) - 6
77
Period = [2]T
Give your answer in simplest form.
Answers
Answer:
In the equation y = 2 cos(5x + 3) - 6, we can ignore the coefficients 2 and -6 for the purposes of calculating the period because they do not change the period. They only change the amplitude (2) and vertical shift (-6) of the function.
The coefficient 5 in front of x inside the cosine function affects the period of the function. It is a horizontal compression/stretch of the graph of the function.
The period of the basic cosine function, y = cos(x), is 2π. When there is a coefficient (let's call it b) in front of x, such as y = cos(bx), the period becomes 2π/b.
So, in your case, b = 5, so the period T of the function y = 2 cos(5x + 3) - 6 is:
T = 2π / 5
This is the simplest form for the period of the given function.
James is a years old. His sister is four years younger than him. His mother is 28 years older than his sister. If the mother is y, which formula describes the relationshio between James and his mother's age?
Answers
Answer:
M = a + 24, where a is James' age and M is his mother's
Step-by-step explanation:
a = James' age
His sister is 4 years younger than him:
a - 4 represents his sister's age.
His mother is 28 years older than his sister:
(a - 4) + 28
or a + 24 represents his mother's age
Let M = his mother's age
M = a + 24
(q10) Consider an aquarium of width 2 ft, length 4 ft, and height 2 ft. Find the force on the longer side of the aquarium?
Answers
The force on the longer side of the aquarium is 515200 N.
Given,Aquarium's width = 2 ft, length = 4 ft, and height = 2 ft.To find:The force on the longer side of the aquarium.Solution:The longer side of the aquarium is 4 ft long.
The force on the longer side of the aquarium can be calculated using the formula:
F = ρghA
Where,F = force on the surface ρ = density of the fluid h = depth of the fluidA = area of the Surface We know that the density of water is ρ = 1000 kg/m³.
The area of the surface is A = l × h = 4 × 2 = 8 sq ft (as the aquarium is rectangular)
The depth of the fluid (water) on the longer side is h = 2 ft.
The force on the longer side can be calculated as follows:
F = ρghA= 1000 × 32.2 × 2 × 8= 515200 N
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2(cos^4 60 +sin^4 30) -(tan^2 60 +cot^2 45) +3*sec^2 30
Answers
The value of the expression [tex]2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.[/tex]
Let's simplify the expression step by step:
Recall the values of trigonometric functions for common angles:
cos(60°) = 1/2
sin(30°) = 1/2
tan(60°) = √(3)
cot(45°) = 1
sec(30°) = 2
Substitute the values into the expression:
[tex]2(cos^4 60 + sin^4 30) - (tan^2 60 + cot^2 45) + 3sec^2 30[/tex]
= [tex]2((1/2)^4 + (1/2)^4) - (\sqrt{(3)^2 + 1^2} ) + 3(2^2)[/tex]
= 2(1/16 + 1/16) - (3 + 1) + 3*4
= 2(1/8) - 4 + 12
= 1/4 - 4 + 12
= -15/4 + 12
= -15/4 + 48/4
= 33/4
Therefore, the value of the expression [tex]2(cos^4 60 + sin^4 30) -(tan^2 60 + cot^2 45) + 3\times sec^2 30 is 33/4.[/tex]
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The volume of the rectangular pyramid below is 468 units. Find the value of x.
Answers
The value of x is: x=12.
Here, we have,
given that,
The volume of the rectangular pyramid below is 468 units.
we know that,
Note that the area B of the rectangular base with length x and width 9 units is:
B = 9x
Then, the volume V = 468 cubic units of the pyramid is related to its base area B = 9x and height h=13 as follows:
V = 1/3 Bh
substituting the values we get,
so, we get,
x = 12
So, the value of x is 12.
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show work if possible
Answers
Answer:
B. 14,525
Step-by-step explanation:
If a tablet costs $35 and the school is purchasing tablets for every student, then the total cost to buy tablets for the whole school would be:
$35 x 415 = $14,525
Therefore, the answer is B. $14,525.
You need to purchase a cover for this pool. A company sells covers for
$2.25 per square foot. Based on the area of the pool, how much would
the cover cost? Enter a number only - no symbols.
30
18
18
6
Answers
Answer:
1, 215
Step-by-step explanation:
To calculate the cost of the cover, we need to know the area of the pool. Assuming that the pool is rectangular and has the dimensions given by the four numbers provided (30, 18, 18, 6), we can calculate the area as follows:
Area = length * width
Area = 30 * 18
Area = 540 square feet
Therefore, the cover for this pool would cost:
Cost = Area * Price per square foot
Cost = 540 * $2.25
Cost = $1,215
So the cover would cost $1,215.
Question 16 of 20
A scientist does an experiment taking the blood pressure of a group of dogs.
aged 10 and older that have high blood pressure but are not given medication
and the blood pressure of another group of dogs aged 10 and older that have
high blood pressure and are being given a new blood pressure medication.
The group of dogs that are not given medication is referred to as the.
OA. control group
OB. effectiveness group
OC. correlation group
O D. treatment group
Answers
The correct answer is "A. control group."
In an experiment, the control group refers to the group of subjects that does not receive any treatment or intervention.
They are used as a comparison or baseline to evaluate the effects of the treatment being tested.
In this case, the control group consists of dogs aged 10 and older with high blood pressure who are not given any medication.
By comparing the blood pressure measurements of this control group to the group of dogs receiving the new blood pressure medication, the scientist can determine the effectiveness of the medication.
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A fair die is rolled. What is the probability of rolling an odd number or a number less than 3?
Answers
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
Recall that the sample space for the results obtained by rolling a fair dice is {1,2,3,4,5,6}. So, the total number of outcomes is 6.
Since the desired outcome is rolling an odd number or a number less than 3, so the set of desired outcomes is {1,2,3,5}. Hence, the number of desired outcomes is 4.
Therefore, the required probability is:
[tex]\frac{\text{number of desired outcomes}}{\text{number of all outcomes}}=\frac{4}{6}=\frac{2}{3}[/tex]
Answer:
probability of rolling an odd number or a number less than 3 is [tex]\frac{2}{3}[/tex] or a 2 in 3 chance
Step-by-step explanation:
a die has 6 sides that are numbered 1 to 6.
3 of those sides are even numbers and 3 of those sides are odd numbers.
the question also states LESS THAN 3, which means that it does not include 3 itself, out of the 6 possible numbers, only two of them are less than 3 (1 and 2) so 2 out of 6 sides are less than 3, but one is already included in the probability, then we use the formula
[tex]\frac{number of desired outcomes}{number of total possible outcomes}[/tex] or [tex]\frac{4}{6}[/tex] which can be simplified to [tex]\frac{2}{3}[/tex]
The scores of students on a standardized test are normally distributed with a mean of 300 and a standard deviation of 40. What percentage of scores are below 260?
Answers
The percentage of scores below 260 is 15.87%.
Use the graph attached to answer.
Answers
The function values are:
f(-1) = -9
f(1) = -5
We have,
From the graph,
We have the coordinates as:
(-1, -9) (2, 0), (-4, 0), and (1, -5)
Now,
The coordinates mean (x, y).
x is the x-axis and y is the function value.
f(x) = y
So,
We can have,
When x = -1, y = -9 or f(-1) = -9
And,
When x = 1, y = -5 or f(1) = -5
Thus,
The function values are:
f(-1) = -9
f(1) = -5
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KITES The kite shown is made of two congruent triangles. If m∠BAD=m∠BCD=45°
, find m∠ABD
Answers
Answer:
Step-by-step explanation:
Triangle BDA right angled at A ⇒ BDA = 90
ABD = BDA - BAD = 90 - 45 = 45
The total angle of a kite is............
Answers
Since a kite is a quadrilateral, it has the value of 360 total degrees.
need help right now!!!!
Answers
The area of the trapezium is 99.225 inches².
How to find the area of a trapezium?A trapezium is the a quadrilateral. Therefore, the area of the quadrilateral can be calculated as follows:
area of the trapezium = 1 / 2 (a + b)h
where
a and b are the basesh = height of the trapeziumTherefore,
area of the trapezium = 1 / 2 (6.3 + 12.6)10.5
area of the trapezium = 1 / 2 (18.9)10.5
area of the trapezium = 198.45 / 2
area of the trapezium = 99.225 inches²
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Trianglr FDP is reduced with a scale factor of 1/2 and a center of (0,0). Find the coordinates of the new coordinates of the vertex?D’ (_, _)
Answers
The new coordinates of the vertex D are given as follows:
D'(0, -2.5).
What is a dilation?A dilation is defined as a non-rigid transformation that multiplies the distances between every point in a polygon or even a function graph, called the center of dilation, by a constant factor called the scale factor.
The coordinates of the vertex D are given as follows:
D = (0, -5).
The scale factor is given as follows:
k = 1/2.
Hence the dilated coordinates are given as follows:
D'(0, -2.5).
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Belle is a ranger at Roaring Rivers State Park. In surveying the hiking trails for a park brochure, she found that 48% of the trails are rated as easy and 63% of the trails are rated as easy or have a scenic overlook. If 11% of the trails are rated as easy and have a scenic overlook, what is the probability that a randomly selected trail has a scenic overlook?
Answers
P(E) = 0.48 (48% of trails are rated as easy)
P(E ∪ O) = 0.63 (63% of trails are either easy or have a scenic overlook)
P(E ∩ O) = 0.11 (11% of trails are both easy and have a scenic overlook)
We can use these probabilities to calculate P(O), the probability of a trail having a scenic overlook, as follows:
P(E ∪ O) = P(E) + P(O) - P(E ∩ O)
Substituting the given values:
0.63 = 0.48 + P(O) - 0.11
Now, let's solve for P(O):
0.63 - 0.48 + 0.11 = P(O)
0.26 = P(O)
Therefore, the probability that a randomly selected trail has a scenic overlook is 0.26 or 26%.
What is the population projection of Okrika in 2023 if her population was 5000 at the last census of 2006(17yrs ago)? show working please, thanks.
Answers
Using an exponential growth function or equation, the population of Okrika in 2023 with a population of 5,000 in 2006 is projected to be 8,264.
What is an exponential growth function?An exponential growth function is a mathematical equation that shows a constant rate of growth in the value or number over a period.
Exponential growth functions or equations are depicted as y = a(1 + r)ⁿ, where y is the final value, a is the initial value, (1 + r) is the growth factor, r is the growth rate, and n is the time or number of years.
Population of Okrika in 2006 = 5,000
Annual growth rate = 3% = 0.03 (3/100)
Exponential growth factor = 1.03 (1 + 0.03)
The number of years between 2023 and 2006 = 17 years
Let the projected population in 2023 = y
Exponential growth equation or function: y = 5,000 (1.03)¹⁷
y = 8,264.
Thus, based on an exponential growth function, we can conclude that at 3% annual growth rate, the population of Okrika in 2023 will be 8,264.
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Question Completion:Assume a population growth rate of 3% per year for Okrika.
5. Graph the function f(x) = (2)* on the coordinate plane.
y
-10 9
87
6
54
32
1.
10
-1
3
4
S
6
-7
-8
-9
-10
1
3
$
6
7
8
9
X
10
Answers
The graph of the function f(x) = (2)ˣ is added as an attachment
Sketching the graph of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = (2)ˣ
The above function is an exponential function that has been transformed as follows
Initial value = 1
Growth factor = 2
Next, we plot the graph using a graphing tool by taking not of the above transformations rules
The graph of the function is added as an attachment
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The length of timber cuts are normally distributed with a mean of 95 inches and a standard
deviation of 0.52 inches. In a random sample of 30 boards, what is the probability that the
mean of the sample will be between 94.7 inches and 95.3 inches ?
O 0.998
O 0.436
O 0.002
O 0.950
Answers
The probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.
Option B is the correct answer.
We have,
To find the probability that the mean of the sample will be between 94.7 inches and 95.3 inches, we can use the Central Limit Theorem.
According to the Central Limit Theorem, the distribution of sample means approaches a normal distribution as the sample size increases.
In this case, the mean of the population (μ) is 95 inches and the standard deviation of the population (σ) is 0.52 inches.
Since the sample size is sufficiently large (n = 30), we can assume that the distribution of sample means will be approximately normal.
To calculate the probability, we need to standardize the sample mean using the z-score formula:
z = (x - μ) / (σ / √n)
where:
x = sample mean
μ = population mean
σ = population standard deviation
n = sample size
Let's calculate the z-scores for the lower and upper limits:
z1 = (94.7 - 95) / (0.52 / √30)
z2 = (95.3 - 95) / (0.52 / √30)
Now, we can use a standard normal distribution table or a calculator to find the probability associated with these z-scores.
Using a standard normal distribution table or a calculator, we find:
P(z1 < Z < z2) ≈ 0.436
Therefore,
The probability that the mean of the sample will be between 94.7 inches and 95.3 inches is approximately 0.436.
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If point P (-2,1) is reflected across the line y = 2 what are the coordinates of its reflection image?
Answers
Answer:
P'(-2,3)
Step-by-step explanation:
We see that P(-2,1) is 1 point down y = 2, so reflection across the line y = 2 will be 1 point up y = 2, so the answer is (-2,3)
Write a complete two-column proof for the following information.
Given: m1 = 62° and lines t and l intersect
Prove: m4 = 62°
Answers
The two column proof is written as follows
Statement Reason
< 1 = 62 degrees given
< 1 + < 2 = 180° Linear pairs are supplementary.
< 4 + < 2 = 180° Linear pairs are supplementary.
< 1 + < 2 = < 4 + < 2 Substitution property of equality
< 1 = < 4 Subtraction property of equality
< 1 = < 4 = 62 degrees Vertical angle theorem
What are Vertical angles?When two lines intersect, vertical angles are created, and in this instance, the angles opposite each another are equal.
What are congruent angles?Two angles are said to be congruent when they are equal to each
Solving the problem
< 1 + < 2 = 180° are a linear pair = 180
< 4 + < 2 = 180° are a linear pair = 180°
equating both
< 1 + < 2 = < 4 + < 2
< 1 = < 4
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find the inverse of the function
Answers
Answer:
[tex]g^{-1}(x)=3x+12[/tex]
Step-by-step explanation:
The explanation is attached below.
What is the sin B?
/21
B
5
2
sin (B) =
[?]
Answers
Answer:
Step-by-step explanation:
sin (B) = [tex]\frac{2}{5}[/tex]
On September 26, 2010, Holly received $7,500 from his father. He settled this amount
on March 6, 2011 with interest of $141.80.
a. What was the time period of the loan, expressed in days (rounded up to the next
day)?
Answers
The time period of the loan in days is A = 187 days
Given data ,
To determine the time period of the loan in days, we need to calculate the number of days between September 26, 2010, and March 6, 2011.
September 26, 2010 - March 6, 2011
To calculate the number of days, we consider:
September 2010: 30 days
October 2010: 31 days
November 2010: 30 days
December 2010: 31 days
January 2011: 31 days
February 2011: 28 days (since it is not a leap year)
March 2011: 6 days
Adding these days together:
On simplifying the equation , we get
30 + 31 + 30 + 31 + 31 + 28 + 6 = 187 days
Hence , the time period of the loan, rounded up to the next day, is approximately 187 days.
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50 POINTS
Ron has a homeowner’s insurance policy, which covers theft, with a deductible of d dollars. Two bicycles, worth b dollars each, and some tools, worth t dollars, were stolen from his garage. If the value of the stolen items was greater than the deductible, represent the amount of money the insurance company will pay algebraically.
Answers
Algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).
Let's denote the amount of money the insurance company will pay as P. In this scenario, if the value of the stolen items is greater than the deductible, the insurance company will cover the loss, and Ron will receive compensation for the stolen items.
The total value of the stolen items can be calculated by adding the value of the bicycles (2b) and the value of the tools (t). So, the total value of the stolen items is 2b + t.
If the total value of the stolen items is greater than the deductible (d), then the insurance company will pay the difference between the total value and the deductible. Mathematically, this can be represented as:
P = (2b + t) - d
Therefore, algebraically, the amount of money the insurance company will pay, represented as P, is equal to the total value of the stolen items (2b + t) minus the deductible (d).
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Find the discount for a $455 designer purse that is on sale for 30% off.
Answers
Answer:
Final Price: $318.50
You save: $136.50
Step-by-step explanation:
To find the discount for a $455 designer purse that is on sale for 30% off, we can follow these steps:
Step 1: Calculate the discount amount
Discount Amount = Original Price * Discount Percentage
= $455 * 30% = $455 * 0.3 = $136.50
Step 2: Calculate the final price after the discount
Final Price = Original Price - Discount Amount
= $455 - $136.50 = $318.50
The discount for the $455 designer purse that is on sale for 30% off is $136.50. The final price after the discount is $318.50.
Answer:
Step-by-step explanation:
Discount: subtract the percentage from the sale price:
$455.00 x 30% = $136.50
then you subtract the amount $136.50 from the original price of $455.00 = $318.50 The customer will pay $318.50 because a discount was for 30% off from the original price.
Find the discount for a gaming console that costs $545 but is on sale for 25% off.
Answers
Answer:
$136.25 is how much you're saving (the discount)
$408.75 is the sale price
Step-by-step explanation:
How much you're saving: [tex]\$545(0.25)=\$136.25[/tex]
How much you'll pay after the discount: [tex]\$545-\$136.25=\$408.75[/tex]
Verónica Ana y Luis pintan una barda y les pagan 300 cuánto dinero debería recibir cada quien
Answers
Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.
Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).
Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.
Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.
100 POINTS
Don and Celine have been approved for a $400,000, 20-year mortgage with an APR of 3.35%. Using the mortgage and interest formulas, set up a two-month amortization table with the headings shown and complete the table for the first two months.
Answers
To set up the amortization table, we can use the mortgage and interest formulas as follows:
Mortgage formula:
M = P [ i(1 + i)^n / (1 + i)^n - 1]
where M is the monthly payment, P is the principal (the amount borrowed), i is the monthly interest rate (APR divided by 12), and n is the total number of payments (20 years multiplied by 12 months per year).
Interest formula:
I = P * i
where I is the monthly interest payment, P is the remaining principal balance, and i is the monthly interest rate.
Using these formulas, we can set up the following amortization table for the first two months:
Month Payment Principal Interest Balance
1 $400,000
2
To fill in the table, we need to calculate the monthly payment (M) and the monthly interest payment (I) for the first month, and then use these values to calculate the principal payment for the first month. We can then subtract the principal payment from the initial balance to get the balance for the second month, and repeat the process to fill in the remaining columns.
To calculate the monthly payment (M), we can use the mortgage formula:
M = P [ i(1 + i)^n / (1 + i)^n - 1]
where P is the principal amount, i is the monthly interest rate, and n is the total number of payments.
Plugging in the given values, we get:
M = 400,000 [ 0.00279 (1 + 0.00279)^240 / (1 + 0.00279)^240 - 1]
M = $2,304.14
Therefore, the monthly payment is $2,304.14.
To calculate the interest payment for the first month, we can use the interest formula:
I = P * i
where P is the remaining principal balance and i is the monthly interest rate.
Plugging in the values for the first month, we get:
I = 400,000 * 0.00279
I = $1,116.00
Therefore, the interest payment for the first month is $1,116.00.
To calculate the principal payment for the first month, we can subtract the interest payment from the monthly payment:
Principal payment = Monthly payment - Interest payment
Principal payment = $2,304.14 - $1,116.00
Principal payment = $1,188.14
Therefore, the principal payment for the first month is $1,188.14.
To calculate the balance for the second month, we can subtract the principal payment from the initial balance:
Balance = Initial balance - Principal payment
Balance = $400,000 -$1,188.14
Balance = $398,811.86
Therefore, the balance for the second month is $398,811.86.
Using these values, we can complete the first two rows of the amortization table as follows:
Month Payment Principal Interest Balance
1 $2,304.14 $1,188.14 $1,116.00 $398,811.86
2
To fill in the remaining columns for the second month, we can repeat the process using the new balance of $398,811.86 as the principal amount for the second month. We can calculate the interest payment using the same method as before, and then subtract the interest payment from the monthly payment to get the principal payment. We can then subtract the principal payment from the balance to get the new balance for the third month, and repeat the process for the remaining months of the amortization period.
X^x = 4^x +16 solve for x
Answers
The value of x converges to approximately 2.5615
Given is an equation, we need to solve for x, xˣ = 4ˣ + 16
To solve the equation xˣ = 4ˣ + 16, we'll use algebraic methods. Unfortunately, this equation does not have an explicit algebraic solution that can be found using elementary functions.
However, we can use numerical methods or approximation techniques to find an approximate solution.
One common numerical method for solving equations is the Newton-Raphson method.
Let's apply it to this equation:
Start with an initial guess for x, let's say x = 1.
Iterate using the following formula:
x(n+1) = x(n) - f(x(n)) / f'(x(n))
where f(x) = x^x - 4^x - 16 and f'(x) is the derivative of f(x) with respect to x.
Repeat step 2 until the value of x converges to a solution.
Let's perform a few iterations:
1st iteration:
x(1) = 1 - (1^1 - 4^1 - 16) / (1 * 1^0 - 4 * 4^0)
= 1 - (-11) / (-3)
≈ 3.6667
2nd iteration:
x(2) = 3.6667 - (3.6667^3.6667 - 4^3.6667 - 16) / (3.6667 * 3.6667^2.6667 - 4 * 4^2.6667)
≈ 2.6141
3rd iteration:
x(3) = 2.6141 - (2.6141^2.6141 - 4^2.6141 - 16) / (2.6141 * 2.6141^1.6141 - 4 * 4^1.6141)
≈ 2.5615
By continuing these iterations, you can refine the solution to any desired level of accuracy.
In this case, the value of x converges to approximately 2.5615.
Learn more about Newton-Raphson method click;
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