is 12, -15, -18, -21 arithmetic

The number of iterations required is 6.

Given a starting guess of [90, yo] = [1, 2], Newton's method for optimization takes 6 iterations to find a minimum of the function f(x, y) = 12a^2 – 7x + 7 +10y – xy to a tolerance of 10^-8.Step-by-step explanation:

Newton's method is an iterative process to approximate the roots of an equation or optimization of a function.

To solve this problem, we need to apply Newton's method to the function f(x, y) = 12a^2 – 7x + 7 +10y – xy as follows:

Given a starting guess of [90, yo] = [1, 2], we can find the solution using the following formula:xn+1 = xn - f'(xn)/f''(xn)where xn is the current guess, f'(xn) is the derivative of f at xn, and f''(xn) is the second derivative of f at xn.

Here, f(x, y) = 12a^2 – 7x + 7 +10y – xy, so we have (x, y) = [-7 - y, 10 - x]f''(x, y) = [0, -1; -1, 0]

We need to apply this formula until the difference between xn and xn+1 is less than or equal to the tolerance of 10^-8.

This means that we need to keep iterating until |xn+1 - xn| <= 10^-8.

Given the assumption of quadratic convergence, we can also calculate the number of iterations required as follows:|xn+1 - xn| ≈ |xn - xn-1|^2/|xn+1 - 2xn + xn-1|

Using this formula, we can calculate the number of iterations required to reach the tolerance of 10^-8.

Here are the results of the first six iterations:x1 = [1, 2]x2 = [4.125, 2.9]x3 = [4.223382352941176, 2.979411764705882]x4 = [4.223639551849474, 2.979707510729614]x5 = [4.223639551862697, 2.979707510767132]x6 = [4.223639551862697, 2.979707510767132]

We can see that the difference between x5 and x6 is less than 10^-8, so we have found a solution to the desired tolerance.

Therefore, the number of iterations required is 6.

To know more about Newton's method visit:

https://brainly.in/question/17763377

#SPJ11

Answer:

65,760

Step-by-step explanation:

move decimal over two places to make a percent a decimal so .37

then multiply that times the 48000 to get 17,760 and then add that to the original 48000 to get 65,760

Answer:

If the radius is 6mm, the diameter is 12mm.

If the diameter is 22 ft, the radius is 11 ft.

Step-by-step explanation:

1st one) When you try to find the diameter of any circle, and you already have the radius, you need to multiply it by two (double it)

6 x 2 = 12mm

2nd one) Then to do the opposite, you need to divide the diameter by 2.

22/2 = 11 ft

Hope this helped :)

Answer: 45

Step-by-step explanation:

Answer:

#4 is B

#5 is also B

Step-by-step explanation:

i big brain

Answer:

4. b) [tex]4x^2-20xy+25y^2[/tex]

5. b) [tex]x^2+14x+49[/tex]

Step-by-step explanation:

4. [tex](2x-5y)^2[/tex]

First, one must rewrite the exponential equation as a multiplication problem,

[tex](2x-5y)(2x-5y)[/tex]

Now distribute, multiply every term in one of the parenthesis by every term in the other parenthesis,

[tex]=(2x-5y)(2x-5y)\\\\=(2x)(2x)+(2x)(-5y)+(-5y)(2x)+(-5y)(-5y)[/tex]

Now simplify the given expression,

[tex]=(2x)(2x)+(2x)(-5y)+(-5y)(2x)+(-5y)(-5y)\\\\=4x^2-10xy-10xy+25y^2[/tex]

Combine like terms,

[tex]=4x^2-20xy+25y^2[/tex]

5.[tex](x+7)^2[/tex]

To solve this problem, one should follow the same series of steps as they did to solve the last expression. First, rewrite the exponential expression as a multiplication problem.

[tex](x+7)(x+7)[/tex]

Now distribute, multiply every term in one of the parenthesis by every term in the other parenthesis,

[tex]=(x)(x)+(7)(x)+(7)(x)+(7)(7)[/tex]

Simplify the expression,

[tex]=(x)(x)+(7)(x)+(7)(x)+(7)(7)\\\\=x^2 + 7x + 7x + 49[/tex]

Finally, combine like terms,

[tex]=x^2+14x+49[/tex]

The number of ways to arrange the 11 donors in line is 11!. 11! = 39,916,800.

The donors can be in line in different ways.

To calculate the number of distinguishable ways, we can use the concept of permutations. Since all the donors are distinct (different blood types), we need to find the total number of permutations of these donors.

The total number of donors is 4 (type O+), 4 (type A+), and 3 (type B+), giving a total of 11 donors.

The number of ways to arrange these donors in line can be calculated using the formula for permutations. The formula for permutations of n objects taken all at a time is n!.

Therefore, the number of ways to arrange the 11 donors in line is 11!.

Calculating 11!, we get:

11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 39,916,800.

Hence, the donors can be in line in 39,916,800 different ways.

Learn more about line here

https://brainly.com/question/18831322

#SPJ11

Answer:

It increases by 2.5

Step-by-step explanation:

yeah

Answer:

A would be the answer I would choose

Answer: 91 centimeters

Step-by-step explanation:

Answer:

91

Step-by-step explanation:

68+23=91

Answer:

94.25 feet.

Step-by-step explanation:

Divide total miles by number of days:

151.2 / 24 = 6.3 miles per day

Answer:

37.999749573966

Step-by-step explanation:

Brainliest?

Answer:

Only the mean increased.

Step-by-step explanation:

The mean is the total divided by the number of scores, and since adding 21 will increase the total score significantly, the mean increases.

The median is still 7.

(a)The power is 1/2, which is less than 1 the improper integral ∫(1 / √(x)) dx from a to infinity diverges.

b)The value of the integral of ∫(1 / √(x)) dx from 1 to infinity is ln(√2 + 1).

c) The general solution to the differential equation dy/dx = (2x - 2) / (x² + 3x - 2) is y = ln|x - 1||x + 2| + C, where C is a constant.

To determine if the improper integral converges or diverges, to evaluate the integral:

∫(1 / √(x)) dx from a to infinity

This integral represents the area under the curve of the function 1/√(x) from x = a to x = infinity.

To determine convergence or divergence, the p-test for improper integrals. For the p-test, the power of x in the denominator, which is 1/2.

If the power is greater than 1, the integral converges. If the power is less than or equal to 1, the integral diverges.

To confirm the result using a trigonometric substitution, let's substitute x = tan²(t):

√(x) = √(tan²(t)) = tan(t)

dx = 2tan(t)sec²(t) dt

substitute these values into the integral:

∫(1 / √(x)) dx = ∫(1 / tan(t))(2tan(t)sec²(t)) dt

= ∫2sec(t) dt

To determine the limits of integration. Since the original integral was from 1 to infinity, to find the corresponding values of t.

When x = 1, tan²(t) = 1, which implies tan(t) = ±1. the positive value because dealing with positive values of x.

tan(t) = 1 when t = π/4

The integral with the appropriate limits:

∫(1 / √(x)) dx = ∫2sec(t) dt from t = 0 to t = π/4

Evaluating the integral:

∫2sec(t) dt = 2ln|sec(t) + tan(t)| from t = 0 to t = π/4

Plugging in the limits:

2ln|sec(π/4) + tan(π/4)| - 2ln|sec(0) + tan(0)|

ln(√2 + 1) - ln(1)

ln(√2 + 1)

The given differential equation is:

dy/dx = (2x - 2) / (x^2 + 3x - 2)

To find the general solution,  by factoring the denominator:

dy/dx = (2x - 2) / [(x - 1)(x + 2)]

decompose the fraction into partial fractions:

dy/dx = A/(x - 1) + B/(x + 2)

To find the values of A and B, both sides of the equation by the denominator (x - 1)(x + 2):

2x - 2 = A(x + 2) + B(x - 1)

Expanding the right side and collecting like terms:

2x - 2 = Ax + 2A + Bx - B

Matching the coefficients of x and the constant terms on both sides, the following system of equations:

A + B = 2 (coefficient of x)

2A - B = -2 (constant term)

Solving this system of equations,  A = 1 and B = 1.

Substituting these values back into the partial fraction decomposition:

dy/dx = 1/(x - 1) + 1/(x + 2)

integrate both sides with respect to x:

∫ dy = ∫ (1/(x - 1) + 1/(x + 2)) dx

Integrating each term separately:

y = ln|x - 1| + ln|x + 2| + C

Combining the logarithmic terms using properties of logarithms:

y = ln|x - 1||x + 2| + C

This is the general solution to the given differential equation.

To know more about infinity here

https://brainly.com/question/16887086

#SPJ4

Answer:

The triangle is isosceles.

Step-by-step explanation:

This means that one angle's sine is the same as the other's cosine.

Answer:

lets divide the figure into two parts.

triangle base=2ft+2ft+6ft

triangle base=10ft

area of triangle = 1/2×base×height

area of triangle = 1/2×10ft×12ft

area of triangle =60ft²

area of square=side²

area of square=(6ft)²

area of square=36ft²

Answer:

$42.84

Step-by-step explanation:

P = 85 * 6 = 510

Formula:

I = Prt

Given:

P = 510

r = 2.1% or 0.021

t = 4

Work:

I = Prt

I = 510(0.021)(4)

I = 42.84

There is no polynomial attached ; considering the hypothetival

Answer:

x³ = leading term.

2 = leading Coefficient

1 = constant term.

Step-by-step explanation:

Considering an hypothetical situation ;

For any polynomial such as 2x³ + 3x + 1

The polynomial is represented as : ax³ + bx + c

Where a = leading Coefficient ;

x³ = leading term

c = constant term

Therefore ;

The leading term in this hypothetical question is :

x³ = leading term.

2 = leading Coefficient

1 = constant term.

Answer:

True.

Step-by-step explanation:

given equation: (tan x - 1)/(tan x + 1) = (1 - cot x)/(1 + cot x)

1. manipulate the right side by using trigonometric identities

(tan(x) - 1)/(tan(x) + 1) = (-cos(x) + sin(x))/(cos(x) + sin(x))

2. manipulate the right side by using trigonometric identities

(-cos(x) + sin(x))/(cos(x) + sin(x)) = (-cos(x) + sin(x))/(cos(x) + sin(x))

Both sides of the equation are now equal -> (tan x - 1)/(tan x + 1) = (1 - cot x)/(1 + cot x) is true.

Answer:

c ) 2480 cm²

Step-by-step explanation:

Surface Area of a Triangular prism =

S = bh + lb + 2ls

b = 30cm

h = 8cm

s = 17 cm

l = 35cm

The surface area = 30cm × 8 cm + 35 × 30 cm + 2(35 × 17)

= 240 cm² + 1050 cm² + 1190 cm²

= 2480 cm²

Option c is the correct option

Answer:

$1.40

Step-by-step explanation:

4 quarters

1 quarter = 25 cents

Therefore, 4 quarters = 1/25 x 4/x

multiply 4 by 25, since 1 quarter = 25 cents

4 x 25 = 100

4 quarters = 100 cents

which equals $1

8 nickels

1 nickle = 5 cents

Therefore, 8 nickles = 1/5 x 8/x

multipy 8 by 5, since 1 nickel = 5cents

8 x 5 = 40

8 nickels = 40 cents

So add both 40 cents and 100 cents, which equals 140 cents.

But you still have to change the cents to dollars.

Which is 100 cents = $1

Add 40 cents

= $1.40

Answer:

16 = 3x

Step-by-step explanation:

It is an equilateral triangle. The formula for the perimeter of an equilateral triangle is P = 3a.

3X IS ANSWER AND IT IS SIMPLE BECAUSE P= 3X

The answer is b=18. To solve, multiply 6 by 3 to get 18. This is called doing the inverse operation. Since the equation is a division equation, we would have to multiply in order to find the missing variable.

The confidence coefficient for a 98% confidence interval is 2.33, indicating the number of standard deviations away from the mean.

To construct a confidence interval, we use a critical value that corresponds to the desired level of confidence. In this case, the confidence level is 98%, which means there is a 98% chance that the true population parameter falls within the confidence interval.

The critical value for a 98% confidence interval can be found using the standard normal distribution. Since the sample size is relatively small (13 measurements), we typically use the t-distribution instead. However, when the sample size is large (typically considered to be greater than 30), the t-distribution closely approximates the standard normal distribution.

For a 98% confidence level, the critical value is 2.33. This value represents the number of standard deviations away from the mean that includes 98% of the distribution.

Therefore, the correct answer is (D) 2.33 as the confidence coefficient for a 98% confidence interval.

Learn more about interval here:

brainly.com/question/11051767

#SPJ11

Answer: May

Step-by-step explanation: 9 is greater than 8 don't worry about the signs

we need a sample size of at least 248 to have a probability of 0.8664 that the sample mean is within 0.8 of the population mean.

Given a population with standard deviation 8, we have to calculate the sample size required so that the probability is 0.8664 that the sample mean is within 0.8 of the population mean.To solve the problem, we have to use the formula as follows:$$n = \frac{z^2\sigma^2}{d^2}$$

Where, n = sample sizeσ = population standard deviation d = precision level z = z-score

So, z can be found using the standard normal table. In this case, we need to find the z-score that corresponds to the probability of 0.8664 plus half of the remaining probability of 1 - 0.8664, which is equal to 0.0668.Using the standard normal table, we find the z-score that corresponds to the 0.9334 probability, which is 1.48 (approximately).Now, we can substitute all the values into the formula and solve for n.$$n = \frac{z^2\sigma^2}{d^2}$$$$n = \frac{(1.48)^2 \cdot 8^2}{(0.8)^2}$$$$n = 247.15$$

Therefore, we need a sample size of at least 248 to have a probability of 0.8664 that the sample mean is within 0.8 of the population mean.

To know more about probability visit:

https://brainly.com/question/13604758

#SPJ11

The needed sample size is given as follows:

n = 250.

We first must use the z-score formula, as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In which:

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

The p-value of the z-score in this problem is given as follows, considering the symmetry of the normal distribution:

0.5 + 0.8864/2 = 0.9432.

Hence the z-score is given as follows:

z = 1.58.

Then the sample size is obtained as follows:

[tex]1.58 = \frac{0.8}{\frac{8}{\sqrt{n}}}[/tex]

[tex]\sqrt{n} = 15.8[/tex]

n = 15.8²

n = 250.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ4

Answer:

$20

Step-by-step explanation:

Answer:

48 degrees

Step-by-step explanation:

Supplementary angles add up to 180 degrees.

If one angle is 132 degrees, the other must be 48 degrees.