Answer:
Below
Step-by-step explanation:
1/3 x = - 2/5 <=====multiply both sides of the equation by 3 to get
x = -6/5 = - 1 1/5
Mary weighed 7 1/2pounds when she was born. What number makes the statement true? 7 1/2 = ?/2
3. "Seventeen less than twice a number is -49."
Answer: the number is -16
Step-by-step explanation: if you add 17 to -49, you will get -32. you do this because it is 17 less than NOT more than. that would be called inverse operations. then, you divide that number by 2 to get -16. again, you use inverse operations because you are going backwards to try and find the number.
Answer: -16
Step-by-step explanation: So, to solve, we should write an equation. It should look like this:
2x - 17 = -49
So, using inverse operations, we would add 17 to - 49, which is -32, then divide that by 2, which would be -16. I hope this helped!
P.S. our new equation would look like 2(16) - 17 = -49
32-17 = 49
32 + -17 = 49
49 = 49
It checks out.
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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Does the histogram appear to depict data that have a normal distribution? O A. The histogram appears to depict a normal distribution. The frequencies generally decrease to a minimum and then increase. O B. The histogram does not appear to depict a normal distribution. The frequencies generally increase and the histogram is roughly symmetric. O C. The hidtogram does not appear to depict a normal distribution. The frequencies generally decrease to a minimum and then increase, and the histogram is roughly symmetric. OD. The histogram appears to depict a normal distribution. The frequencies generally increase to a maximum and then decrease, and the histogram is roughly symmetric The table below shows the frequency distribution of the weights (in grams) of pre-1964 quarters. Frequency Weight (g) 6.000-6.049 6.050-6.099 6.100-6.149 6.150-6.199 6.200-6.249 6.250 6.299 6.300-6.349 6.350-6.399 Use the frequency distribution to construct a histogram. Does the histogram appear to depict data that have a normal distribution? Why or why not?
The histogram appears to roughly estimate a normal distribution. The frequencies normally increase to a maximum and then decrease, and the histogram is symmetric.
The Graph of Normal Distribution is bell-shaped. Here the value of y is less for the lower value of x and then the value of y is increased for a larger value of x, but after some time value of y again getting decreases as the value of x increases.
For the Histogram to appear to be a normal distribution, the graph of the histogram must have the same nature. Thus, option B is only the correct option.
The histogram is made up of many columns and bars that are vertical with no gaps between bars with different labels of numeric data of different heights showing the size of the group of different labels.
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Two sides of a triangle are 17 and 53. The third side is?
Answer:
the answer would be e because you can't determine the side length
Answer: (B)
Step-by-step explanation:
Step 1: Find minimum values of the third side.
53-17 = 36
Step 2: Find maximum values of the third side.
17+53 = 70
Step 3: Find equation
36 < x < 70
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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Each of the 9 reindeer have 8 jingle bells on their collar. There are 12 more bells on the reins. How many bells in all?
Answer: 84 bells
Step-by-step explanation:
12 + 9x8
84
Due to the tide, the water level rises and falls daily in Buzzard's Bay. D gives the depth of the water, in meters, t hours after midnight on a certain day. What is the best interpretation for the following statement? The value of the derivative of D at t = 8 is equal to -0.5. Choose 1 answer a. At 8 a.m. the water level decreased at a rate of 0.5 meters per hour. b. At 8 a.m. the water level decreased at a rate of 0.5 meters. c. At 8 a.m. the water level was 0.5 meters below sea level. d. Until 8 a.m. the water level decreased at a rate of 0.5 meters per hour.
The correct interpretation for the statement D'(8) = -0.5 is (c) At 8 a.m. the water level was 0.5 meters below sea level.
How to interpret the function notation D'(n)From the question, we have the following parameters that can be used in our computation:
The function D gives the depth of the water, in meters, t hours after midnight on a certain day
This means that
D = depth in meters
t = time in hours
From the question, we have
Notation = D(n)
Also, from the question, we have
D'(8) = -0.5
This is the inverse of the function D(t)
So, the values of the parameters are
D(t) = -0.5
t = 8
This means that the number of hours is 8 and the depth is -0.5 meters
Hence, the interpretation of D'(8) = -0.5 is (c) At 8 a.m. the water level was 0.5 meters below sea level.
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Which expression is equivalent to (m−2n−4)−4? m8n16 m−8n−16 m−6n−8 1 over the quantity m raised to the sixth power times n raised to the eighth power end quantity
Answer: C m-6n-8
Step-by-step explanation:
Which expression is equivalent to (m−2n−4)−4?
A m8n16
B m−8n−16
C m−6n−8
D 1 over the quantity m raised to the sixth power times n raised to the eighth power end quantity
(m-2n-4)-4
(2n-4)
(2x-4)
(n-8 )
(m- 4)-4
4+4
m-6
which = C m−6 n−8
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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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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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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let w represent the number of attempted experiments to get one experiment that is not successful. the random variable w has a geometric distribution with mean 4 and standard deviation 3.5. which of the following is the best interpretation of the standard deviation? responses a single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments. a single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments. a single value randomly selecte
The best interpretation of the standard deviation on this problem is given as follows:
A single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments.
How to interpret the standard deviation?The standard deviation of a data-set is calculated as the square root of the sum of the differences squared between each observation of the data-set and the mean, divided by the number of observations in the data-set.
The interpretation of this calculation is that the standard deviation represents by how much each value of the distribution is expected to vary from the mean, on average.
This means that the correct statement is given as follows:
A single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments.
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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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Please help me with this!
1) express the original claim in symbolic form
2) identify the null and the alternative hypotheses
The alternative hypothesis is often abbreviated as Ha or H1. When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < o
What is hypothesis?
A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientists typically build their scientific ideas on prior observations that cannot be adequately explained by the current body of knowledge.
In statistics, the null hypothesis is usually denoted by letter H with subscript '0' (zero), such that H0. It is pronounced as H-null or H-zero or H-nought
At the same time, the alternative hypothesis expresses the observations determined by the non-random cause.It is represented by H1 or Ha.
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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!!
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:
A fair coin is tossed 10 times. Find the probability of satisfying the condition that that the coin does not land on tails twice in a row
The probability of tossing 10 tails in a row is [tex]\frac{1}{1024}[/tex]
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that,
When a fair coin is tossed 10 times, the sample size (n) is:
n = [tex]2^{10}[/tex]
This is so because a fair coin has 2 sides.
So, we have:
n = 1024
There is only one occurrence of having 10 tails in a row in the 1024 possible outcomes.
So, the probability is:
P = [tex]\frac{1}{1024}[/tex]
Therefore,
The probability of tossing 10 tails in a row is [tex]\frac{1}{1024}[/tex]
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If f(x) = x³ + 14x² + 61x + 84, which of the following is not a factor of f(x)?
4p2 divided by 2! - 4c2
Answer:
Step-by-step explanation:
12.5663706144
Write the complex equation 8 + 3; in trigonometric form.
The complex equation 8 + 3; in trigonometric form is z = 8.544[cos(20.6) + isin(20.6)}.
What is trigonometric form ?
Here, we'll utilize that fundamental transformation to recast z = a + bi in a different (sometimes more practical) form that is based on the polar transformation. The trigonometric form of a complex number is the name of this new representation.
Given
8 + 3i
Required
Rewrite in trigonometric form.
The trigonometric form of a complex equation is
z = r[cosθ + isinθ]
Let a = 3 and b = 8
Where
r is calculated by
r² = b² + a²
And
θ is calculated by
θ = arctan(a/b)
Substituting 3 for a and 8 for b
r² = a² + b² becomes
r² = 3² + 8²
r² = 9 + 64
r² = 73
√r² = √73
r = √73
r = 8.544
Calculating θ
θ = arctan(a/b) becomes
θ = arctan(3/8)
θ = arctan(0.375)
θ = 20.556°
θ = 20.6 --- Approximated
Hence, z = r[cosθ + isinθ] becomes
z = 8.544[cos(20.6) + isin(20.6)}
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Which model shows the problem 1 divided by 1/6 ?
The model that shows the problem 1 divided by 1/6 is option 1.
What is meant by circle?Every point in a plane that is at a specific distance from the center, or the circle's center, forms a shape. To put it another way, it is the curve that a moving point in a plane draws to keep a constant distance from another point. The radius of a circle is the separation of any point from the center. A positive integer is typically necessary for the radius. Except as specifically stated, this article discusses circles in the Euclidean plane and other aspects of Euclidean geometry.
In particular, a circle is a straight, closed curve that separates the plane into its inner and exterior.
Therefore, The model that shows the problem 1 divided by 1/6 is option 1.
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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
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Find the midpoint of the line segment with the given endpoints.
Answer
2x73
Step-by-step explanation:
Answer:
(11.5, 7.5)
Step-by-step explanation:
17 + 6 / 2 = 11.5
2 + 13 / 2 = 7.5
Can you help me with this
2. Natalie is selling candles to raise money for her softball team. The team has two different options for selling the candles. The first option is to sell a package of 5 candles for $18. The second option is to sell individual candles for $4 each.
(a) The team wants to earn $1404. How many candles do the members need to sell if they sell candles only in packages? How many candles do they need to sell if they sell only single candles? Explain your answer using an equation for each situation.
(b) Describe at least one advantage of selling the candles in packages. Describe at least one disadvantage of selling the candles in packages
a) The amounts that the team needs to sell is given as follows:
Packages: 390 candles.Single candles: 351 candles.b) The advantage and disadvantage is given as follows:
Advantage: Better opportunity cost when a person needs one candle, the person will have to purchase the entire package.Disadvantage: Lower revenue per candle.How to obtain the amounts?The amounts needed are found applying the proportion, considering the costs and the number of candles.
A package of 5 candles for $18, hence the number of candles needed to earn $1404, in packages, is given as follows:
5 candles - $18
n candles - $1404
Applying cross multiplication, we have that:
18n = 5 x 1404
n = 5 x 1404/18
n = 390 candles.
With a single candle, the number of candles is calculated as follows:
1404/4 = 351 candles.
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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
Answer to this required:
Answer:
B
Step-by-step explanation:
the hypotenuse is z
For the Pythagorean theorem:
x² + y² = z²
use the intermediate value theorem to show that there is a root of the given equation in the specified interval.
To use the intermediate value theorem to show that there is a root of the given equation in the specified interval, we first need to find the values of the function at the two endpoints of the interval. Let's say the function is denoted by f(x) and the interval is [a, b].
If f(a) and f(b) have opposite signs (one is positive and the other is negative), then by the intermediate value theorem, there must be at least one root of the equation f(x) = 0 in the interval [a, b]. This is because the intermediate value theorem states that if a function is continuous on a closed interval and the function takes on different values at the endpoints of the interval, then there must be at least one point in the interval where the function takes on the value of the intermediate value between the two endpoints.
For example, suppose we have the equation f(x) = x^2 - 3 and we want to show that there is a root of the equation in the interval [1, 2]. We can evaluate the function at the two endpoints of the interval:
f(1) = 1^2 - 3 = -2
f(2) = 2^2 - 3 = 1
Since f(1) and f(2) have opposite signs, by the intermediate value theorem, there must be at least one root of the equation f(x) = 0 in the interval [1, 2]. To find the root, we can use a root-finding algorithm such as bisection or Newton's method.
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A local entrepreneur would like to know if those who live in an urban or rural community are more likely to buy a real Christmas tree. He takes a random sample of 100 people who reside in the city and a separate random sample of 100 people who live in the village and asks them if they buy a real tree at Christmas time. Of the urban participants, 22 buy a real tree. Of the rural participants, 28 buy a real tree. Let p1 = the proportion of all people who live in rural communities and buy a real Christmas tree, and let p2 = the proportion of all people who live in urban communities and buy a real Christmas tree. What is the p-value?
.32
.16
.07
.18
The value of p is 0.16. So the option b is correct.
A local entrepreneur takes a random sample of 100 people.
Of the urban participants, 22 buy a real tree.
Of the rural participants, 28 buy a real tree.
Let p1 = the proportion of all people who live in rural communities and buy a real Christmas tree.
Let p2 = the proportion of all people who live in urban communities and buy a real Christmas tree.
We have to find the p-value
p1 = X1/N1
p1 = 28/100
p1 = 0.28
p2 = X2/N2
p2 = 22/100
p2 = 0.22
p = (X1 + X2)/(N1 + N2)
p = (28+22)/(100+100)
p = 0.25
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2
Test statistic
z = (p1 - p2)/√(p*(1-p)*(1/N1 + 1/N2))
z = (0.28-0.22)/√(0.25*(1-0.25)*(1/100 + 1/100))
z = 0.9798
P-value Approach
P-value = 0.16
Hence, the option A is correct. 0.16 is the p-value.
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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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