find the exact length of the curve y=23(x2−1)3/2,1≤x≤3.

Muslim scholars blended mathematical ideas from Greece, India, and Persia in the development of algebra and trigonometry.

There is solid proof of social mixing in how Muslims concentrated on arithmetic during the Islamic Brilliant Age, which endured from the eighth to the fourteenth century CE. During this time, researchers from different pieces of the Muslim world, as well as from Greece, India, and Persia, met up to share information and thoughts.

One illustration of this social mixing should be visible in the improvement of variable based math, which was vigorously affected by crafted by Indian mathematicians. Muslim researchers deciphered and developed Indian texts, integrating new ideas and images into their own numerical practices.

One more model is the improvement of geometry, which was impacted by crafted by Greek mathematicians. Muslim researchers deciphered and developed Greek texts, adding new applications and refinements to the discipline.

Generally, the social mixing of numerical thoughts and customs assumed a huge part in the improvement of Islamic science, and assisted with laying out a rich and various heritage that keeps on impacting the field today.

To learn more about cultural blending in muslims, refer:

https://brainly.com/question/24710037

#SPJ4

Sorry i miscalculated this one

Answer:

-3/2

Step-by-step explanation:

(see attached for reference)

the formula for slope is given as :

slope, m = (y₂-y₁) / (x₂-x₁)

in our case , we are given

(x₁,y₁) = (-4, 13)

(x₂, y₂) = (6, -2)

substitute these into the formula above:

m = (y₂-y₁) / (x₂-x₁)

= [-2 - 13] / [6 - (-4) ]

= -15 / 10

= -3/2

the general solution of the differential equation is given by cos y = C√(x^2 + 1) The correct option is (d) None of these.

We are given the differential equation:

(x^2 + 1) tan y dy/dx = x

We can solve this equation by separation of variables. We begin by multiplying both sides by dx/tan y:

(x^2 + 1) dy/tan y = x dx

Next, we can use the substitution u = x^2 + 1, which implies du/dx = 2x:

dy/tan y = (x du)/(2u - 2)

We can separate the variables as follows:

(tan y) dy = (x du)/(2u - 2)

We can integrate both sides:

∫(tan y) dy = (1/2)∫(x du)/(u - 1)

Using the substitution v = u - 1, which implies du = dv, we get:

∫(tan y) dy = (1/2)∫x dv/v

Integrating the right-hand side using ln |v| as the antiderivative, we get:

∫(tan y) dy = (1/2) ln |v| + C

Substituting back for v, we get:

∫(tan y) dy = (1/2) ln |u - 1| + C

Substituting back for u and simplifying, we get:

∫(tan y) dy = (1/2) ln |x^2 + 1| + C

Integrating the left-hand side using ln |cos y| as the antiderivative, we get:

ln |cos y| = (1/2) ln |x^2 + 1| + C

Simplifying and exponentiating both sides, we get:

cos y = ±C√(x^2 + 1)

Therefore, the general solution of the differential equation is given by:

cos y = C√(x^2 + 1)

where C is an arbitrary constant. Hence, the correct option is (d) None of these.

Learn more about differential equation here

https://brainly.com/question/1164377

#SPJ11

The general solution to the given differential equation is

y = ± √(1 / (2ln|t| + 4/t - C2))

To solve the given differential equation, we can use the method of separable variables. Let's go through the steps:

Rearrange the equation to separate the variables:

t^2y' + 2ty - y^3 = 0

Divide both sides of the equation by t^2:

y' + (2y/t) - (y^3/t^2) = 0

Now, we can rewrite the equation as:

y' + (2y/t) = (y^3/t^2)

Separate the variables by moving the y-related terms to one side and the t-related terms to the other side:

(1/y^3)dy = (1/t - 2/t^2)dt

Integrate both sides of the equation:

∫(1/y^3)dy = ∫(1/t - 2/t^2)dt

To integrate the left side, let's use a substitution. Let u = y^(-2), then du = -2y^(-3)dy.

-1/2 ∫du = ∫(1/t - 2/t^2)dt

-1/2 u = ln|t| + 2/t + C1

-1/2 (y^(-2)) = ln|t| + 2/t + C1

Multiply through by -2:

y^(-2) = -2ln|t| - 4/t + C2

Now, take the reciprocal of both sides to solve for y:

y^2 = (-1) / (-2ln|t| - 4/t + C2)

y^2 = 1 / (2ln|t| + 4/t - C2)

Finally, taking the square root:

y = ± √(1 / (2ln|t| + 4/t - C2))

Therefore, the general solution to the given differential equation is:

y = ± √(1 / (2ln|t| + 4/t - C2))

Learn more on differential equation here https://brainly.com/question/1164377

#SPJ1

The correct answer is D.

The variable of time that could cause a student’s GPA to increase is studying.

For such more questions on GPA

https://brainly.com/question/19426550

#SPJ8

As per the given graph, the shape of the coordinate is square.

The term coordinate in math is defined as a set of numbers or numbers and letters together that show you a position on a map.

Here we given that  the coordinates (1, 1), (4, 4), (7, 1), and (4, -2) are joined.

Then we have to identified the form of the shape that has been formed using the coordinates.

Here we know that when the coordinates are joined, then the following graph can be obtained and when we observe that all the sides of the figure formed are of the same length and the diagonals bisect each other at 90°.

Through the graph we have identified that the lengths of the diagonals are equal and the opposite sides are parallel.

Therefore, the properties of a square are matched.

To know more about Coordinates here,

https://brainly.com/question/27749090

#SPJ4

The condition imposed such that a₁X₁ + a₂X₂ +.....+ aₙXₙ is an unbiased estimator of μ must be that ∑a = 1

We are given that X₁, X₂, ... Xₙ constitute a random sample from the population with the mean μ.

This implies, E(X) = μ

Now we have another set of data here, a₁X₁ + a₂X₂ +.....+ aₙXₙ

For a₁X₁ + a₂X₂ +.....+ aₙXₙ to be an unbiased estimator of μ, we should have

E(∑aX) = μ

or, ∑a E(X) = μ

Now we already know that

E(X) = μ

Hence we get

∑a = 1

Hence condition imposed must be that ∑a = 1

To learn more about Estimation visit

https://brainly.com/question/14368422

#SPJ4

Correct Question

If X₁, X₂, ... Xₙ constitute a random sample from the population with the mean μ, what condition must be imposed on the constants a₁, a₂, ... aₙ so that a₁X₁ + a₂X₂ +.....+ aₙXₙ is an unbiased estimator of μ?

And The Answer is:

..........a)12

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{a = - 11}}}}}\)

Step-by-step explanation:

\( \sf{4a - 2(3a + 8) = 6}\)

Distribute 2 through the parentheses

\( \longrightarrow{ \sf{4a - 6a - 16 = 6}}\)

Collect like terms

\( \longrightarrow{ \sf{ - 2a - 16 = 6}}\)

Move 16 to right hand side and change it's sign

\( \longrightarrow{ \sf{ - 2a = 6 + 16}}\)

Add the numbers: 6 and 16

\( \longrightarrow{ \sf{ - 2a = 22}}\)

Divide both sides by 2

\( \longrightarrow{ \sf{ \frac{ - 2a}{ - 2} = \frac{22}{ - 2}}} \)

Calculate

\( \longrightarrow{ \sf{a = - 11}}\)

Hope I helped !

Best regards! :D

Answer:

5/16= 0.3125 lbs

Step-by-step explanation:

Answer:

the answer is 80 can i have brainlyist for answeroing first

Step-by-step explanation:

The x-intercept is 5 and the y-intercept is 2.

The standard form of the line is 2x + 5y = 10.

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis. In other words, the x -intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0.

Hence, the x-intercept is 5 and the y-intercept is 2.

Let's find the equation in standard form.

Ax + By = C

where

Using slope intercept form,

y = mx + b

where

Hence, using (5, 0) and (0, 2)

m = 2 - 0 / 0 - 5

m = - 2 / 5

Therefore.

y = - 2 / 5x + 2

Hence, let's multiply through by 5 to eliminate the fraction

5y = -2x + 10

Therefore, the standard form is as follows:

2x + 5y = 10

learn more x and y-intercepts here: https://brainly.com/question/14180189

#SPJ1

Step-by-step explanation:

2x, and it's acute isoscels triangle!

Hey love!

Answer:

x = 67.5 deg

Classification: Acute isosceles triangle

Step-by-step explanation:

We know that x is equal on both sides, since a whole triangle equals 180 degrees we can subtract 45 degrees from 180 dividing it into two, equaling a acute triangle since every degree is under 90 in an isosceles shape.

Hope this helps you out! ✿◕ ‿ ◕✿ Sincerely, Kelsey from Brainly.

~ #LearnWithBrainly ~

The mean absolute deviation for the group of household incomes is approximately 14.8 (rounded to the nearest tenth).

To calculate the mean absolute deviation (MAD) for a group of data, we follow these steps:

Find the mean (average) of the data set.

Subtract the mean from each data point, obtaining the deviations.

Take the absolute value of each deviation.

Find the mean of the absolute deviations.

Given the household incomes for 10 different households:

38, 45, 76, 93, 50, 54, 29, 44, 62, 31

Let's calculate the MAD step by step:

Find the mean (average):

Mean = (38 + 45 + 76 + 93 + 50 + 54 + 29 + 44 + 62 + 31) / 10

Mean = 482 / 10

Mean = 48.2

Calculate the deviations:

Deviation for each data point = Data point - Mean

Deviation for 38 = 38 - 48.2 = -10.2

Deviation for 45 = 45 - 48.2 = -3.2

Deviation for 76 = 76 - 48.2 = 27.8

Deviation for 93 = 93 - 48.2 = 44.8

Deviation for 50 = 50 - 48.2 = 1.8

Deviation for 54 = 54 - 48.2 = 5.8

Deviation for 29 = 29 - 48.2 = -19.2

Deviation for 44 = 44 - 48.2 = -4.2

Deviation for 62 = 62 - 48.2 = 13.8

Deviation for 31 = 31 - 48.2 = -17.2

Take the absolute value of each deviation:

Absolute deviation for each data point = |Deviation|

Absolute deviation for -10.2 = 10.2

Absolute deviation for -3.2 = 3.2

Absolute deviation for 27.8 = 27.8

Absolute deviation for 44.8 = 44.8

Absolute deviation for 1.8 = 1.8

Absolute deviation for 5.8 = 5.8

Absolute deviation for -19.2 = 19.2

Absolute deviation for -4.2 = 4.2

Absolute deviation for 13.8 = 13.8

Absolute deviation for -17.2 = 17.2

Find the mean of the absolute deviations:

Mean Absolute Deviation (MAD) = (10.2 + 3.2 + 27.8 + 44.8 + 1.8 + 5.8 + 19.2 + 4.2 + 13.8 + 17.2) / 10

MAD = 148 / 10

MAD = 14.8

To the nearest tenth, this means that the mean absolute deviation for the group of household incomes is around 14.8.

for such more question on mean absolute deviation

https://brainly.com/question/16850458

#SPJ8

Answer: There are 24336000 different codes that are possible.

Step-by-step explanation:

We know that,

Total alphabets = 26

Total digits = 10

Choices for First place = 26+10=36

Choices for next 3 places = 10 x 10 x 10 = 1000

Choices for last 2 places = 26 x 26 = 676

Total different codes are possible = 36 x 1000 x 676

=24336000

Hence, there are 24336000 different codes that are possible.

23.1 months long should the loan last for her to stay inside her spending limit.

Given that,

Merissa needs a $12,000 loan to buy a used yacht. She examines her monthly spending plan and determines that $250 is the most she can afford to pay each month. A 6.1% loan is available from the bank.

We have to find how long should the loan last for her to stay inside her spending limit.

We know that,

A series of payments made over time are called an annuity.

The future value = annuity x [(1 + i)ⁿ - 1] / i

This can be calculated using the formula for future value annuities, which is;

FV(annuity) = P [(1 + i)ⁿ - 1] / i

So,

12000 = 250 ((1 + 0.061)ⁿ)-1) / 0.061

Now n will be

n = 23.1 approximately 2 years.

Therefore, 23.1 months long should the loan last for her to stay inside her spending limit.

To learn more about month visit: https://brainly.com/question/29180072

#SPJ1

The main strength of projective tests is that they have high inter-rater reliability, meaning different examiners are likely to find similar results when administering the test to the same individual.

The main strength of projective tests lies in their ability to yield consistent results across different examiners. This high inter-rater reliability ensures that if multiple examiners administer the test to the same individual, they are likely to arrive at similar findings. This reliability is important in establishing the consistency and trustworthiness of the test.

Furthermore, projective tests are often considered valid, meaning they measure the psychological constructs or traits they are designed to assess. Although projective tests rely on subjective interpretation and are not as standardized as other psychological assessment methods, they can provide valuable insights into an individual's thoughts, feelings, and motivations. They allow individuals to project their unconscious or hidden aspects onto ambiguous stimuli, providing a window into their psychological functioning.

Overall, the main strengths of projective tests lie in their inter-rater reliability and potential for valid psychological assessment, offering unique perspectives and understanding of individuals' inner experiences.

Learn more about projective tests here:

https://brainly.com/question/32690533

#SPJ11

The input value that produces the same output value for f(x) and g(x) on the graph is x = 1.To find the input value that produces the same output value for both functions, we need to determine the x-coordinate of the point(s) where the two lines intersect.

These points represent the values of x where f(x) and g(x) are equal.

The line labeled f(x) passes through the points (-2, 4), (0, 2), and (1, 1). Using these points, we can determine the equation of the line using the slope-intercept form (y = mx + b). Calculating the slope, we get:

m = (2 - 4) / (0 - (-2)) = -2 / 2 = -1

Substituting the point (0, 2) into the equation, we can find the y-intercept (b):

2 = -1(0) + b

b = 2

Therefore, the equation for f(x) is y = -x + 2.

Similarly, for the line labeled g(x), we can use the points (-3, -3), (0, 0), and (1, 1) to determine the equation. The slope is:

m = (0 - (-3)) / (0 - (-3)) = 3 / 3 = 1

Substituting (0, 0) into the equation, we can find the y-intercept:

0 = 1(0) + b

b = 0

Thus, the equation for g(x) is y = x.

To find the input value that produces the same output for both functions, we can set the two equations equal to each other and solve for x:

-x + 2 = x

Simplifying the equation:

2x = 2

x = 1.

For more such questions on Intersect:

https://brainly.com/question/28744045

#SPJ8

Answer:

34°

Step-by-step explanation:

A triangle measures 180°

An isosceles triangle has two angles and sides with equal measurements.

We know that one angle is 112°. Thus, we can use that to form an equation to solve for the unknown values:

112° + x + x = 180°

112° + 2x = 180°

2x = 68

x = 34°

The other two angles each measure 34°.

Check:

112 + 34 + 34 = 180

hope this helps and is right!! p.s. i really need brainliest :)

Answer:

34°

Step-by-step explanation:

Sum of interior angles of a triangle is 180°

Two of the interior angles of an Isosceles triangle are equal

Given one of the interior angles is 112° then the remaining two angle must be equal:

⇒ 112 + 2x = 180

⇒ 2x = 68

⇒ x = 34°

Answer:

$28.42

Step-by-step explanation:

First let's calculate the cost per gallon.

We can do this by simply dividing the cost of 4 gallons by 4

1 gallon of milk cost 16.24/4 = 4.06

We want to find the cost of 7 gallons.

We can easily do this by multiplying the cost of one gallon by 7

7 gallons of milk cost 7 * 4.06 = $28.42

In a diagram,

Then,

For example, suppose that n=2; thus,

We can form a new triangle DEF whose side EF is parallel to CA; therefore,

The given equation is ex+2^-x+2 cos x-6= 0. We are to find an approximation of its root in [1.2] to an absolute error less than 10^-10 with one of the methods covered in class.

Therefore, the correct option is (D)

Let's check the given equation graphically in the given interval i.e [1.2]We can use Newton Raphson method to approximate the root of the equation. Newton Raphson MethodNewton Raphson method is used to find the roots of a differentiable function. Newton Raphson method is based on the following formula:Xn+1 = Xn- f(Xn)/f'(Xn)Where,Xn = Current approximationXn+1 = Next approximationf(Xn) = Function value at Xnf'(Xn) = Derivative of function at XnHere, the given function is ex+2^-x+2 cos x-6= 0.Let's find its derivative:dx/dy (ex+2^-x+2 cos x-6)= ex - 2^-x ln 2 - 2 sin xHere, x = 1.2Taking initial approximation X0 = 1.2

Using the Newton Raphson formula

X1 = X0 - f(X0)/f'(X0)

Putting the values:

f(X0) = e1.2 + 2^-1.2 + 2 cos 1.2 - 6 = -0.287

f'(X0) = e1.2 - 2^-1.2 ln 2 - 2

sin 1.2 = 2.2311 X1 = 1.2 - (-0.287/2.2311) = 1.327091X1 = 1.327091 Now, Let's find the absolute error.Absolute Error = | X1 - X0 |Absolute Error = | 1.327091 - 1.2 | = 0.127091 Since the value of absolute error is greater than 10^-10, we need to perform one more iteration.Using X0 = 1.327091Using the Newton Raphson formula

X2 = X1 - f(X1)/f'(X1)Putting the values:

f(X1) = e1.327091 + 2^-1.327091 + 2 cos 1.327091 - 6 = -0.00000002925f

'(X1) = e1.327091 - 2^-1.327091 ln 2 - 2 sin 1.327091 = 2.225228576X2 = 1.327091 - (-0.00000002925/2.225228576) = 1.3270910564Now, let's find the absolute error. Absolute Error = | X2 - X1 |Absolute Error = | 1.3270910564 - 1.327091 | = 0.0000000564Since the absolute error is less than 10^-10, we can say that the approximation of the root in [1.2] is 1.3270910564.

To know more about equation visit:

https://brainly.com/question/29657983

#SPJ11

Using the master theorem, the Θ-class are: a) T(n) = Θ(n)b) T(n) = Θ(n) and c) T(n) = Θ(√n log n).

a) T(n)=2T(n/2)+n³

To find the Θ class of T(n), we need to apply the Master Theorem. In the Master Theorem, if T(n) = aT(n/b) + f(n) where a >= 1, b > 1, and f(n) is an asymptotically positive function, then:

T(n) = Θ(nᵈ)

where d = logₐ(b).

Here a = 2, b = 2 and f(n) = n³.

So, d = log₂(2)

= 1T(n)

= Θ(nᵈ)

= Θ(n¹)

= Θ(n)

Therefore, the Θ class of T(n) is Θ(n).

b) T(n)=2T(n/2)+3n−2

Similarly to part (a), we can find the Θ class of T(n) by using the Master Theorem.

In this case, a = 2, b = 2 and f(n) = 3n - 2.

Here, d = log₂(2)

= 1T(n)

= Θ(nᵈ)

= Θ(n¹)

= Θ(n)

Therefore, the Θ class of T(n) is Θ(n).

c) T(n)=4T(n/2)+nlogn

For this recurrence relation, a = 4, b = 2 and f(n) = nlogn.

In this case, d = log₄(2) = 0.5.

So,

T(n) is

= Θ(nᵈ)

= Θ(n⁰.⁵)

= Θ(√n log n)

Therefore, the Θ class of T(n) is Θ(√n log n).

Hence, the correct options are:a) T(n) = Θ(n)b) T(n) = Θ(n)c) T(n) = Θ(√n log n).

Learn more about the master theorem from the given link-

https://brainly.in/question/55070777

#SPJ11

Step-by-step explanation:

sss similarity theorem

The latest time for pickup, found by converting the 150 minutes maximum time provided by the school, from minutes to hours is about 5:45 pm

Minutes can be converted into hours by dividing the number of minutes by 60, which is the number of minutes in an hour.

The time that school ends = 3:15 pm

The latest time for pick up after school care = 150 minutes after school ends

Therefore, the latest time for pick up after school care = 3:15 pm + 150 minutes

60 minutes = 1 hour

150 minutes = (1/60) × 150 = 2.5

The latest for pick up = 3:15 pm + 2.5 hours = 5:45 pm

Learn more on unit conversion here: https://brainly.com/question/14614674

#SPJ4

The dimensions of the cylindrical can that will minimize the cost of the metal to manufacture it is 0.04 m and 0.027 m for height and radius respectively.

The given information of the question is that we have to create a cylindrical can that holds 1.4 litres of oil and we have to find the dimensions that will minimize the cost of the metal to manufacture the can.

We will solve the given problem through Lagrange Multipliers method.

Steps for solving the given problem are as follows:

Step 1: Let us assume that the cylindrical can has radius r and height h.

Therefore, we have to find the dimensions of r and h to minimize the cost of the metal.

Step 2: The total surface area (SA) of the cylindrical can is given as: SA = 2πr² + 2πrh

This equation represents the cost of the metal to manufacture the cylindrical can.

Step 3: The volume of the cylindrical can is given as: V = πr²h = 1.4 litres.

Now, let us convert 1.4 litres into cubic metres.

1 litre = 10⁻³ cubic metres 1.4 litres = 1.4 × 10⁻³ cubic metres

V = 1.4 × 10⁻³ = πr²h

Therefore, h = (1.4 × 10⁻³)/(πr²)

Step 4: Now, we have to use the Lagrange Multipliers method to find the dimensions that will minimize the cost of the metal.

Let us assume that C is the cost of the metal.

C = k(2πr² + 2πrh)

This is the objective function.

Now, let us assume that f is the constraint function.

f = πr²h - 1.4 × 10⁻³

This is the constraint function.

Step 5 : The next step is to find the partial derivatives of both the objective function and the constraint function with respect to r, h and λ (Lagrange Multiplier).

∂C/∂r = 4πrk + 2πh∂C/∂h

= 2πr(k + λ) + 2πr²∂C/∂λ

= f∂f/∂r

= 2πrh∂f/∂h

= πr²∂f/∂λ

= 0

Step 6: Now, we have to solve these equations and find the values of r and h that minimize the cost of the metal.

4πrk + 2πh = 2πr(k + λ) + 2πr²......(1)πr²h = 1.4 × 10⁻³......(2)

2πrh = λπr²......(3)

Substitute (3) in (1) and simplify it.

4πrk + 2πh = 2πr(k + λ) + 2πr²2πr(k + λ) + λπr² = 2πr² + 2πhλr² = 2h/k

Substitute λr² = 2h/k in (2) and simplify it.

π(2h/k) = 1.4 × 10⁻³h

= (1.4 × 10⁻³)(k/2π)π(2/k)(1.4 × 10⁻³)(k/2π)

= 1.4 × 10⁻³r²

= 1.4 × 10⁻³/(2πh/k)

= 0.00001003h

= 0.04 m and r

= 0.027 m.

For similar question on cylindrical.

https://brainly.com/question/28103147

#SPJ11

In the video about the construction of the insect phylogeny, the researchers faced the problem that there was not enough computational power in all of the world to construct every possible tree.

The use of computing algorithms, tools, and programmes to phylogenetic analysis is known as computational phylogenetics. The purpose is to create a phylogenetic tree that represents a hypothesis about a set of genes, species, or other taxa's evolutionary ancestry.

There was not enough computational power to construct every possible tree in all of the world. So the probable solution for this problem will be:

Use math to avoid constructing improbable trees

To learn more about Phylogenetic, click here https://brainly.com/question/2189834

#SPJ4