Answer:
Positive, two-tailed
Step-by-step explanation:
a professor at a certain school polled 12 colleagues about the number of meetings they attended in the last five years (x) and the number of papers they submitted to peer reviewed journals (y) during the same period. the summary data are as follows: n
The number of meetings they attended in the last five years (x) and the number of papers they submitted to peer reviewed journals (y) during the same period is [tex]-8.6+3.15[/tex].
What is formula for slope and intercept is?
[tex]$$\begin{aligned}& b=\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& a=\bar{y}-b \bar{x} \\& \hat{y}=a+b x\end{aligned}$$[/tex]
The slope is
[tex]$$\begin{aligned}b & =\frac{n \sum x y-\left(\sum x\right)\left(\sum y\right)}{n \sum x^2-\left(\sum x\right)^2} \\& =\frac{12 \times 318-(12 \times 4)(12 \times 4)}{12 \times 232-(12 \times 4)^2} \\& =3.15\end{aligned}$$[/tex]
The intercept is
[tex]$$\begin{aligned}a & =\bar{y}-b \bar{x} \\& =4-3.13 \times 4 \\& =-8.6\end{aligned}$$[/tex]
The regression equation is
[tex]$$\begin{aligned}\hat{y} & =a+b x \\& =-8.6+3.15 x\end{aligned}$$[/tex]
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Researchers have collected data on the hours of studying in a week and the exam grade of a student. You are given the data below. Hours of Studying 1 3 3 3 5 Exam Grade 55 75 80 85 100 (1) Develop the least squares regression equation. (6 points) (2) Estimate the exam grade of a student with 2 hours of studying. (3 points) (3) Compute the coefficient of determination. (6 points) (4) Perform a t test to test whether the exam grade is significantly related to the number of hours of studying with a = 0.01. What is your conclusion? (5 points) (5) Perform an Ftest to test whether the exam grade is significantly related to the
since to> t∝/ ₂₁n-2 we reject H₀ and conclude that the exam grade is significant related to the no of hours of studying
X = 1 3 3 3 5
Y= 55 75 80 85 100
What is hypothesis ?
A hypothesis is an unproven claim that is backed up by all the information that is now available and a lot of weaker results in mathematics.
n=5
∑x=15
∑x²=53
∑y=395
∑x²=32275
∑xy=1275
Sxx= ∑x²-1/n (∑x)² =8
Syy= ∑y²-1/n (∑y)² =1070
Sxy= ∑xy²-1/n (∑x)(∑y) =90
= Sxy/sxx =90/8 =11.25
x= 395/5 =11.25 (15/5)
=45.25
y=45.25 +11.25 x
if x=2, y=45.25 +11.25 (2) = 67.75
3. coefficient of determination
R² = SSR/SST = β₁ SXY/SYY
R₂ = 11.25 X 90/1070
=0.946
4. M = SYY -β₁ SXY/n-2
=1070-11.25(90)
=19.167
Hypothesis = H₀ :β₁ =0
H₀ :β₁ [tex]\neq[/tex]0
Test statistic = t = β₁/
t₀ =11.25/
t₀=7.27
critical value= t∝/₂₁n-2
= t0.005
=5.841
since to> t∝/ ₂₁n-2 we reject H₀ ( Hypothesis) and conclude that the exam grade is significant related to the no of hours of studying
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What is the variable part of the term -6bx?
The variable part is x and b.
What is variable?A mathematical object is represented by a symbol known as a variable. A variable can be a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set. Algebraic computations using variables solve a variety of problems in a single operation. By substituting the numerical values of the equation's coefficients for the variables that represent them in the quadratic formula, the quadratic formula, for instance, can be used to solve any quadratic equation.
Given a equation -6bx
here -6 is constant because it cannot be changed;
a number that has a proper worth in a given circumstance or generally or that is normal for some substance or instrument.
and x, b are variables,
A variable is an amount that might change inside the setting of a numerical issue or examination.
Hence for the equation x and b are variables.
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Max found a car he wants to buy that costs $16,000. He can
afford to pay $250 a month for the car. His bank offers him a car
loan of 7.3%. How will the length of his loan be for this payment
amount?
Answer: To calculate the length of a loan, you need to know the total cost of the loan, the monthly payment amount, and the interest rate. In this case, the total cost of the car is $16,000, the monthly payment amount is $250, and the interest rate is 7.3%.
First, you need to calculate the total interest that will be paid on the loan. This can be done by multiplying the total cost of the loan by the interest rate, and then dividing by 100 to convert the result to a percentage. In this case, the total interest paid would be $16,000 * 7.3 / 100 = $1,168.
Next, you need to subtract the total interest from the total cost of the loan to find the total amount of the loan that will be used to pay for the car. In this case, the total amount of the loan used to pay for the car would be $16,000 - $1,168 = $14,832.
Finally, you can use this total amount and the monthly payment amount to calculate the length of the loan by dividing the total amount by the monthly payment amount. In this case, the length of the loan would be $14,832 / $250 = 59.32 months, or just over four years. The answer is 59.32 months.
Step-by-step explanation:
Using the graph below, find f(-2)
Answer:
f(-2) =3
Step-by-step explanation:
f(-2) = value of the function when x = -2
Using the graph find the value of the function when x = -2
The value is 3
f(-2) =3
The following coordinates are each a result of a single transformation. What type of transformation occurred for each image?
D (3,7)---> D' (-7,3) Select One
Answer:
This is a 90° counterclockwise rotation
Step-by-step explanation:
When you rotate a point 90 °counterclockwise the x x and y coordinate values interchange and the new x coordinate has a negative sign while the y-coordinate retains the original sign
What is 4 + 4? ....................................
The value of 4 plus 4 will be 8.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
It should be noted that addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
In this case:
4 + 4
= 8
The value is 8.
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The perimeter of a square is 56. Express the length of a diagonal of the square in simplest radical form.?
The length of a diagonal of the square in simplest radical form is; 2√7
What is the length of the diagonal of the square?We are given that;
Perimeter of square = 56
Now, the formula for perimeter of a square is;
P = 4s
where s is side length of square. Thus;
56 = 4s
s = 56/4
s = 14
Now, the diagonal of a square is given by the formula;
Diagonal = √(2s²)
Thus;
Diagonal = √(2 * 14²)
Diagonal = √(2 * 2 * 7)
Diagonal = 2√7
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The measures of the angles of a triangle are shown in the figure below. Solve
for x.
Answer:
x = 5
Step-by-step explanation:
To solve this problem, we need to utilize the triangle sum theorem.
⭐What is the triangle sum theorem?
the sum of all angles in a triangle equals to 180°1. Set up the equation as per the triangle sum theorem
(5x+6) + 43 + 106 = 180
2. Add the constants
5x + 155 = 180
3. Subtract 155 from the LHS and RHS
5x = 25
4, Divide the LHS and RHS by 5 to isolate x
∴ x = 5
⭐if this response helped you, please mark it the "brainliest"!⭐
A stationary shop orders a batch of pens from a factory.
The factory could make the batch of pens in 20 days using 12 machines.
Due to a fault, only 3 machines were used for the first 8 days.
All 12 machines were used from day 9 onwards.
Work out the total number of days taken to make the batch of pens
Answer:
22
Step-by-step explanation:
(8 + 20) - ((8 * 9) ÷ 12)
Using PEMDAS, let us find the product to get;
(8 + 20) - (72/12)
Next operation is to divide what is in the bracket to get:
(8 + 20) - 6
Next operation is addition of the bracket content to get; 28 - 6
Next operation is to carry out subtraction to get: 22
Thus, the total number of days taken to make the batch of pens is 22.
Question 7
Provide an appropriate response.
Suppose x is a uniform random varlable with a = 40 and b = 80. Find the probability that a randomly selected observation is between 43 and 75.
Help me please ASAP (ﾒ﹏ﾒ)
Answer:
A ' ( -21, 14 )
B ' ( 28, 14 )
C ' ( -7, -7 )
Step-by-step explanation:
The scale factor is k = 7. This tells us to multiply each coordinate, of each point, by the scale factor to get the dilated points.
For example, point A is at (-3, 2) and moves to A ' (-21, 14) after multiplying the x,y coordinates by 7. The same applies for points B and C as well.
The dilation rule can be written as (x,y)—-> (7x,7y)
As a result of the dilation, triangle A'B'C' has sides that are 7 times longer compared to the corresponding sides of triangle ABC.
Example: side AB = 7 units, side A'B' = 49 units
Hopes this helps!!
Determine whether the integers in each of these sets are pairwise relatively prime. a) 11, 15, 19 b) 14, 15, 21 c) 12, 17, 31, 37 d) 7, 8, 9, 11
Note that Option A is pairwise and is relatively prime.
Option B is not relatively primeOption C is also a relatively primeOption D is also relatively prime.What does it mean for a list of integers to be pairwise relatively prime?If every pair of elements in a list of integers is relatively prime, the list is pairwise relatively prime. For example, the numbers 121, 122, and 123 are relatively prime pairwise (even though they are each composite).
You can tell if a set of numbers are relatively prime if they do not share a common factor other than ±
Looking at set a:
11, 15, 19
Writing their prime factorization
11 = 11
15 = 3 x 5
19 = 19, hence since any pair of these numbers does not have any common factor, hence they are relatively prime.
Looking at set b:
14, 15, 21
Writing their prime factorization, we have:
14 = 7 x 2
15 = 3 x5
21 = 3 x 7
15, and 21 share a common factor of 3 while
14 and 21 share a common factor of 7, therefore, they are NOT relatively prime.
Looking at set c)
12, 17, 31, 37
Writing their prime factorization,
12 = 3 x 2²
17 = 17
31 = 31
37 = 37
In this case, no pair of these numbers have any common factor. Hence they are relatively prime.
Looking at set d)
7,8,9, 11, spelling out their prime factorization
7=7
8=2³
9=3²
11=11
Thus, any pair of these numbers do not have a common factor, hence they are relatively prime.
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If 2w - 1 = 13, what is the value of 2w?
6
14
7
12
Answer: 7
Step-by-step explanation: 13+1=14
2*?=14 2*7=14
q.16 find the number of ways to put eight different books in five boxes, of no box is allowed to be empty. (5 points)
The number of ways to put eight different books in five boxes, of no box is allowed to be empty will be 403200.
As, it is given that,
No box is allowed to be empty.
An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are organized in a linear or sequential manner. For instance, the set A=1,2 has a permutation of 2, which is 1,2, or 2,1. There is no alternative way to organize the components of set A,
So, we can put one book in each box in [tex]8 P_5[/tex] mays.
Now remaining 3 books we can put in by [tex]${ }_5 P_3$[/tex] ways
Total number of ways will be [tex]$=8 P_5 \cdot 5 P_3$[/tex]
Now calculating the value,
[tex]=\frac{8 !}{(8-5) !} * \frac{5 !}{(5-3) !}\\\\=\frac{8 !}{3 !} \times \frac{5 !}{2 !}\\\\=403200[/tex]
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Answer to this required:
Answer:
B
Step-by-step explanation:
the hypotenuse is z
For the Pythagorean theorem:
x² + y² = z²
Mary weighed 7 1/2pounds when she was born. What number makes the statement true? 7 1/2 = ?/2
Johanntakes a random sample of 101010 of his coworkers and asks them each howmany hours they worked in the past week. Assume that their hours workedare independent, and let HHH represent the average number of hours worked. Is HHH a binomial variable
The average number of hours worked is not a binomial variable as there is no success or failure in the scenario.
What is binomial variable?In probability theory and statistics, the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success or failure, is known as the binomial distribution with parameters n and p.
A variable with two possible forms is said to have a binomial distribution. It could result in success or failure, heads or tail, and yes or no. If a coin is tossed, for instance, it could land on its head or its tail. It is a binomial variable as a result.
Here, there may be more than two values for the typical hours worked. It is not a binomial variable as a result.
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determine the present value p you must invest to have the future value a at simple interest rate r after time t.
The present p value which have to be invest in future is $7619.05 at simple interest rate r.
Simple Interest:
Simple interest (S.I) is a method of calculating the amount of interest on a specific amount of money.
The simple interest formula helps determine the amount of interest given a principal, interest rate, and term.
The formula for simple interest is:
SI = PTR/100
where SI = simple interest
P = principal
R = interest rate (percentage)
T = term (years)
For calculating total amount
Amount (A) = principal Book (P) + Interest (I)
where
Amount (A) is the total amount repaid at the end of the borrowed period.
The simple interest total amount formula can also be written as:
A = P(1 + RT)
where
A = Total amount after specified period
P = Principal or original loan amount
R = Interest rate (annual)
T = Time (annual )
According to the Question:
Simple interest: I = PTR ---------------------------- (1)
Future amount : A = p + I = p + PTR ------------------ (2)
Given that:
r = 10% = 0.1
t = 6 months = 0.5 year
A = future amount = 8000
Now,
8000 = p + p (. 1)(0.5)
⇒ 8000 = 1.05 p
⇒ p = 8000/1.05
⇒ p = $ 7,619.05
Now,
Putting the value of p in equation (2)
I = 7619.05 (0.1) (0.5 ) = 380.95
7619.05 + 380.90 = $8,000
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which polynomial is the product of (4x-3)(x^2+2x-6)
Answer:
4x³ + 5x² - 30x + 18
Step-by-step explanation:
(4x - 3)(x² + 2x - 6)
each term in the second factor is multiplied by each term in the first factor.
4x(x² + 2x - 6) - 3(x² + 2x - 6) ← distribute parenthesis
= 4x³ + 8x² - 24x - 3x² - 6x + 18 ← collect like terms
= 4x³ + 5x² - 30x + 18
What is the fourth root of 625
The required answer is the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.
To find the fourth root of 625, we need to determine the number that, when raised to the power of 4, equals 625. Here's the step-by-step process:
Step 1: Start with the number 625.
Step 2: Take the fourth root of 625.
Since we're looking for the fourth root, we need to find a number that, when raised to the power of 4, equals 625.
Step 3: Determine the number that, when raised to the power of 4, equals 625.
To find this number, we can use the concept of exponentiation. Let's denote the unknown number as "x". Mathematically, we have [tex]x^4 = 625[/tex]..
Step 4: Solve the equation [tex]x^4 = 625[/tex].
To solve this equation, we need to find the value of x. Taking the fourth root of both sides of the equation, we have [tex]\sqrt[4]{(x^4)} =\sqrt[4] {625}.[/tex]
The fourth root of 625 is (625)^(1/4).
Step 5: Simplify the expression.
We can simplify [tex]\sqrt[4]{ 625}[/tex] as follows:
[tex]\sqrt[4]{ 625} = \sqrt[4]{ 5^4}= 5^{4/4} = 5^1 = 5.[/tex]
Therefore, the fourth root of 625 is 5. In summary, the fourth root of 625 is 5.
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A stamp collection consists of 3c 12c and 15c stamps. The number of 3c stamps is five times the number of 12c stamps. The number of 15c stamps is four less than the number of 12c stamps. The total value of the stamps in the collection is $3.18. What is the number of 15c stamps in the collection?
In a conceptual replication, the _________ are the same, but the _________ is/are different from the original study.a. independent variables; dependent variablesb. variables; operationalizationc. methods; participantsd. researchers; outcomes
In a conceptual replication, the variables are the same, but the operationalization is/are different from the original study.
The researcher seeks to recreate the basic idea of the research in a conceptual replication. An exact replication involves the researcher reproducing, or attempting to duplicate, the precise circumstances of the original study.
A replication attempt in which the primary effect of interest is the same but tested in a different sample and captured in a different way than that reported originally .
A conceptual replication is sometimes used to investigate what constraints limit the extent to which an effect may be observed and generalised (e.g., only within certain contexts, with certain samples, and using certain measurement methodologies) in order to evaluate and advance theory.
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For a data set of weights (pounds) and highway fuel consumption amounts (mpg) of ten types of automobile, the linear correlation coefficient is found and the P-value is 0.013. Write a statement that interprets the P-value and includes a conclusion about linear correlation
The P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is 1.3% which is low so there is sufficient evidence to conclude that there is a linear correlation between weight and highway fuel consumption in automobiles.
Given that,
The complete statement is,
The p-value is given as:
[tex]p=0.013[/tex]
Express as percentage
[tex]p=1.3[/tex] %
This means that the probability that the linear correlation coefficient is at least as extreme is 1.3%.
From the z-table, we have:
[tex]z = 1.81[/tex], when the p-value is 0.013
This value of z-score is low, compared to the percentage of the scores have a z-score of between -1 and 1.
So, the p-value implies that it is likely that there is a linear correlation between the variables.
Hence, the texts that complete the three blanks are: "1.3%", "low" and "is"
Therefore,
The P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is 1.3% which is low so there is sufficient evidence to conclude that there is a linear correlation between weight and highway fuel consumption in automobiles.
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is the following a qualitative or quantitative variable?: the type of flowers you plant in your garden
Qualitative variables include all observable qualities or characteristics of a group or population that can not be measured numerically.
What is Qualitative?
The goal of qualitative research is to collect and examine non-numerical data in order to comprehend people's attitudes, beliefs, and motivations in relation to their social reality.
Quantitative Variable
Quantitative variables, as the name implies, are those that can be expressed by a numerical value.
1. Quantitative (Discrete)
2. Quantitative (Continuous)
3. Quantitative (Discrete)
4. Qualitative (nominal)
5. Qualitative (nominal)
6. Qualitative (nominal)
7. Qualitative (nominal)
8. 9. Quantitative (Continuous)
10. Qualitative (nominal)
11. Quantitative (Continuous)
12. Qualitative (ordinal)
13. Qualitative (nominal)
14. Quantitative (Discrete)
15. Qualitative (nominal)
Complete question: Which is the following a qualitative or quantitative variable?
1)ordinal
2)Continuous
3)nominal
4) All of these
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How many 1/2 inch cubes fit along it’s 2 1/2 length?
Five 1/2 inch cubes fit along it’s 2 1/2 length.
What is meant by length?An object's longest or largest dimension is a measured distance. Dimensions: 10 ft. see Weights and Measures, Metric System Table
An object's length, which is a measurement of its longest side, is its most stretched dimension. Your dog, for instance, would measure its length from the point of its nose to the end of its tail. The space between its top and bottom feet is greater than that of the creature's head.
In addition to utilizing handspan, foot span, and other methods, one can measure length in many units, such as centimeters, inches, meters, and so on.
Let x be the number of 1/2 cubes to fit 2 1/2 length
(1/2)x= 2 1/2
(1/2)x=5/2
x=5
Therefore, five 1/2 inch cubes fit along it’s 2 1/2 length.
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Factor completely and find all the zero(s)
Answer:
Factors are (x-1) (4x²-1)
Zero(s) are x = 1, x = 1/2, x = -1/2
Step-by-step explanation:
Given function is
4x³ - 4x² - x + 1
= 4x³ - x - 4x² + 1
= x(4x² - 1) - 1(4x² - 1)
= (x - 1) (4x² - 1) (Factors of the equation)
To find the zero(s),
Either, Or,
x - 1 = 0 4x² - 1 = 0
or, x = 1 or, x² = 1/4
or, x = √(1/4)
or, x = +- 1/2
Cooperative-Learning Activity Using the Quadratic Formula to Plan a Patio
Professionals, such as architects, engineers, contractors, and project managers, work collaboratively
to successfully complete quality projects. In this activity, you will need to help your group recommend
to a homeowner one of two patio options. Below is the information you will use to help with this
project.
A homeowner wants to build a patio around a 35-foot by 20-foot rectangular swimming pool.
The homeowner has two options and a budget of $40,200 (which all needs to be used) for the
patio.
Option 1 Surround the pool with a concrete band of equal width on all sides. The concrete
costs $50 per square foot.
Option 2 Surround the pool with a tile band of equal width on all sides. The tile costs $80 for
each square foot tile.
The homeowner should go with option 1 for his budget of $40,200 to use complete budget.
What is Quadratic equation?Any equation that can be rearranged in the standard form as is referred to as a quadratic equation (from the Latin quadratus, "square").
ax² + bx + c = 0
where x is a value that is unknown, a, b, and c are numbers that are known, and a is a negative number. The numbers a, b, and c are the equation's coefficients; they are referred to as the constant or free term, the quadratic coefficient, and the linear coefficient, respectively.
Solutions of the equation and roots or zeros of the expression on its left-hand side are the values of x that satisfy the equation. There can only be two solutions to a quadratic equation. One suggests that there is only one solution, which is a double root.
Given a rectangular pool of 35-foot by 20-foot
area of pool = 35 x 20 = 700 sq. foot
and to built a patio around pool of equal width,
budget of patio of $40,200 all amount to be used,
Option 1: Surround the pool with a concrete band of equal width on all sides. The concrete costs $50 per square foot.
the area covered by amount is 40200/50 = 804
let width of patio be x
new length = 35 + x and new breadth = 20 + x
area covered by patio = new area including width - area of pool
new area including width = area covered by patio + area of pool
new area including width = 804 + 700 = 1504
1504 = (35 + x)(20 + x )
1504 = x² + 35x + 20x + 700
x² + 55x - 804 = 0
solving the equation by quadratic formula
x = (-b ± [tex]\sqrt{b^{2} - 4ac }[/tex])/ 2a
where a = 1, b = 55, and c = -804
x = (-55 ± [tex]\sqrt{(55)^{2} - 4*1*(-804) }[/tex])/2
x = (-55 ± √(3025 + 3216))/2
x = (-55 ± 79)/2
taking positive values
x = (-55 + 79)/2 = 12
new length = 35 + 12 = 47 foot
new breadth = 20 + 12 = 32 foot
area covered by patio = (47x32) - (35x20)
area covered by patio = 804 sq. foot
and cost will be 804 x 50 = $40,200
for option 2: Surround the pool with a tile band of equal width on all sides. The tile costs $80 for each square foot tile.
area for patio = 40200/80 = 502.5
since the area is in fraction the cost will come in approximation.
Hence the homeowner should go with option 1 for complete use of budget.
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When you start from a given set of rules and conditions and determine what must be true, you are using reasoning.
A. conjunctive
B. inductive
C. deductive
D. conductive
In deductive reasoning, you start from a given set of rules and conditions to determine must be true
In the process, we eliminated the one that do not met the rules and conditions. Which ever option left after the deduction, that must be the truth
hope this helps
Answer:
C. Deductive
Step-by-step explanation:
Hope this helps :)
Find the distance traveled by a particle with position (x, y) as t varies in the given time interval. Compare with the length of the curve.
x = sin2t, y = cos2t, 0≤t≤3π
The distance traveled by a particle with position (x, y) as t varies in the time interval 0 ≤ t ≤ 3π be, 6π units.
Given, a particle with position (x, y) move across a distance as t varies in the given time interval 0 ≤ t ≤ 3π
where, x = sin2t, y = cos2t
On using the length of the curve concept, we get
d = ∫√((dx/dt)² + (dy/dt)²) dt
as, x = sin2t and y = cos2t
dx/dt = 2cos2t
dy/dt = -2sin2t
On substituting the values, we get
d = ∫√(4cos²2t + 4sin²2t) dt
d = ∫2 dt
d = 2∫dt
d = 2×(3π - 0)
d = 6π
So, the distance traveled by the particle be, 6π
Hence, the distance traveled by the particle be, 6π
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