From distance formula, the distance covered by a particle with position (x, y) as time, t is equals to the [tex] 18\sqrt{2}[/tex].
The distance d, traveled by the particle with position vector, r(t) = <x(t), y(t) > over the interval [a,b] is calculated by following
[tex]d = \int_{a}^{b} ( (\frac{dx}{dt})² +(\frac{dy}{dt})² )dt[/tex]. We have a particle with position value (x, y) as t varies in the time interval. The parametric equations are, x = 3 sin² (t), y = 3 cos²(t), on the
time interval [0,3π]. Now the derivative of above parametric equations with respect to time t are [tex]\frac{dx}{dt} = 6 sin(t)cos(t) [/tex] = 3 sin(2t)
[tex]\frac{dy}{dt} = -6 sin(t)cos(t) [/tex]
= - 3 sin(2t)
Therefore, the required distance travelled by particle in the interval [0,3π] is written as [tex]d = \int_{0}^{3π} \sqrt{( (3 sin(2t))² + (-3 sin(2t))²) dt} \\ [/tex]
[tex]= \int_{0}^{3π} \sqrt{ ( 9 sin²(2t) + 9sin²(2t))}dt \\ [/tex]
[tex]= \int_{0}^{3π} \sqrt{18sin²(2t)dt}[/tex]
[tex]= 3\sqrt{2}\int_{0}^{3π} |sin(2t)|dt[/tex]
[tex]= 3\sqrt{2}[ \int_{0}^{\frac{π}{2}} sin(2t)dt - \int_{\frac{π}{2}}^{π} sin(2t)dt + \int_{π}^{\frac{3π}{2}} sin(2t)dt - \int_{\frac{π}{2}}^{2π}sin(2t)dt + \int_{2π}^{\frac{5π}{2}}sin(2t)dt - \int_{\frac{5π}{2}}^{3π}sin(2t)dt \\ [/tex]
[tex]= 3\sqrt{2}([ \frac{cos(2t)}{2}]_{0}^{\frac{π}{2}} - [\frac{cos(2t)}{2}]_{\frac{π}{2}}^{π} + [\frac{cos(2t)}{2}]_{π}^{\frac{3π}{2}} - [\frac{cos(2t)}{2}]_{\frac{3π}{2}}^{2π} + [\frac{cos(2t)}{2}]_{2π}^{\frac{5π}{2} }- [ \frac{cos(2t)}{2}]_{\frac{5π}{2}}^{3π})\\ [/tex]
[tex]= 3\sqrt{2}([ \frac{1}{2} +{\frac{1}{2}] - [\frac{-1}{2}- \frac{1}{2}}] + [\frac{1}{2}+ \frac{1}{2}] - [\frac{-1}{2} - \frac{1}{2}] + [\frac{1}{2} + \frac{1}{2}]- [ \frac{-1}{2} - \frac{1}{2}])\\ [/tex]
[tex]= 3\sqrt{2}(6)[/tex] =[tex]= 18\sqrt{2}[/tex]
Hence, the required distance is [tex] 18\sqrt{2}[/tex].
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Help pleasee. I have no idea how to do this
Four fiths of the footballs team's 30 points were scored on pass plays. How many points did the team score on pass plays?
Answer: 24 points
Step-by-step explanation:
4/5 is equal to 0.80. Multiply 30 by 0.80 and you get 24 points.
Fierro brothers, a discount broker, charges their customers a $19 flat fee per trade. The sondo investment house charges a 2% commission. For what amount of stock would both brokers charge the same commission?
Answer:
yes it will be the same
Step-by-step explanation:
Let’s call the amount of stock traded “x”. Then we can set up an equation like this:
$19 = 0.02x
To solve for x, we can divide both sides by 0.02:
$950 = x
Therefore, if you trade $950 worth of stock, both Fierro Brothers and Sondo Investment House would charge you the same commission.
pls help
which number would make the statement true?
click full image
Answer:
0.535 is the correct choice.
a relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 92 months and a standard deviation of 3.6 months. when this computer-relay microchip malfunctions, the entire satellite is useless. a large london insurance company is going to insure the satellite for 50 million dollars. assume that the only part of the satellite in question is the microchip. all other components will work indefinitely. a button hyperlink to the salt program that reads: use salt. (a) for how many months should the satellite be insured to be 96% confident that it will last beyond the insurance date? (round your answer to the nearest tenth of a month.) (no response) incorrect: your answer is incorrect. months (b) if the satellite is insured for 84 months, what is the probability that it will malfunction before the insurance coverage ends? (round your answer to four decimal places.) (no response) incorrect: your answer is incorrect. (c) if the satellite is insured for 84 months, what is the expected loss to the insurance company (in dollars)? (round your answer to the nearest dollar.) $(no response) incorrect: your answer is incorrect. (d) if the insurance company charges $3 million for 84 months of insurance, how much profit does the company expect to make (in dollars)? (round your answer to the nearest dollar.) $(no response) incorrect: your answer is incorrect.
The satellite should be insured for 98 months (rounded up to the nearest month) to be 96% confident that the microchip will last beyond the insurance date.
To answer this question, we need to find the number of months for which we can be 96% confident that the microchip will not malfunction. This means we want to find the value of x such that P(X > x) = 0.04, where X is the random variable representing the life expectancy of the microchip.
We know that X follows a normal distribution with mean μ = 92 months and standard deviation σ = 3.6 months. Therefore, we can standardize X to the standard normal distribution Z ~ N(0, 1) using the formula
Z = (X - μ) / σ
We can then rewrite the probability P(X > x) as
P(X > x) = P(Z > (x - μ) / σ)
1.75 = (x - 92) / 3.6
Solving for x, we get
x = 98 months
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The given question is incomplete, the complete question is:
A relay microchip in a telecommunications satellite has a life expectancy that follows a normal distribution with a mean of 92 months and a standard deviation of 3.6 months. when this computer-relay microchip malfunctions, the entire satellite is useless. a large london insurance company is going to insure the satellite for 50 million dollars. assume that the only part of the satellite in question is the microchip. all other components will work indefinitely. a button hyperlink to the salt program that reads: use salt.for how many months should the satellite be insured to be 96% confident that it will last beyond the insurance date?
which graph represents f(x) =3x-2
The graph that represents f(x) =3x-2 is the graph (b)
Which graph represents f(x) =3x-2From the question, we have the following parameters that can be used in our computation:
The equation: f(x) = 3x - 2
From the above equation, we have
f(x) = 3x - 2
The above equation is a linear function with the following features
Slope = 3
y-intercept = -2
This means that the graph intersects with the y axis at y = -2
Using the above as a guide, we have the following:
The graph intersects with the y axis at y = -2 and has a slope of 2 is graph (b)
Hence, the graph that represents f(x) =3x-2 is graph (b)
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Jim's family recently moved to a new
city. The city's population has been
growing, and based on recent trends,
Jim expects it to continue growing
exponentially. This table shows the
expected population in the next two
years.
Time (years)
Population
840,000
882,000
Time (years)
1
2
Find an expression for P(t), the city's
population t years from now. Write your
answer in the form P(t) = a(b)t, where a
and b are integers or decimals. Do not
round.
P(t) =
To find an expression for P(t), we can use the two given data points to create a system of equations. We can assume that the population is growing exponentially, which means that the population at time t is given by:
P(t) = a(b)^t
where a and b are constants that we need to determine.
Using the first data point, we have:
840,000 = a(b)^1
which simplifies to:
840,000 = ab
Using the second data point, we have:
882,000 = a(b)^2
We can solve for a in terms of b by dividing the second equation by the first equation:
882,000/840,000 = (a(b)^2)/(ab)
Simplifying, we get:
1.05 = b
Substituting this value of b into the first equation, we get:
840,000 = a(1.05)
Solving for a, we get:
a = 800,000
Therefore, the expression for P(t) is:
P(t) = 800,000(1.05)^t
This means that the city's population t years from now can be calculated by multiplying the initial population of 800,000 by 1.05 raised to the power of t.
Answer:
Step-by-step explanation:
city. The city's population has beengrowing, and based on recent trends,Jim expects it to continue growingexponentially. This table shows theexpected population in the next twoyears.Time (years)Population840,000882,000Time (years)12Find an expression for P(t), the city'spopulation t years from now. Write youranswer in the form P(t) = a(b)t, where aand b are integers or decimals. Do notround.P(t) =
When Gina first started working for a pro football player, he had 4,125 followers and she was able to increase his followers by 9% per month. How long would it take the football player to double his current online following of 105,326? Round answer to two decimal places
It would take about 8.59 months for the football player to double his current following, assuming that his follower count continues to increase at a rate of 9% per month.
To find out how long it would take for the football player to double his current online following of 105,326, we need to find the distance from his starting point to the doubling point. In other words, we need to find out how many followers he needs to gain in order to have 2 times his current following.
To do this, we can use the formula for exponential growth:
A = P(1 + r)ⁿ
where A is the final amount, P is the initial amount, r is the rate of growth (in decimal form), and t is the time (in months).
In this case, we want to find t, the time it would take for the football player to double his current following. So we can rewrite the formula as:
2P = P(1 + 0.09)ⁿ
Simplifying this equation, we can divide both sides by P:
2 = (1 + 0.09)ⁿ
Taking the natural logarithm of both sides, we get:
ln(2) = t ln(1 + 0.09)
Solving for t, we divide both sides by ln(1 + 0.09):
t = ln(2) / ln(1 + 0.09)
Using a calculator, we get t ≈ 8.59 months.
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I don't get it... please help thanks in advance
Answer:
Set your calculator to degree mode.
[tex] \tan( \alpha ) = \frac{23}{35} [/tex]
[tex] \alpha = {tan}^{ - 1} \frac{23}{35} = 33.31[/tex]
The angle of elevation of the sun is about 33°.
Geometry Pleeeeeease help !!!!Find the values of x and y. Write your answer in simplest form.
The values of x and y in the simplest form in the triangles are computed and listed below
Finding the values of x and y in the simplest form.Figure (1)
Using the proportion of similar triangles, we have
x/6 = 6/9
So, we have
x = 36/9
This gives
x = 4
Next, we have
y^2 = 6^2 + 4^2
y^2 = 52
y = 2√13
Figure (2)
Using the proportion of similar triangles, we have
x/6 = 6/2
So, we have
x = 36/2
This gives
x = 18
Next, we have
y^2 = 6^2 + 18^2
y^2 = 360
y = 6√10
Figure (3)
Using the pythagoras theorem of right triangles, we have
y^2 = 40^2 - 32^2
y^2 = 576
y = 24
Next, we have
x^2 = 30^2 - 24^2
x^2 = 324
x = 18
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Triangle ABC is similar to triangle DEF. What is DE?
The measure of DE, given that Triangle ABC is similar to Triangle DEF, is 53. 09 units .
How to find the measure of DE ?To find the measure of DE, you need to use the corresponding sides of BC and EF to find the scale factor that shows the difference in the sizes of corresponding sides.
The scale factor is:
= 31 / 8
= 3. 875
Now, since the value of the corresponding side of AB is 13.7 units, the measure of DE would be :
= 13. 7 x 3. 875
= 53. 09 units
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At a local store, 2 bagels and 2 cups of coffee cost $4.40. The cost of 3 bagels and 4 cups of coffee is $7.80.
Part A:
Write a system of equations to represent this situation.
Part B:
Solve the system of equations by substitution and interpret its meaning.
Whether has a saving acc he depos the same amount of money each month after 3 month had 150 in the acc after 5 month he had 300 in the acc make a table values interesting the two points
Regularly depositing the same amount into a savings account can lead to a large rise in the account balance over time with the appropriate plan and dedication.
What is amount?An undefined number or quantity of something is referred to as an amount and can be used in a variety of different settings. Any number, quantity, length of time, or amount of data can be referred to as an amount. Amount in terms of money refers to the total amount being paid or received. The quantity of physical items is the total number of those items. The length or duration of a work or event can be referred to as the amount in terms of time. The entire quantity of data points or pieces of information is referred to as the amount in terms of data.
Here in the question:
Month | Amount Deposited | Account Balance
1 | 150 | 150
2 | 150 | 300
3 | 150 | 450
4 | 150 | 600
5 | 150 | 750
As seen in the table above, after five months, a 150 initial deposit into a savings account can grow to a balance of 750 with monthly deposits of the same amount for the next four months. This demonstrates that consistent saving can have a considerable impact on a savings account's overall balance.
Since interest is calculated using the compounding principle, regular deposits can enhance the amount that can be earned over time. This indicates that interest may be accumulated on both the initial deposit and any prior interest in the account. So, by consistently contributing the same amount of money to a savings account, it is feasible to dramatically raise the account's overall balance.
In conclusion, it is clear that consistent contributions to a savings account can be an excellent strategy to build wealth. Regularly depositing the same amount into a savings account can lead to a large rise in the account balance over time with the appropriate plan and dedication.
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Matt is painting the trim in his living room. He leans a ladder against the wall so that it forms an angle
elevation with the floor of 56°. If it is a 12-foot ladder, how high up on the wall does it reach? Round to
the nearest tenth.
Answer:
9.9 inches
Step-by-step explanation:
Visualize the scenario for a second. If the ladder is leaning against the wall, we can assume that it is the hypothenuse of the triangle that is forming here. The angle of elevation in this scenario is the angle formed by the ladder and ground.
Next, recall each trig function and determine which best belongs. We have the hypothenuse and we need the side opposite the angle. Therefore, we use sine. (probably using a calculator for trig questions)
Therefore, we can now set up our equation and solve. (x is the height of the wall)
sin 56 = [tex]\frac{x}{12}[/tex] Initial equation
12 sin 56 = x Multiply each side by 12 so that we get x by itself.
x ≈ 9.9 Punch 12 sin 56 into a calculator and your done!
Therefore, the answer is about 9.9 inches. (If you got something different, make sure that your calculator is in degrees and not radians! Some calculators abbreviate it as DEG and RAD respectively.)
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
The best measure of variability for the data is A. The range is the best measure of variability, and it equals 8.
How to find the range ?The range is the difference between the highest value and the lowest value in the dataset. In this case, the highest number of rose bouquets is 9, and the lowest is 1. This is the data shown on the line plot.
Range = Highest Value - Lowest Value
Range = 9 - 1
Range = 8
The range is the best measure of variability, and it equals 9. The IQR is used when there are outliers that can affect the data.
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Anumeha mows lawns. She charges an initial fee and a constant fee for each hour of work.F represents Anumeha's fee (in dollars) for working t hours. F = 6 + 12t How much does Anumeha charge for each hour of work?
Answer:
if she worked 2h it would be 2×12 for the hourly charge which would be 24and then the 24+6where 6 is the base charge.
Step-by-step explanation:
The intial few would be 6.as we can see in the equation
f(t)=6+12t
t would be the amount of hours and 12 is the rate per hour.
Martin is building a wire-screen chicken coop in the shape of a rectangular prism. The coop has a height of 42 inches, a width of 36 inches, and a length of 48 inches. Martin wants to determine the total surface area of the coop in order to purchase the correct amount of wire screening.
Which of the following expressions represents the total surface area of the right rectangular prism with the dimensions given above?
The total surface area of the wire-screen chicken coop is 10512 square inches.
What is surface area?The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area
According to the given information:the total surface area of the right rectangular prism, we use the formula:
2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively.
We are given the height, width, and length of the wire-screen chicken coop, which are 42 inches, 36 inches, and 48 inches, respectively.
Substituting these values in the formula, we get:
2(36)(48) + 2(36)(42) + 2(48)(42)
Multiplying out, we get:
= 3456 + 3024 + 4032
Adding these terms, we get the total surface area:
= 10512
Therefore, the total surface area of the wire-screen chicken coop is 10512 square inches.
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a b c or d please help quick
Answer:
D.
Step-by-step explanation:
By looking at them I feel like D. is the best option
at how many points on the interval is the line tangent to parallel to the secant line connecting the function endpoints?
The line tangent to f(x) = x + sin(x) is parallel to the secant line connecting the endpoints at x = π on the interval [-2π, 2π].
Let's begin by finding the slope of the secant line connecting the endpoints of the function. The endpoints of the function on the interval [-2π, 2π] are (-2π, -2π + sin(-2π)) and (2π, 2π + sin(2π)), which evaluate to (-2π, 0) and (2π, 0), respectively.
The slope of the secant line is
m = (0 - 0)/(2π - (-2π)) = 0
Since we want the tangent line to be parallel to the secant line, the slope of the tangent line should also be 0. We can find the equation of the tangent line using the point-slope form
y - (x + sin(x)) = 0
y = x + sin(x)
To find the points on the interval where the tangent line is parallel to the secant line, we need to find the values of x where the derivative of f(x) is equal to 0 (i.e., where the slope of the tangent line is 0). The derivative of f(x) is
f'(x) = 1 + cos(x)
Setting this equal to 0 and solving for x, we get
cos(x) = -1
x = π
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The given question is incomplete, the complete question is:
At how many points on the interval [-2pi, 2pi] is the line tangent to f(x)=x+sin x parallel to the secant line connecting the function endpoints?
Evaluate: 2 × [(6 + 1)² + 1]
Answer:
100
Step-by-step explanation:
2 x [(7)^2+1]
2x(49+1)
2x(50)
100
Select the correct answer.
Scatter plot graph in quadrant 1 of a coordinate plane. 12 points are plotted approximated at (2, 3), (4, 5), (5.8, 4), (5.9, 6.1), (3, 13), (4.9, 7.9), (5.5, 9.1), (6.5, 8), (6.5, 10), (7.5, 7.1), (8, 9), and (8.1, 10.1).
Which point represents the outlier?
A.
(2, 3)
B.
(4, 5)
C.
(3, 13)
D.
(8, 9)
Answer:
d
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
c
Can someone help me out with this question please
The x-coordinate when Q has a y-coordinate of -4 is given as follows:
x = 3 or x = -3.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The radius of a circle represents the distance between the center of the circle and a point on the circumference of the circle, while the diameter of the circle is the distance between two points on the circumference of the circle that pass through the center. Hence, the diameter’s length is twice the radius length.
The circle in this problem has the parameters given as follows:
Center at the origin.Radius of 5.Hence the equation is given as follows:
x² + y² = 25.
When the y-coordinate is of -4, the x-coordinate is given as follows:
x² + (-4)² = 25
x² + 16 = 25
x² = 9
x = -3 or x = 3.
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For the month of January, the amount of
snowfall was 3 inches above average.
Required polynomial is (x+3) where x is amount of average snowfall.
Here given in January, the amount of snowfall was 3 inches above average.
1. The average snowfall for January was a certain amount (let's call this 'A' inches).
2. The actual snowfall for January was 3 inches more than the average.
3. To calculate the actual snowfall for January, we can use the equation: Actual Snowfall = Average Snowfall (A) + 3 inches.
So, if we knew the average snowfall (A), we could easily find the actual snowfall by adding 3 inches to it.
Let amount of average snowfall be x inches.
So, snowfall in January month = (x+3) inches .
Therefore, required polynomial is (x+3) where x is amount of average snowfall.
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Correct answer is " Find a polynomial of the statement For the month of January, the amount of snowfall was 3 inches above average"
Dana has 9 CDs. She has 1/5 as many as Sonya. How many CDs does Sonya have?
Answer:
Usemos la variable s para representar la cantidad de CD que tiene Sonya.
Luego, dado que Dana tiene 1/5 de la cantidad que tiene Sonya, podemos escribir la siguiente ecuación y resolverla para s:
1 s = 9
5
Multiplica ambos lados de la ecuación por 5 para resolver:
5 * 1 s = 9 * 5
5
s = 45
Sonya tiene 45 CD.
If you know the length of the short leg of a 30-60-90 triangle, how do you find the length of the other, longer leg?
The length of the longer leg of this 30-60-90 triangle is 6.93 units.
In a 30-60-90 triangle, the length of the shorter leg is opposite to the 30-degree angle. The longer leg is opposite to the 60-degree angle, and the hypotenuse is opposite to the 90-degree angle.
The ratio of the sides in a 30-60-90 triangle is always the same. The length of the shorter leg is half of the length of the hypotenuse. The longer leg is the square root of three times the length of the shorter leg.
Let's use this information to solve a problem. Suppose you have a 30-60-90 triangle with a shorter leg of length 4 units. We can use the ratio to find the length of the longer leg.
The length of the hypotenuse is twice the length of the shorter leg, which is 2 times 4 units = 8 units.
The longer leg is the square root of three times the length of the shorter leg, which is the square root of three times 4 units = 6.93 units.
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Draw a coordinate plane. Plot the points: A(3, 4), B(2, 2), C(5, 8), D(7, 12), and E(9, 14). All but one of the points are on the same line. Which one is not?
The point that is not on the same line as the others is E(9, 14).
How to find the point ?The point that is not on the same line as the others would not have the same slope as the others.
Slope between A ( 3, 4) and B (2, 2):
= (4 - 2) / (3 - 2) = 2 / 1
= 2
Slope between B (2 , 2) and C (5, 8):
= ( 8 - 2 ) / (5 - 2)
= 6 / 3
= 2
Slope between C ( 5, 8) and D(7, 12):
= (12 - 8) / (7 - 5)
= 4 / 2
= 2
Slope between D ( 7, 12) and E ( 9, 14):
= ( 14 - 12) / (9 - 7)
= 2 / 2
= 1
We can therefore see that E ( 9, 14) is the odd one out and is not on the same line.
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The mean and the standard deviation of the sample of 100 bank customer waiting times are x⎯⎯ = 5.33 and s = 2.207. Calculate a t-based 95 percent confidence interval for µ, the mean of all possible bank customer waiting times using the new system. Are we 95 percent confident that µ is less than 6 minutes?. Assume normality.
95% confidence that the population mean is less than 6 minutes since the upper limit of the confidence interval is below 6 minutes.
95% confidence that the population mean is within the range of 4.897 to 5.763 minutes.
The t-based 95 percent confidence interval for the population mean:
CI =[tex]\bar x\pm t\alpha/2 \times (s/\sqrt n)[/tex]
[tex]\bar x[/tex] is the sample mean, s is the sample standard deviation, n is the sample size, tα=/2 is the t-value corresponding to the desired level of confidence and (s/√n) is the standard error of the mean.
The sample size is 100, the sample mean is 5.33, and the sample standard deviation is 2.207, the standard error of the mean is:
s/√n
= 2.207/√100
= 0.221
The t-value corresponding to a 95% confidence level with 99 degrees of freedom (100 - 1), look it up in a t-distribution table or use a calculator.
The t-value is approximately 1.984.
The 95% confidence interval for the population mean is:
CI = 5.33 ± 1.984 × 0.221
= [4.897, 5.763]
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this is what i need help with
Answer:
Step-by-step explanation:
x = [tex]\sqrt{12^{2}+9^{2} }[/tex]
x = 15
six integers have a range of 13. The integers are 5,9,7,12,3,x. Find the value of x
Thus, for the given range of data of six integers the value of x is found as: x = 16.
Explain about the range of data:The difference here between maximum and smallest values in a data set is known as the range. Employing the exact same units as the data, it measures variability. More variability is shown by larger values.
Take the highest value and deduct the lowest value from it to determine the range in statistics.
A data set's range
Range is equal to the highest and lowest values.
Since the formula subtracts any smaller value from the larger one, it is impossible for it to be negative.
Given data:
six integers: 5,9,7,12,3,x.
Range = 13
The formula for the range ;
Range = maximum value - minimum value
x - 3 = 13
x = 13 + 3
x = 16
Thus, for the given range of the data of six integers the value of x is found as: x = 16.
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The length of a rectangle is
double its width and the area of
the rectangle is 288 cm². What is
the perimeter of the rectangle?
The perimeter of the rectangle is 72 cm.
what you mean by perimeter?Perimeter is the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all sides or edges of the shape.
The perimeter is usually measured in units such as centimeters (cm), meters (m), feet (ft), or inches (in), depending on the unit of measurement used for the sides or edges.
Let's start by assigning variables to the length and width of the rectangle.
Let x be the width of the rectangle in cm.
Then, the length of the rectangle is double the width, which is 2x cm.
We know that the area of the rectangle is 288 cm², so we can set up an equation:
Area = Length x Width
288 = 2x * x
Simplifying the equation, we get:
288 = 2x²
Dividing both sides by 2, we get:
144 = x²
Taking the square root of both sides, we get:
x = ± 12
Since x cannot be negative (as it represents a length), we take x = 12 cm as the width of the rectangle.
The length of the rectangle is 2x, which is 24 cm.
Now we can find the perimeter of the rectangle, which is given by the formula:
Perimeter = 2(Length + Width)
Substituting the values we found, we get:
Perimeter = 2(24 + 12) = 72 cm
Therefore, the perimeter of the rectangle is 72 cm.
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