The arc length of the curve is 1.3125
What do you understand by length of the curve?The length of an arc is the separation of two locations along a segment of a curve.
A defined integral between the two points is used to calculate the area under a curve between two points. Integrate y = f(x) between a and b's limits to find the area under the curve y = f(x) between x = a & x = b. Integration within the defined bounds can be used to calculate this area.
the arc length formula
[tex]$$L=\int_C d s=\int_a^b \sqrt{1+\left(\frac{d x}{d y}\right)^2} d y$$[/tex]
now
[tex]$$\begin{aligned}16 x y^2-y^6 &=8 \\y^2\left(16 x-y^4\right) &=8 \\16 x-y^4 &=8 y^{-2} \\16 x &=8 y^{-2}+y^4 \\x &=\frac{1}{2} y^{-2}+\frac{1}{16} y^4\end{aligned}$$[/tex]
[tex]\frac{d x}{d y}=-y^{-3}+\frac{1}{4} y^3[/tex]
now differential line element is
[tex]$$\begin{aligned}d s &=\sqrt{1+\left(\frac{d x}{d y}\right)^2} d y \\&=\sqrt{1+\left(-y^{-3}+\frac{1}{4} y^3\right)^2} d y \\&=\sqrt{1+y^{-6}-\frac{1}{2}+\frac{1}{16} y^6} d y \\&=\sqrt{y^{-6}+\frac{1}{2}+\frac{1}{16} y^6} d y \\&=\sqrt{\left(y^{-3}+\frac{1}{4} y^3\right)^2} d y \\&=\left(y^{-3}+\frac{1}{4} y^3\right) d y\end{aligned}$$[/tex]
now arc length of the curve in the given interval
[tex]$$\begin{aligned}L &=\int_C d s \\&=\int_1^2\left(y^{-3}+\frac{1}{4} y^3\right) d y \\&=\left[-\frac{1}{2} y^{-2}+\frac{1}{16} y^4\right]_1^2 \\&=-\frac{1}{2}\left(\frac{1}{2^2}-\frac{1}{1^2}\right)+\frac{1}{16}\left(2^4-1^4\right) \\&=\frac{\mathbf{2 1}}{\mathbf{1 6}} \approx \mathbf{1 . 3 1 2 5}\end{aligned}$$[/tex]
this is the arc length of the curve
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An odd number is not divisible by 2.
no
Step-by-step explanation:
because it's a prime number
a trapezoid was transformed on a coordinate grid using the rule (x, y) → (–x, y). which of the following describes this transformation?
The transformation is called a reflection across X axis because the point (x,y) is projected from across X-axis as (x,-y).
What is transformation?A point, lines, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after.
transformation, refers to the object's ultimate shape and location.
According to the given data:This rule is represented by the reflect placed above a white x axis transformation (x, y) (–x, y).
While the x-coordinate remains the same, the y-coordinate has shifted from its initial position.
The overall description of this is (x, y) (–x, y).
The X-coordinate of a point that is reflected all across the X-axis remains constant. The Y-coordinate, on the other hand, is changed towards the opposite sign.
The transformation is called a reflection across X axis because the point (x,y) is projected from across X-axis as (x,-y).
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A stack of logs has 22 logs on the bottom layer. Each subsequent layer has 4 fewer logs than the previous layer. If the top layer has two logs, how many total logs are there in the pile?
Answer: ok here is ur answer
The total number of logs in the pile is 6.
Step-by-step explanation: i rlly hope this helps i hope u have a good day/night (: <3
HELP NEEDED ASAP/NOW......NO LINKS AND NO JOKING PLS
AUBSERD ANSWERS WILL BE REPORTED
From the given graph, we have that:
The ordered pairs are given as follows: (-5,2), (-3,0), (0,-3), (3,-6), (5, -8).
The table is given by:
x = -5, g(x) = 2.x = -3, g(x) = 0.x = 0, g(x) = -3.x = 3, g(x) = -6.x = 5, g(x) = -8.In function notation, we have that:
g(-5) = 2, g(-3) = 0, g(0) = -3, g(3) = -6, g(5) = -8.
How to get the ordered pairs from the graph of a function?To get the ordered pairs from the graph of a function, we have to:
Get the x-coordinate, that is, the value of the point on the horizontal axis.Get the y-coordinate, that is, the value of the point on the vertical axis.An ordered pair has the following notation: (x,y).
Hence, from the points on the graph, the ordered pairs are given as follows:
(-5,2), (-3,0), (0,-3), (3,-6), (5, -8).
How to write the ordered pairs in the table?To write the table from each ordered pair (x,y), we have that y = g(x), hence:
x = -5, g(x) = 2.x = -3, g(x) = 0.x = 0, g(x) = -3.x = 3, g(x) = -6.x = 5, g(x) = -8.How to write the function notation?We take the g(x) points from the table, replacing x by it's numeric value, hence:
g(-5) = 2, g(-3) = 0, g(0) = -3, g(3) = -6, g(5) = -8.
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What is 1+1? I really need help
Honestly don't understand this
Use the number line below, where RS = 4y+4 , ST=3y+4 , and RT=43. a. What is the value of y? b. Find RS and ST.
Ignore the equation on the top just use the number line
Answer: a. y=5
b. RS=24, ST=19
Step-by-step explanation:
a. RT=RS+ST
43=4y+4+3y+4
43=4y+3y+4+4
43=7y+8
7y=35
y=5
b. RS=4y+4
RS=4(5)+4
RS=20+4
RS=24
ST=3(5)+4
ST=15+4
ST=19
Lisa's work finding the value of the expression 9 + 2(1-7) is shown below. Determine whether or not her work is correct. If it is incorrect, show Lisa how to find the correct value. Problem: 9 + 2(1-7) Step 1: Step 2: Answer: 9+2(-6) 11(-6) -66
Answer:
9 + 2(1 - 7)
= 9 + 2(-6) Simplify the subtraction expression inside the parenthesis.
= 9 - 12 Multiply.
= -3 Subtract.
Each hour, 7.5 liters drain from a large water tank. The tank initially held 83 liters of water. What does the expression 83−7.5t represent?
The expression 83 - 7.5 t represents the amount of water that is left in the tank after t hours as 7.5 l of water drains every hour from the large water tank.
We are given that:
7,5 l of water drains from the large water tank every hour.
Also, the water level in the large water tank initially was 83 l
We need to tell what does the expression 83 - 7.5 t represent.
It represents the amount of water that is left in the tank after t hours as 7.5 l of water drains every hour from the large water tank.
Therefore, the expression 83 - 7.5 t represents the amount of water that is left in the tank after t hours as 7.5 l of water drains every hour from the large water tank.
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The forecasting method that is appropriate when the time series has no significant trend, cyclical, or seasonal effect is _____.
The forecasting method that is appropriate when the time series has no significant trend, cyclical, or seasonal effect is moving averages.
What is forecasting?Using past data as inputs, forecasting is a process that produces accurate predictions of the future course of trends. Businesses use forecasting to decide how to spend their budgets and make plans for forthcoming costs. Typically, this is based on the anticipated demand for the provided goods and services. Forecasting is a tool used by investors to predict if certain events, such sales projections, would raise or lower the price of a company's stock. For businesses that require a long-term view on operations, forecasting also offers an essential benchmark.
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Please help im stuck this is geometry
Answer:
Hello,
Answer D
Step-by-step explanation:
AC=22
BC=x+14
AB=x+10
Hence AB+BC=AC
x+10+x+14=22
2x+24=22
2x=22-24
2x=-2
x=-1
Anthoy drew a pentagon with each side measuring 6inches. carol drew a hexagon with each side measuring5 inches which shape has a greater perimeter? write an equation to help explain your answer
Both the shapes will have the same Perimeter.
It is given that :
Anthony drew a pentagon whose each side measures 6inches
Whereas, Carol drew a hexagon whose each side measures 5inches
The formula to calculate the Perimeter of the Pentagon is: 5*a
and, the formula to calculate the Perimeter of the Hexagon is: 6*a
In the given formulas, 'a' represents the measure of the side for both the Pentagon & Hexagon.
Calculating, Perimeter of Pentagon P1 = 5 * a, where a = 6 inches
=> P1 = 5*6 => P1 = 30inch
Calculating, Perimeter of Hexagon P2 = 6*a, where a = 5 inches
=> P2 = 6*5 => P2 = 30inch
We get P1 = P2
Hence, Both the Pentagon & the Hexagon have equal Perimeters of 30inch
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PLEASE HELP ASAP. I am stuck
a. how far is the delivery from the starting point in miles
b. which vehicle would take longer to finish the delivery, the car or the truck
and how much longer would the faster vehicle be than the slower one.
Please explain why
Part A
Answer: 360 milesReason:
The graph shows the highest point occurs when y = 360. After this point, the truck turns around to go back to the starting point (the warehouse perhaps).
In other words, the truck starts at y = 0 when it's at the warehouse. It travels 360 miles to reach the customer, which is represented as the highest point of the V shaped curve. This process takes 6 hours.
Then another 6 hours elapses when the truck drives back to the warehouse. We assume the same route is used, and similar traffic conditions occur for each leg of the trip.
============================================================
Part B
Answer: The truckReason:
The graph shows that the truck takes 12 hours to get back to the warehouse. We look at the x intercept because this is when the distance from the start is back to y = 0 again.
Now we need to find out how long the car takes on its trip.
We'll plug in y = 0 into the car's equation and solve for x.
y = -72|x-5| + 360
0 = -72|x-5| + 360
72|x-5| = 360
|x-5| = 360/72
|x-5| = 5
x-5 = ± 5
x-5 = 5 or x-5 = -5
x = 5+5 or x = -5+5
x = 10 or x = 0
x = 0 or x = 10
This tells us that the car is at the warehouse when x = 0 and when x = 10.
Therefore, the car takes 10 hours to do a round trip, and it's the faster vehicle.
The content dimension of a message deals with the _____ of a message, while the relational dimension of a message deals with the _____ of a message.
The content dimension of a message deals with the what of a message, while the relational dimension of a message deals with the how of a message is the correct answer.
Content dimensions is a generic concept to have multiple variants of a content node. It involves the information being explicitly discussed. The content repository supports any number of dimensions. The content dimension is the meaning of the actual message itself.
"Relational dimension of communication is a concept in which we have similar weight and impact as that of the message. This concept deals with the quality or nature of the relationships and networks."
Hence we can conclude that the content dimension of a message deals with the what of a message, while the relational dimension of a message deals with the how of a message is the correct answer.
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Can you create three different integer problems
that are equal to -15?
1. - 15 =
2. - 15 =
3. - 15 =
What could be an equation of a trend line for the data provided below?
Distance (mi) 2, 2.5 , 3 , 3.5 , 4.
Time (min) 23 , 28 , 34 , 34 , 40.
( photo would be shown )
a : y =6x+12
b : Y=8x+15
c : y=8x+8
b : y=6x+6
Answer:
Step-by-step explanation:
b : Y=8x+15
From 2008 to 2010, the cost of houses rose by 60%. if the cost of houses rose by 40% from 2008 to 2009, to the nearest percent, how much did the cost rise from 2009 to 2010?
The increase in cost from 2009 to 2010 is 14.28%
In order to solve this question we will be taking the following example:
Let the cost of the house in 2008 = $1000
Increase in cost from 2008 to 2010 = 60%
Cost of the house in 2010 = 1000 + 60%*1000 = $1600
Increase in cost from 2008 to 2009 = 40%
Cost of the house in 2009 = 1000 + 40%*1000 = $1400
Increase in cost from 2009 to 2010 = 1600 - 1400 = $200
Percentage increase in cost from 2009 to 2010 = (Increase in cost/Cost of the house in 2009)*100
=(200/1400)*100
= 14.28% or 14%
Therefore, there has been an increase of 14.28% in the cost of houses from 2009 to 2010
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34. marissa hiked 1 3/4 miles in 3/4 hours. at that rate, how far can she hike in one hour?
By unitary method, Marissa can hike 7/3 miles in an hour.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Given:
[tex]1\frac{3}{4}[/tex] = 7/4miles are hiked in 3/4 hours.
To find: the number of miles hiked in one hour
Finding:
By unitary method,
Miles hiked in 3/4 hours = 7/4
Miles hiked in 1 hour = 7/4(4/3) = 7/3
Hence, by unitary method, Marissa can hike 7/3 miles in an hour.
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Explain the three reporting options in sap erp. how are these different from each other? how are these different from the reporting options available in sap bi?
There are three reporting sections
First section Second section Third sectionHow do these contrast with the reporting choices offered by SAP Bi?Part One:
The following three reporting options are available in SAP ERP:
General Reports: These reports are pre-delivered by SAP and are made available in several regional formats to aid with basic HCM reporting. InfoSet (Ad-hoc)
Query Tool: This sophisticated tool can be used to answer one-time queries about SAP HR (Ad Hoc) or different info types of data that are accessible in SAP applications
Custom ABAP Reports: These are programs created by SAP developers using the ABAP programming language.
Second Section
Custom ABAP Reports General Reports InfoSet (Ad-hoc) Query, Tool
Pre-delivered SAP reports in multiple regions in the format that is accessible to assist with basic HCM reporting Don't need to be developed. Possess intricate developments. Can be transformed into an SAP query It is impossible to convert a query to SAP. Because it is unrelated to the ABAP workbench, content or output format cannot be modified.Third Section
The following are some of the reporting possibilities offered by SAP BI:
I Demand-driven BI. SAP dashboards, in Standard reports for SAPBusiness One, are Drag and relate Options for reporting in SAP ERPTransaction processing is done using them. Reports are only two-dimensional.To learn more about SAP Bi, visit:
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Cailyn is packing 1-centimeter cubes into a prism. What is the volume of the prism.
If Cailyn is packing 1-centimeter cubes in a prism of same dimensions and in the same manner as as shown in the figure attached, where Joe is packing 1-centimeter cubes into the prism, then the volume of the prism is 210 cm³.
As per the question statement, Cailyn is packing 1-centimeter cubes in a prism of same dimensions and in the same manner as as shown in the figure attached, where Joe is packing 1-centimeter cubes into the prism.
We are required to calculate the volume of the prism.
As we can see from the reference diagram attached hereby, our prism can hold a 7 cubes along its length, 6 cubes along its width and 5 cubes along its height.
And since the constituent cubes are all identical and of volume 1 cm³, it means that all the dimensions (length, width and height) of each of the constituent cubes is 1cm.
Therefore, length of our prism [tex]=(7*1)=7[/tex] cm,
Width of our prism [tex]=(6*1)=6[/tex] cm,
And, height of our prism [tex]=(5*1)=5[/tex] cm.
Therefore, volume of our prism = (length * width * height)
[tex]=(7*6*5)\\=(42*5)\\=210[/tex]
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Employees at company p sent 6.1 x 10^4 emails this year doing company business, compared to employees at company c, who sent 191,00 emails. find the difference in the numbers of emails sent by each company. answer in scientific notation without units. the coefficient may be exact or rounded to 2 decimal places.
The difference in the numbers of emails sent by each company is 4.19 × 10⁴.
The number of emails sent by company p = 6.1 × 10⁴
Converting scientific notation to real number
The number of emails sent by company p = 6.1 × 10000
Performing multiplication
The number of emails sent by company p = 61,000
The number of emails sent by company c = 191,00
Finding the difference using subtraction operation
Difference in number of mails = 61000 - 19100
Performing subtraction
Difference = 41,900
Converting the real number in scientific notation
Difference = 4.19 × 10⁴
Hence, the difference in the numbers of emails sent by each company is 4.19 × 10⁴.
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8x55 nnnnnnnnnnnnn what is the answer
Answer:
440
Step-by-step explanation:
Answer:
440
Step-by-step explanation:
Hm
(08.05 MC)
Functions 1 and 2 are shown:
Function 1: f(x) = -4x² + 6x + 3
Y
Function 2
N
2
Which function has a larger maximum?
Answer:
The function from the above scenario that has a larger maximum is function 1.
What is the function about?
Note that the first function is;
x = - b/ 2 a = 6 /8 = 3/4
f ( 3/4 ) = - 4 * 9/16 + 6 * 3/4 + 3
= - 9 /4 + 18 / 4 + 3
= 2.75 + 3 = 5.25
y max = 5.25
The second Function is:
y max = 2
Therefore we can see that the first function has a larger term that is ( 5.25 > 2 ).
The function f is defined as follows
f(x)=3x^2+1
if the graph of f is translated vertically downward by 8 units, it becomes the graph of function g
FIND THE EXPRESSION FOR G(X)
g(x)=?
Answer:
g(x)=3x²-7
Step-by-step explanation:
Subtract 8 from 3x²+1.
3x²+1-8=3x²-7
g(x)=3x²-7
Hope this helps!
Please mark as brainliest if correct!
PLEASE HELP!!
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Based on the figure on the graph, match the described transformations with the transformed figures.
reflected across the x-axis
rotated 180° clockwise
translated 9 units to the
right and 2 units down
reflected across the y-axis
The transformation of the given image follows the pattern; Reflection across the x-axis, then translation by 2 units downwards, the reflection across the y-axis.
How to carry out transformation reflection?
From the given first image, we see that it is in the first quadrant but by the second image, we see that it is now mirrored along the horizontal axis. Thus, we can say that it is reflected across the x-axis.
After reflection, across the x-axis, we see that it was translated down by 2 units.
The last transformation is that we see it is now in quadrant 3 which means it was now reflected across the y-axis.
The transformation of the given image follows the pattern; Reflection across the x-axis, then translation by 2 units downwards, the reflection across the y-axis.
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the question is on the image.
Answer: Mr Blade is typing at about 30 words per minute
Step-by-step explanation: all you have to do is multiply 9 x 40 since that is the amount of wpm (words per minute) by amount of time it takes Mr Adi and 9 x 40 = 360 than you have to divided 360 by 12 since that is the amount of time it takes Mr Blade to type the story and 360 divided by 12 equals 30
What is 510 of 2550? I am very very very thankful
Answer:
Use divide 510/2550 it will be 0.2
Answer:
20% or 0.2
Step-by-step explanation:
If you were to use the substitution method to solve the following system, choose the new equation after the expression equivalent to y from the first equation is substituted into the second equation. 6x − y = 1 4x − 3y = −11 (6 points) Group of answer choices 4(−6x + 1) − 3y = −11 4(6x + 1) − 3y = −11 4x − 3(6x − 1) = −11 4x − 3(−6x − 1) = −11
The new equation that will be formed is x − 3(6x − 1) = −11 (third option).
What is the substitution method?The substitution method is one of the methods that is used to solve simultaneous equations. It entails making one of the variables subject of the formula and substituting for it in the second equation. Other methods that can be used to solve simultaneous equations are the graph method and the elimination method.
The two simultaneous equations given are:
6x − y = 1 equation 1
4x − 3y = −11 equation 2
When y in equation 1 is made subject of the formula, the equation formed is:
y = 6x - 1 equation 3
Substitute for y in equation 2
4x - 3(6x - 1) = -11
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there were twice as many four-door cars as two-door cars in the parking lot. there were 36 cars in the lot. how many had four doors? how many had two doors?
the number of two door cars in the parking lot is 12 and the number of four door cars in the parking lot are 24.
We are given that the number of four door cars in a parking lot is equal to twice the two door cars.
Let the two door cars be x
Four door cars = 2 x
Also, we are given that total cars = 36
So, we get the equation:
x + 2 x = 36
3 x = 36
x = 36 / 3
x = 12
Two door cars = x = 12
Four door cars = 2 x = 2 ( 12) = 24
Therefore, we get that, the number of two door cars in the parking lot is 12 and the number of four door cars in the parking lot are 24.
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calculate the circumference of a circle with a: radius of 72,5mm
Answer:
4553
Step-by-step explanation:
2 x pi x r