find the arc length function for the curve y = sin−1(x) 1 − x2 with starting point (0, 1).

Answers

Answer 1

Tthe arc length function for the curve y = sin−1(x) 1 − x2 with starting point (0, 1) is L(x) = (1/2) * (pi/2 - sin−1(x)) + (1/2) * x * sqrt(1 - x^2), where x is between 0 and 1.

To find the arc length function for the curve y = sin−1(x) 1 − x2 with starting point (0, 1), we first need to find the derivative of the function. Taking the derivative of the function, we get:

dy/dx = 1 / sqrt(1 - x^2)

Now, we can use the formula for arc length to find the arc length function:

L(x) = ∫[0,x] sqrt(1 + (dy/dx)^2) dx

Substituting the derivative of y with respect to x into this formula, we get:

L(x) = ∫[0,x] sqrt(1 + (1 / (1 - x^2))^2) dx

This integral can be evaluated using a substitution or by using a table of integrals. After evaluating the integral, we get the arc length function for the curve:

L(x) = (1/2) * (pi/2 - sin−1(x)) + (1/2) * x * sqrt(1 - x^2)

Therefore, the arc length function for the curve y = sin−1(x) 1 − x2 with starting point (0, 1) is L(x) = (1/2) * (pi/2 - sin−1(x)) + (1/2) * x * sqrt(1 - x^2), where x is between 0 and 1.

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Related Questions

The cost of a 4 pack of apple juice is $ 2.24. Write an equation that relates the cost in dollars, y, to the number of apple juice cartons, x.

Answers

Answer:

Cost = y/x

Step-by-step explanation:

The cost of a 4 pack of apple juice is $ 2.24.

We need to write an equation that relates the cost in dollars, y, to the number of apple juice cartons, x.

As 4 packs = $2.24

1 pack = 0.56

So, the equation can be :

Cost = y/x


The weight of the items in a truck is ton.
How many pounds do the items in the
truck weigh?

Answers

1 ton equals 2000 pounds. Therefore the answer is 2000

Please help or I’m gonna fail

Please help or Im gonna fail

Answers

Answer:

D. 3/4

Step-by-step explanation:

If Gabe's Soccer Ball Company is able, due to competitive pressure, to charge $60 for a new soccer ball, while one soccer ball costs $28 to make, plus $15,000 per month in overhead costs (mostly Gabe's extravagant salary) find: a. The average cost c(x) of producing each soccer ball b. Algebraically find the number of soccer balls Gabe's company must produce per month in order to break even (Profit = 0). Profit = Total Revenue – Total Cost c. Algebraically find the number of soccer balls Gabe's company must make to earn a profit of $10,000 per month. d. If Gabe took a pay cut to reduce the overhead costs to $8,000 per month, how many fewer balls would the company have to sell to break even. (There are multiple ways to get this result).

Answers

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Selling price= $60

Unitary variable cost= $28

Fixed costs= $15,000

First, we need to calculate the average total cost:

Average cost= total cost / number of units

For example, for 1 unit and 10,000 units:

1 unit:

Average cost= 15,028/1 = 15,028

10,000 units:

Average cost= (15,000 + 28*10,000) / 10,000

Average cost= $29.5

Now, we can calculate the break-even point in units:

0= (60*x) - (28*x) - 15,000

x= number of units to break-even

0= 32x - 15,000

15,000/32= x

468.75=x

break-even point in units= 469

For the desired profit of $10,000:

10,000 = (60*x) - (28*x) - 15,000

25,000= 32x

781.25= x

Break-even point= 782 units

Finally, fixed costs dropped by $8,000:

0= 32x - 7,000

x= 7,000/32

x= 218.75

Break-even point= 219

Difference= 250 units

Determine the number of real solutions of 2x^2−5x+20=0


a) Infinitely Many
b) None
c) 1
d)2

Answers

Answer:

Infinitely Many

Step-by-step explanation:

I. GIVEN TRIANGLE POR, DETERMINE THE FOLLOWING.

please help me out with this ​

I. GIVEN TRIANGLE POR, DETERMINE THE FOLLOWING. please help me out with this

Answers

34

Step-by-step explanation:

 122

This is a lengthy question ill go through all the formulas

This is a right triangle which means u can use pythagorean theorem to find QP

formula :

\(a^{2} +b^{2} =c^{2}\)

Note that \(c^{2}\) is always the hypotenuse(the hyp is always opposite to ninety degrees)

so lets substitute

=> \(a^{2} +17^{2} =28^{2}\)

=> \(a^{2} +289 =784\)

subtract 289 both sides

\(= > a^{2}=495\)

Now square root both

\(\sqrt{ a}^{2}=\sqrt{495}\)

==> \(3\sqrt{55}\) or 22.2 (answer)

But for the other three u have to use another formula any of sin, tan,cos while using For example angle Q and then use any and do inverse it will be very easy after u know all the formulas of Sin,cos, tan

SOHCAHTOA

^

Thats an acronym   for the formula

Sin= Opposite/ hyp

Cos= Adjustent/Hyp

Tan= Opposite/Adjustent

Which algebraic expression below represents four multiplied by a number?
A. 4 – x
B. x + 4
C. 4x
D.

Answers

Answer:

Step-by-step explanation:

option c is correct

product of two numbers can be written as 4x

Describe the likelihood that the next mountain goat, deer, and moose caught are all unmarked. <3

Describe the likelihood that the next mountain goat, deer, and moose caught are all unmarked. &lt;3

Answers

Answer: im on the same question

Step-by-step explanation:

sorry

The probability is the ratio of the favorable event to the total number of events. Then the probability of the elk caught in the park being unmarked will be 92.44%.

What is probability?

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.

The total number of elk is 5,625.

The number of elk that were marked is 225.

Then the number of elk that were unmarked will be

→ 5625 - 225 = 5,200

Then the probability of the elk caught in the park being unmarked will be

\(\rm P = \dfrac{5200}{5625}\\\\P = 0.9244 \ or \ 92.44\%\)

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NEED HELP ASAPPP!!
A sales promotion for Christmas is advertising all PS5 games for $45.25 per game, up to 6 games, with a $10 subscription fee. The total cost, y, for x number of PS5 games can be modeled by a linear function.

What is the range of the function for this situation?
A. {0,1, 2, 3, 4, 5, 6}

B. {0,55.25, 100.50, 145.75, 191.00, 236.25, 281.50}

C. 0 ≤ y ≤ 281.50

D. 0 ≤ x ≤ 6

Answers

Answer:

0 ≤ y ≤ 281.50

Step-by-step explanation:

i did the math

)) A farmer placed an order for 16 2/3 tons of fertilizer. He calculates that the corn fields
will require 8 5/6 tons of it. How much fertilizer will the farmer have left for his other crops?

Answers

Answer:

7 5/6

Step-by-step explanation:

16 2/3 - 8 5/6

16 4/6- 8 5/6

7 5/6

Find the largest number δ such that if |x − 1| < δ, then |2x − 2| < ε, where ε = 1.
δ ≤
Repeat and determine δ with ε = 0.1.
δ ≤

Answers

If ε = 1, the maximum value of δ that satisfies the condition |x - 1|. satisfied <; δ means |2x - 2| <; ε is δ ≤ 0.5. For ε = 0.1, the maximum value of δ that satisfies the condition is δ ≤ 0.05 for largest number.

We need to find the maximum value of δ such that |x - 1|. Applies <; δ, then |2x - 2| <; e.

If \(ε = 1\):

We begin by analyzing the inequality |2x - 2|. <; 1. Simplify this inequality to -1 <. 2x - 2 <; 1. Add 2 to all parts of the inequality and you get 1 <. 2x < 3. Dividing by 2 gives 0.5 < × < 1.5. Since the difference between the upper and lower bounds is 1, the maximum value of δ is 0.5.

If \(ε = 0.1\):

Apply the same procedure to the inequality |2x - 2|. Simplifying to < by 0.1 gives -0.1 <. 2x - 2 <; Add 2 to every part of 0.1 and you get 1.9 <. 2x < 2.1. Divide by 2 to get 0.95 <. × < 1.05. The difference between the upper and lower bounds is 0.1, so the maximum value of δ is 0.05.

Therefore, \(ε = 1 δ ≤ 0.5 and ε = 0.1 δ ≤ 0.05\). 


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Rewrite the following equation in standard form

y = 2x + 8

Answers

Answer:

2x - y = -8

Step-by-step explanation:

The standard form of the equation is -2x + y = 8.

when the angle of an incline with a block resting on it increases the normal support force? A) decreases B) increases C) stays the same

Answers

Answer:

normal force decreases

Step-by-step explanation:

N=mgcosθ, and cosine decreases as theta increases

consider joining our disc*rd server for unlimited hw help! we also have an active giveaway rn. code: RPEdT3erFm <3

Answer:

A) decreases

Step-by-step explanation:

As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.

hari drags a load of 60 kilogram along a distance of 12 m what amount of work does he do also mention mention the type of work​

Answers

Hari does 7,056 joules of work while dragging the load of 60 kilograms along a distance of 12 meters. The type of work performed in this scenario is mechanical work.

The amount of work done can be calculated using the formula:

Work = Force × Distance × cos(θ)

In this case, the force applied by Hari is equal to the weight of the load, which can be calculated using the equation:

Force = Mass × Acceleration due to gravity

Given that the mass of the load is 60 kilograms and the acceleration due to gravity is approximately 9.8 m/s², the force can be calculated as:

Force = 60 kg × 9.8 m/s² = 588 N

Since the force and distance are in the same direction, the angle (θ) between them is 0°, and therefore the cosine of 0° is 1.

Plugging in the values into the work formula:

Work = 588 N × 12 m × cos(0°)

    = 588 N × 12 m × 1

    = 7,056 N·m (joules)

Hence, Hari does 7,056 joules of work while dragging the load. This work is categorized as mechanical work since it involves the application of a force to move an object along a distance.

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Assignment
If tun (A+B) =1/7 and tan A=1/3, find Tan B​

Answers

Answer:

\( - \frac{ 2}{11} \)

Step-by-step explanation:

\( \tan (A + B) = \frac{\tan A + \tan B}{1 - \tan A . \tan B} \\ \\ \frac{1}{7} = \frac{ \frac{1}{3} +\tan B }{1 - \frac{1}{3} . \tan B} \\ \\ \frac{1}{7} = \frac{ \frac{1 + 3\tan B}{3} }{ \frac{3 -\tan B }{3} } \\ \\ \frac{1}{7} = \frac{1 + 3\tan B}{3 - \tan B} \\ \\ 7(1 + 3\tan B )= 3 - \tan B \\ \\ 7 + 21\tan B = 3 - \tan B \\ \\ 21\tan B + \tan B = 3 - 7 \\ \\ 22\tan B = - 4 \\ \\ \tan B = \frac{ - 4}{22} \\ \\\huge \purple {\boxed {\tan B = - \frac{ 2}{11}}} \)

If AB = 45, find the length of AJ.

If AB = 45, find the length of AJ.

Answers

Answer:

AB= 45 --> In 1st space untill 5th space

So, 45/5 = 9 unit each space

AJ ?

Using 2 space 1st until 2nd

so, 9 unit × 2 = 18 unit

I hope this helps^_^

If AB = 45, find the length of AJ.

NO LINKS!!! PLS HELP ME IM TRYING TO GRADUATE PLSSS !!! Find the midpoint of the segment below and enter its coordinates as an
ordered pair. If necessary, express coordinates as fractions, using the slash
mark (/) for the fraction bar.
(1,-1) (4,-6)

NO LINKS!!! PLS HELP ME IM TRYING TO GRADUATE PLSSS !!! Find the midpoint of the segment below and enter

Answers

Answer:

x = 5/2 , y = -7/2

Step-by-step explanation:

r's your solution

=> formula for finding midpoint =.( X1 + X2/)/2 , (Y1+Y2)/2

=> putting the value of in formula

=> x= 4+1/2 , y = -1-6/2

=> x = 5/2 , y = -7/2

hope it helps

(Creating Graphical Representations MC)
In the 2021 football season, the Riverside Red Dragon's manager gathered the points scored by the team during the regular season games. The following data set shows the values
collected by the manager.
(17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3)
Which of the following stem-and-leaf plots correctly graphs the data set? Key 1|1 = 11

Answers

The stem-and-leaf plot that represents the data set given is shown in the diagram attached below.

What is a Stem-and-leaf Plot?

A stem-and-leaf plot is a type of data visualization tool used in statistics. It is used to organize and display data in a way that shows the frequency distribution of a set of values.

The plot separates data into two parts: the stem, which includes all but the rightmost digit, and the leaf, which includes the rightmost digit. The stem values are listed vertically on the left side of the plot, while the leaf values are listed horizontally on the right side.

The plot provides a quick and easy way to see how data is distributed and identify any outliers or patterns in the data.

The stem-and-leaf plot for the data set, 17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3 is given in the image below.

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(Creating Graphical Representations MC)In the 2021 football season, the Riverside Red Dragon's manager

The probability that a randomly selected person from this sample used the Chrome browser and used a laptop computer is

Answers

The probability that a randomly selected person from this sample used the Chrome browser and used a laptop computer is 0.308.

How to determine the probability

To determine the probability that a person selected would e using the Chrome browser and a laptop, we will proceed as follows:

From the table, Chrome and laptop = 77

Total number of occurrences = 250

Expressing this as a probability, we will have: 77/250

= 0.308

Therefore, the probability would be 0.308

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What is the slope of y=5/4x-7/4

Answers

The answer is:

5/4

Work/explanation:

Let's work out the slope of the line.

The equation is in y = mx + b form where m = slope; b = y intercept.

Similarly, in y=5/4x - 7/4, the slope is 5/4.

Hence, the answer is 5/4.

Using the Linear equation 4x-3y=12, express each of the following.
y in terms of x. y=

Using the Linear equation 4x-3y=12, express each of the following.
x in terms of y. x=

Answers

Using the given linear function, it is found that the expressions are given by:

\(y = \frac{4x}{3} - 4\).\(x = \frac{3y}{4} + 3\).

What is the given linear function?

It is:

4x - 3y = 12.

To find y in terms of x, we isolate y, hence the expression is given by:

\(3y = 4x - 12\)

\(y = \frac{4x}{3} - 4\)

To find x in terms of y, we isolate x, hence the expression is given by:

\(4x = 12 + 3y\)

\(x = \frac{3y}{4} + 3\)

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yooo who tryna talk...im 14 lol no creeps

Answers

Answer:

that is what a creep would say.  

Step-by-step explanation:

No JK :)

LOL

Answer:

me I want to talk cause I need someone to talk to

Which of the following groups of angles can be trisected using only a
compass and straightedge?

A. All angles less than 180°
B. All angles greater than 180°
C. All acute angles
D. All right angles
HELP ASAP PLEASEE!!!

Answers

Answer:

the answer is

All the angles less than 180

HELP HELP HELP.ASAP PLEASE

HELP HELP HELP.ASAP PLEASE

Answers

Answer:

3

Step-by-step explanation:

Y=-6x+2 -12-2y=-4 how many solutions does this linear equation have?

Answers

This linear equation system has a unique solution, which means it has only one solution.The given equations are:

Y = -6x + 2
-12 - 2y = -4

To find the number of solutions for this linear equation system, we can start by solving one equation for one variable and then substituting the solution into the other equation.

Let's solve the first equation, Y = -6x + 2, for Y:

Y = -6x + 2

Now let's solve the second equation, -12 - 2y = -4, for y:

-12 - 2y = -4

Adding 12 to both sides of the equation:

-2y = 8

Dividing both sides of the equation by -2:

y = -4

Now, we can substitute the value of y into the first equation:

Y = -6x + 2

Y = -6x + 2

Since Y is equal to -6x + 2 and y is equal to -4, we can set the two expressions equal to each other:

-6x + 2 = -4

Adding 4 to both sides of the equation:

-6x + 6 = 0

Subtracting 6 from both sides of the equation:

-6x = -6

Dividing both sides of the equation by -6:

x = 1

So, the solution to this linear equation system is x = 1 and y = -4.

Therefore, this linear equation system has a unique solution, which means it has only one solution.

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Find the distance between the points (-5,-2) and (7,3).

Answers

Answer:

Step-by-step explanation:

Find the distance between the points (-5,-2) and (7,3).
Find the distance between the points (-5,-2) and (7,3).

a water treatment plant needs to maintain the ph of the water in the reservoir at a certain level. to monitor this, they take 2 oz. of water at 37 locations every hour, measure the ph at each of those locations, and find their average. if the ph level of the reservoir is ok, the results at each location will have varying results, with an average ph of 8.5 and a standard deviation of 0.22. if the ph level of the reservoir is ok, what is the probability that the sample average is more than 8.47? group of answer choices

Answers

The probability that the sample average is more than 8.47 is 0.4406 if the pH level of the reservoir is ok

To calculate this, we will use a standard normal distribution table and the Z-score formula.

First, we need to calculate the Z-score for the sample average of 8.47. This is done by using the Z-score formula:

Z-score = (x - mean)/standard deviation

where x is the sample average, mean is the average of all samples, and standard deviation is the standard deviation of all samples.


In this case, the Z-score is:

Z-score = (8.47 - 8.50)/0.22 = -0.14


Then, we need to look up the Z-score in a standard normal distribution table. The probability of the sample average being more than 8.47 is equal to 1 minus the Z-score probability. So, in this case, the probability of the sample average being more than 8.47 is equal to 1 - 0.5594 = 0.4406.

Therefore, the probability that the sample average is more than 8.47 is 0.4406 if the pH level of the reservoir is ok.

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12 cookies were plain sugar cookies and 4 had icing on them. What is the ratio of iced cookies to plain cookies, in the lowest terms? 12:4 5:12 3:1 1:3

help

Answers

Answer:

3:1

Step-by-step explanation:

As there is 12 plain cookies and 4 had icing on them

we could write this as 12:4 but both have a factor of 4 simplifying it to 3:1

Pls give me brainliest

pls:(

Travertine at the Getty: Over 1.2 million square feet of travertine stone from Italy was used to construct the Getty Museum. It was mined in large slabs that measured 6 meters high, 12 meters wide, and 2 meters deep. Find the surface area of one of these slabs.

Travertine at the Getty: Over 1.2 million square feet of travertine stone from Italy was used to construct

Answers

The surface area of a "box" (or slab) is simply the area (length x width).

We have two faces whose dimensions are 12 by 2; two faces whose dimensions are 6 by 2; and two faces whose dimensions are 12 by 6. Therefore:

\(\begin{gathered} A1=12\times2\times2=48 \\ A2=6\times2\times2=24 \\ A3=12\times6\times2=144 \end{gathered}\)

So, the surface area of one of these slabs is:

\(A=48+24+144=216\)

Answer: 216 square meters

in a lrage city 64% of the population inder the age of 15 had a cold during hte last winter season a school nurse is hoping ot the lil

Answers

The probability that a randomly selected student from the school have a cold after receiving the flu vaccine is 0.27 or 27%.

The school nurse is hoping to limit the cold's spread among the students in her school. To do this, to administer flu vaccines to the students. However, the flu vaccine is only effective in preventing the cold in 75% of cases.

Now, let's calculate the probability that a randomly selected student from the school have a cold after receiving the flu vaccine.

Let:

P(Cold) be the probability of having a cold in the city (given as 64% or 0.64).

P(Not Cold) be the probability of not having a cold in the city (since P(Cold) + P(Not Cold) = 1).

P(Vaccine Effective) be the probability that the flu vaccine is effective (given as 75% or 0.75).

The probability of not having a cold after receiving the flu vaccine is given by:

P(Not Cold | Vaccine) = P(Not Cold) × P(Vaccine Effective)

P(Not Cold | Vaccine) = (1 - P(Cold)) × P(Vaccine Effective)

P(Not Cold | Vaccine) = (1 - 0.64) × 0.75

P(Not Cold | Vaccine) = 0.36 × 0.75

P(Not Cold | Vaccine) = 0.27

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Complete question:

In a large city, 64% of the population under the age of 15 had a cold during the last winter season. A school nurse is hoping to limit the ...

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