Find the exact length of the curve. x= t/1+t,y=ln(1+t),0≤t≤2
Answers
Therefore, the exact length of the curve is ln|2+sqrt(3)| - ln|2|.
How to find the exact length of a curve?To find the length of the curve, we will use the arc length formula:
L = ∫(a to b) sqrt[dx/dt)^2 + (dy/dt)^2] dt
where a and b are the limits of t, and dx/dt and dy/dt are the derivatives of x and y with respect to t, respectively.
So, let's first find the derivatives of x and y with respect to t:
dx/dt = 1/(1+t)^2
dy/dt = 1/(1+t)
Now, we can substitute these values into the arc length formula and integrate:
L = ∫(0 to 2) sqrt[(1/(1+t)^2)^2 + (1/(1+t))^2] dt
= ∫(0 to 2) sqrt[1/(1+t)^4 + 1/(1+t)^2] dt
= ∫(0 to 2) sqrt[(1+t^2)/(1+t)^4] dt
= ∫(0 to 2) (1+t^2)^0.5 / (1+t)^2 dt
This integral is a bit tricky, but we can simplify it by using the substitution u = 1+t:
du/dt = 1, dt = du
So, the integral becomes:
L = ∫(1 to 3) (u^2-1)^0.5 / u^2 du
This integral can be solved using trigonometric substitution. Letting u = sec(theta), we have:
du = sec(theta) tan(theta) d(theta)
u^2 - 1 = tan^2(theta)
Substituting these into the integral, we get:
L = ∫(0 to pi/3) tan(theta) d(theta)
= ln|sec(theta)| (0 to pi/3)
= ln|2+sqrt(3)| - ln|2|
Therefore, the exact length of the curve is ln|2+sqrt(3)| - ln|2|.
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Related Questions
A. can you think of a situation where it would make the most sense to express your birth year in binary numbers? b. hexadecimal numbers? c. decimal numbers?
Answers
Birth year 2000 in:
(a)Binary numbers = 11111010000
(b)Hexadecimal numbers = 7D0
(c)Decimal numbers = 2000
We usually express our birth year in Decimal numbers. That is, if the birth year is 2000, then we write 2000 as 2000 itself in decimal numbers. This is because we use decimal number system in our daily life.
But we can express any decimal number as binary or hexadecimal numbers too.
Let the birth year we consider be 2000.
(a) We need to find the binary numbers for 2000. We say Binary numbers as the numbers in base 2. Binary numbers consist of 0 and 1 only as digits.
So in order to find the binary representation we divide 2000 by 2 and write down the remainder. Then we again divide the above quotient by 2 and note down the remainder again. We continue this process until we divide the last quotient by 2 and find the remainder. Then the remainders written in the reverse order gives the binary number for 2000.
That is,
2000 = 2 x 1000 + 0
1000 = 2 x 500 + 0
500 = 2 x 250 + 0
250 = 2 x 125 + 0
125 = 2 x 62 + 1
62 = 2 x 31 + 0
31 = 2 x 15 + 1
15 = 2 x 7 + 1
7 = 2 x 3 +1
3 = 2 x 1 + 1
1 = 2 x 0 + 1
Writing the remainders from bottom to top , we get,
11111010000 is the binary expression for 2000.
(b) Hexadecimal number system consist of 16 digits : 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F, where A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.
Now we use the same above process with 2 replaced by 16.
That is,
2000 = 16 x 125 + 0
125 = 16 x 7 + 13
7 = 0 x 16 + 7
Writing down the remainders from bottom to top, we get,
7D0 (Here D represents 13 in hexadecimal number system).
(c) The Decimal number system consists of the digits: 0,1,2,3,4,5,6,7,8,9
So 2000 is originally expressed in the decimal number system itself.
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9 The mapping shows a relationship between x and y.
N
S
Which statement is true of the mapping?
A y is not a function of x, since the y-value 3 corresponds to two different x-values.
By is a function of x, since the y-values do correspond to exactly one x-value.
Cy is not a function of x, since the x-values do not correspond to exactly one y-value.
Dy is a function of x, since the x-values do correspond to exactly one y-value.
Answers
Option (c) is true i.e. y is not a function of x, since the x-values do not correspond to exactly (precisely) one y-value.
What is Function?A function in mathematics from a set X to a set Y allocates exactly (precisely) one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
The items that make up a set are referred to as its elements (or members), and the set is said to contain the elements when they are claimed to belong to it.
The mapping shows a relationship between x and y in this mapping is y is not a function of x, since the x-values do not correspond to exactly one y-value.
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-4n+7+2n=1
ANSWER WITH EXPLAINATION
Answers
Answer:
n = 3
Step-by-step explanation:
-4n + 7 + 2n = 1
Collect like terms
-2n + 7 = 1
Subtract 7 from both sides
-2n = 1 - 7
Do the math on the right side
-2n = -6
Divide both sides by -2
n = 3
Which ordered pair is NOT a solution of y = 2x +1?
A. (3,7)
B. (0,1)
C. (-1,1)
D. (-3,-5)
Answers
Answer:
C. y=2x+1
2×3=6
6+1=7
2×0=0
0+1=1
2×-1=-2
-2+1=-1
therefore answer=C
Plz help me with this..........
Answers
Answer: 18 also you are wellcome
18.
The median will be the average of the two middle numbers.
Dr.Osborne has scheduled Anita Blanchette for a spirometry test and wants you to telephone her the day before the test to prepare her so that optimal results are obtained.
1.) What information do you give Anita before her spirometry so that the best test results can be obtained?
2.) How would you explain the rationale for the performance of this procedure?
Answers
To ensure the best test results, Anita should be provided with the following information before her spirometry:
1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.
2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.
3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.
4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.
The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.
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This is for today someone help me?!!!!!
Answers
angle q and n both equal 56
a rectangle has an area of 34 sqaure feet. A larger rectangle has an area of 124 sqaure feet. what is the percent increase of the larger rectangle to the smaller rectangle
Answers
Answer:
The difference in areas:
124 - 34 = 90 square feetPercent increase:
90/34*100% = 264.71%find the tangent of the cycloid x = r(t-sin t), y = r(1-cos t) at the point where t = pi/3.
Answers
Cycloid is a curve obtained by the locus of a point of a circle that rolls along a straight line. It's a curve that has two curvatures that are inversely proportional to one another. A cycloid is formed by the motion of a point on the circumference of a circle as it rolls along a straight line without sliding.
Let's find the tangent of the cycloid using the given equation and values. Find the tangent of the cycloid x = r(t-sin t), y = r(1-cos t) at the point where t = π/3.The cycloid x = r(t-sin t), y = r(1-cos t) can be differentiated to find the tangent at the given point by finding dx/dt and dy/dt. Let's differentiate the given equation with respect to t.dx/dt = r(1-cos t)dy/dt = r sin tLet's substitute the value of t=π/3 into the obtained equations.dx/dt = r(1-cos (π/3)) = r(1-1/2) = r/2dy/dt = r sin (π/3) = r√3/2So, we can say that the tangent of the cycloid at the point where t=π/3 isdy/dx = dy/dt ÷ dx/dt = r√3/2 ÷ r/2 = √3Therefore, the tangent of the cycloid at the point where t=π/3 is √3.
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Ryosuke is picking up his friend from work. The odometer reads 74,568 when he picks his friend up, and it reads 74,592 when he drops his friend off at his house. Ryosuke's car gets 28 miles per gallon and the price of one gallon of gas is $\$4.05$. What was the cost of the gas that was used for Ryosuke to drive his friend back home from work
Answers
Ryosuke drove his friend 24 miles, which used 1.14 gallons of gas. The total cost of the gas was $4.64, calculated by multiplying 1.14 gallons by the price of one gallon which was $4.05.
1. Calculate the number of miles driven: Subtract the odometer reading when Ryosuke picked his friend up (74,568) from the odometer reading when he dropped his friend off (74,592). This gives us the total number of miles driven (24).
2. Calculate the number of gallons used: Divide the total number of miles driven (24) by the car's gas mileage (28). This gives us the number of gallons used (1.14).
3. Calculate the cost of the gas: Multiply the number of gallons used (1.14) by the price of one gallon of gas ($4.05). This gives us the cost of the gas used ($4.64).
28 miles
= \($\frac{74,592-74,568}{28}$\)
= 1.14 gallons
Cost of gas
= 1.14 gallons x\($\$4.05$\)
= \($\$4.64$\)
1. 74,592 - 74,568 = 24
2. 24 / 28 = 1.14
3. 1.14 x $4.05 = $4.64
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Choose the statement below that is false. Question 2 options: In an observational study, the investigators assign the subjects to treatment or control groups. Controlled experiments can be randomized or non-randomized. Using a random chance procedure to assign subjects to treatment or control groups reduces bias. In a blind experiment, subjects do not know whether they are in the treatment group or control group.
Answers
The false statement among the options is: "In an observational study, the investigators assign the subjects to treatment or control groups."
In an observational study, the investigators do not assign subjects to treatment or control groups. Instead, they observe and collect data on the subjects as they naturally exist in their environments.
In observational studies, the assignment of subjects to groups is not under the control of the investigators, unlike in controlled experiments where researchers can assign subjects to different groups.
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If 4356 students are arranged in the form a square find the number of students in each column
Answers
Step-by-step explanation:
soye9685e06e96elhfouo9tsr0yee3079e97
Answer:
he is weird
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If n is an odd integer, then it is the difference of two perfect squares. The number n is an odd integer if and only if 3n+5=6k+8 for some integer k. . The number n is an even integer if and only if 3n+2=6k+2 for some integer k.
Answers
The statements provided can be rewritten as follows: 1. If n is an odd integer, then there exist integers a and b such that n = a^2 - b^2. 2. n is an odd integer if and only if 3n + 5 is of the form 6k + 8 for some integer k. 3. n is an even integer if and only if 3n + 2 is of the form 6k + 2 for some integer k.
Let's analyze these statements:
1. If n is an odd integer, then there exist integers a and b such that n = a^2 - b^2.
This statement is true and can be proven using the concept of the difference of squares. For any odd integer n, we can express it as the difference of two perfect squares: n = (a + b)(a - b), where a and b are integers. This shows that n can be written as the difference of two squares.
2. n is an odd integer if and only if 3n + 5 is of the form 6k + 8 for some integer k.
This statement is not true. Consider the counterexample where n = 1. In this case, 3n + 5 = 8, which is not of the form 6k + 8 for any integer k.
3. n is an even integer if and only if 3n + 2 is of the form 6k + 2 for some integer k.
This statement is true. For any even integer n, we can express it as n = 2k, where k is an integer. Substituting this into the given equation, we get 3n + 2 = 3(2k) + 2 = 6k + 2, which is of the form 6k + 2.
In conclusion, statement 1 is true, statement 2 is false, and statement 3 is true.
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What is the inverse of the function g(x)=5(x-2)
Answers
Answer:
\(\frac{x-2}{5}\)
Step-by-step explanation:
The inverse function of the function g(x)=5(x-2) is g(x)⁻¹= [( x/5 )+2 )].
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
The inverse function is calculated as:-
y = 5 ( x - 2 )
Replace the variables with each other in the equation.
x = 5 ( y - 2 )
( x/5 ) = y - 2
y = ( x/5 ) + 2
Therefore, the inverse function of the function g(x)=5(x-2) is g(x)⁻¹= [( x/5 )+2 )].
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Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $70 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $285, how many hours did the plumber work?
Write and solve an equation to determine the number of hours worked by the plumber.
50x − 70 = 285; x = 7.1 hours
50x + 70 = 285; x = 4.3 hours
70x − 50 = 285; x = 4.8 hours
70x + 50 = 285; x = 3.4 hours
Answers
Answer: B
Step-by-step explanation:
A $70 is fixed, we have to add $50 each hour. So, it will be 70 + 50x. If he charged $285 overall, this means that 70 + 50x = 285
50x = 285 - 70
50x = 215
x = 215/50 = 4.3
What is the solution of the equation
Answers
Answer: x=-56/3 (the second answer)
Michelle is rolling two six-sided dice, numbered one through six. What is the probability that the sum of her rolls is 8?
Answers
∴ P(A)=0.083
Step-by-step explanation:
Given that Michelle is rolling two six-sided dice, numbered one through six.
To find the probability that the sum of her rolls is 4:
∴ n(s)=36
Let P(A) be the probability that the sum of her rolls is 4
Then the possible rolls with sums of 4 can be written as
n(A)=3
The probability that the sum of her rolls is 4 is given by
=0.083
∴ P(A)=0.083
∴ the probability that the sum of Michelle's rolls is 4 is 0.083
-please give brainliest if correct!
Two students, Stella and Vladimir, completed the conversion
statement 12 feet 8 inches =
inches.
Stella stated that 12 feet 8 inches = 152 inches.
Vladimir stated that 12 feet 8 inches = 9 inches.
Which student is incorrect? Explain.
1. Highlight the measurement to be converted.
2.
Into what units do the students need to convert the given
measurement? Explain.
3.
Is a conversion factor given for the students in the problem? If not,
where could they find it?
4. Circle Stella’s and Vladimir’s answers. Explain how they are different.
5. Which student’s answer is more reasonable? Explain.
6. Should your final answer be a number? Explain.
Answers
1. Completing the conversion of 12 feet 8 inches to inches, Stella who stated that 12 feet 8 inches = 152 inches is correct unlike Vladimir who got 9 inches.
2. Stella and Vladimir need to convert the given measurement into inches.
3. No conversion factor is given for the problem. However, the conversion factor could be found online or using the mathematical table.
4. Stella's and Vladimir's answers differ because Vladimir failed to convert the feet into inches.
5. Stella's answer is more reasonable, and it is correct because 12 feet equal 144 inches plus 8 inches, giving 152 inches.
6. The final answer should not just be a number without indicating the unit of measurement.
What is unit conversion?A unit conversion is the mathematical expression of the same property in a different unit of measurement.
For instance, instead of stating distance in kilometers, it can be depicted in miles. Similarly, instead of reporting time in hours, it can be reported in minutes or seconds.
1 foot = 12 inches
12 feet = 144 inches
12 feet 8 inches = 152 inches (12 x 12 + 8)
Thus, in this situation, the measurement to be converted is feet to inches.
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if we subtract-3y square y square from square y then we get
Answers
Answer:
3
Step-by-step explanation:
Answer:
I don't understand the question dear
factor out x^{2} +4x-12
Answers
Answer:
The factorization of x2+4x−12=(x−2)(x+6)
Step-by-step explanation:
The area of a rectangle is 105 sq in and the length of one side is 7 in. What is the length of the perimeter?
Answers
Perimeter of Rectangle is 44m
What is Perimeter ?A perimeter is a closed path that encompasses, encircles, or delineates a one-dimensional length or a two-dimensional shape.
According to the given information
Area of Rectangle = l × b
Area of Rectangle = 105 \(m^{2}\)
Length of one side = 7 m
Let the length of the adjacent side = b
Area of Rectangle given = 7 × b
105 = 7 × b
b = \(\frac{105}{7}\)
b = 15 m
Perimeter of Rectangle given = 2( l + b )
= 2 ( 7 + 15 )
= 2 × 22
= 44m
Perimeter of Rectangle is 44m
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This data is going to be plotted on a bar chart. Part of the axes are shown below. How many rows tall should the bar for the number of people who take the bus be? Method of Travel Car Bike Walk Bus Train Frequency 13 16 4 10 8
Answers
To determine the number of rows tall the bar for the number of people who take the bus should be on the bar chart, we need to consider the frequency of people who take the bus.
According to the given data:
Method of Travel: Car, Bike, Walk, Bus, Train
Frequency: 13, 16, 4, 10, 8
The bar chart will have the frequency values on the vertical axis. We need to find the frequency value for the "Bus" category.
From the given data, the frequency for the bus is 10.
Therefore, the bar for the number of people who take the bus should be 10 rows tall on the bar chart.
0.4+x(10%)=4.9 solve for x.
Answers
Answer:
x = 45
Step-by-step explanation:
0.4 + x(10%) = 4.9 . . . . . . given
x(10%) = 4.5 . . . . . . . . . subtract 0.4
x = 45 . . . . . . . . . . . . multiply by 10
_____
10 × 10% = 100% = 1
54 x 8181 x 12 x 8271 x 1301 x 812
Answers
Answer:
4.6320447e+16
I used a calculator for this LOL.
The cost of 6 sandwiches and 4 drinks is $53. The code of 4 sandwiches and 6 drinks is $47. How much does one sandwich cost?
Answers
Answer:
$6.50
Step-by-step explanation:
SET UP A SYSTEM OF EQUATIONS WHERE SANDWHICHES IS REPRESENTED BY S AND DRINKS BY D:
6S+4D = 53
4S+6D=47
ADD THEM TOGETHER
10S+10D=100
SOLVE FOR D
10D = 100 - 10S
D = 10-S
SUBSTITUTE THAT VALUE INTO ONE OF THE ORIGINAL EQUATIONS
4S + 6(10-S) = 47
4S + 60 - 6S = 47
COMBINE LIKE TERMS
-2S + 60 = 47
SUBTRACT 60 FROM BOTH SIDES
-2S = -13
DIVIDE BY -2
S = 13/2
S = $6.50
Answer:
One sandwich is going to cost 6.50 while a drink is going to cost 3.50
Step-by-step explanation:
"We want to find and solve a system of equations to find the cost of one sandwich.
Each sandwich costs $6.50
We can start by defining the variables:
x = price of a sandwich
y = price of a drink.
Then from the given information we can write the equations:
6*x + 4*y = $53
4*x + 6*y = $47
We want to solve this for x, then we need to isolate y in one of the equations. Isolating y in the second equation we get:
y = ($47 - 4*x)/6
Now we can replace this in the other equation and solve it for x:
6*x + 4*($47 - 4*x)/6 = $53
6*x + $31.33 - (16/6)*x = $53
(20/6)*x = $53 - $31.33 = $21.67
x = (6/20)*$21.67 = $6.50" solved by
facundo3141592
solve -3-0.5x+13=0.3x+6.2 please show work
Answers
Answer:
x = 4.75
Step-by-step explanation:
And x=4.75
what is the median of these numbers 17 12 54 36 71 28 31 55
Answers
Answer:
The median is 33.5
Step-by-step explanation:
In order to solve for a median it would either be the middle or it would be the average of the middle if there are even amount of numbers. First you would put them in order. 12 17 28 31 36 54 55 and 71. This would mean the the middle number would be 31 and 36. Since you can't have two medians you would find the average of the two so add 31 and 36 which would be equal to 67 then divide by 2 which would equal to 33.5.
The median of numbers 17, 12, 54, 36, 71, 28, 31, 55 is 33.5.
What is the median of a set of numbers?The median of a set of numbers is the middle value when the numbers are arranged in ascending or descending order.
If there are an even number of numbers, the median is the average of the two middle values. If there is an odd number of numbers, the median is the middle number.
To find the median of the given numbers, we first need to arrange them in ascending order:
12 17 28 31 36 54 55 71
Since there are an even number of numbers (8), the median will be the average of the two middle values, which are 31 and 36.
To find the average, we add the two numbers and divide by 2:
(31 + 36) / 2 = 67 / 2 = 33.5
Therefore, the median of the given numbers is 33.5.
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a nutritionist wanted to find out if coffee and tea, as served in restaurants, differed in caffeine content. she went to 30 restaurants. in 15 randomly selected restaurants, she ordered coffee; in the other 15 restaurants, she ordered tea. what statistical test should the nutritionist use to see if coffee and tea differ in mean caffeine content?
Answers
The nutritionist should perform hypothesis testing followed by Independent T-test to see if coffee and tea differ in mean caffeine content .
We need to Know about Hypothesis testing and independent t test to answer this-
Hypothesis testing is a type of statistical test that is used to comapare data and drawing conclusion from them.
An independent t-test is a statistical test that determines whether the means of two unrelated groups are significantly different from each other.
We can find the difference caffeine content following these steps -
1)H0=Null hypothesis=tea and coffee has same caffeine level
HA=tea and coffee has different caffeine level
2)The independent samples t-test is utilized to determine whether two different sample means come from the same population or whether they come from two distinct populations with different mean values. Two populations can be considered independent when the data in one group is not connected to the data in the other group.
The t value obtained should be then performed under hypothesis testing.
3)And the calculated T value should be comaperd with the desired significance level (generally =0.05) and if the t value comes in between the critical values the nutritionist can assume that both tea and coffee has same caffeine level in this null hypothesis will be accepted.
Whereas if the calculated t value doesn't falls in between the critical value then the nutritionist can assume that tea and coffee has different caffeine level.
Hence null hypothesis will be rejected.
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3 shapes are combined to form a composite figure. A semicircle is on the bottom, and then a small rectangle connects the semicircle to a triangle.
How can you decompose the composite figure to determine its area?
as three triangles and a circle
as two triangles, a rectangle, and a circle
as a triangle, a pentagon, and a semicircle
as a triangle, a rectangle, and a semicircle3 shapes are combined to form a composite figure. A semicircle is on the bottom, and then a small rectangle connects the semicircle to a triangle.
How can you decompose the composite figure to determine its area?
as three triangles and a circle
as two triangles, a rectangle, and a circle
as a triangle, a pentagon, and a semicircle
as a triangle, a rectangle, and a semicircle
Answers
The composite figure can be decomposed into a triangle, a rectangle, and a semicircle to determine its area.
To decompose the composite figure and determine its area, we can break it down into simpler geometric shapes based on its components. In this case, the composite figure consists of a semicircle, a small rectangle, and a triangle.
We can decompose the figure as a triangle, a rectangle, and a semicircle. Here's how:
Triangle: The upper part of the figure is a triangle. Calculate its area using the formula A = (base * height) / 2, where the base and height are the appropriate measurements.
Rectangle: The small rectangle connects the semicircle to the triangle. Find its area by multiplying the length and width.
Semicircle: The bottom part of the figure is a semicircle. Calculate its area using the formula A = (π * r^2) / 2, where r is the radius of the semicircle.
Once you have determined the areas of each individual shape, add them together to find the total area of the composite figure.
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Which kind of symmetry does the word TOOT have?
Answers
Answer:
Linear symmetry.
Step-by-step explanation:
The word 'TOOT' can be reflected in y-axis if a point (0,0) on cartesian plane divides the words' TO' and 'OT' equally.