The Euler, explicit Trapezoid, and fourth-order Runge-Kutta methods were applied to a given initial value problem on a grid/mesh of step-size h=0.1 in [0,1]. The results were printed in a table, showing the t values, approximations, and global error at each step.
Euler Method
t Approximation Global Error
0 1 0
0.1 1.011 -0.011
0.2 1.0454 -0.0454
0.3 1.1044 -0.1044
0.4 1.1921 -0.1921
0.5 1.3125 -0.3125
0.6 1.4713 -0.4713
0.7 1.6749 -0.6749
0.8 1.9301 -0.9301
0.9 2.2447 -1.2447
1 2.63 -1.63
Explicit Trapezoid Method
t Approximation Global Error
0 1 0
0.1 1.0055 -0.0055
0.2 1.0246 -0.0246
0.3 1.0592 -0.0592
0.4 1.1021 -0.1021
0.5 1.1564
The Euler method is a numerical technique for solving initial-value problems, which involves approximating the solution of a differential equation by the combination of a series of tangent lines. The explicit trapezoid method is an improved version of the Euler method, which uses the average of two slopes instead of the slope at the previous point whencalculating the next approximation. The fourth-order Runge-Kutta method is a technique that uses a weighted average of four different slopes at different points to approximate the solution of a differential equation.
For the given initial value problem, we applied the Euler method, the explicit Trapezoid method, and the fourth-order Runge-Kutta method on a grid/mesh of step-size h=0.1 in [0,1]. We printed a table of the t values, approximations, and global error at each step.
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What is 9 x (46+70) 5 - 32 (40 - 219) =
The given expression 9x(46+70)5 - 32(40-219) is equal to = 10948.
What is mathematical expression?
A mathematical sentence that contains at least one operation, numbers, and/or variables without the equal sign is known as a mathematical expression.
Expressions does not have equal sign as the equations have.
Considering the given question as:
9x(46+70)5 - 32(40-219) = ?
At first we will solve the expressions inside of the brackets:
= 9x(116)5 - 32(-179)
Now, ,we will solve the rest of the expressions
= 9x580 + 5728
= 5220 + 5728
= 10948
Therefore, the answer of the given question is 10948
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Solve the following equation if d = -2. If necessary, round to the nearest tenth. 2/3(6c+9d)+3/4(8c-16d)=-18
Answer:
c = - 3-----------------------------------
Simplify the equation by distribution, then substitute the value of d and solve for c:
2/3(6c + 9d) + 3/4(8c - 16d) = - 182/3(6c) + 2/3(9d) + 3/4(8c) - 3/4(16d) = - 184c + 6d + 6c - 12d = - 1810c - 6d = - 1810c - 6(-2) = - 1810c + 12 = - 1810c = - 12 - 1810c = - 30c = - 3The graph of the function f(x) = (x + 2)(x + 6) is shown below.
On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0).
Which statement about the function is true?
The function is positive for all real values of x where
x > –4.
The function is negative for all real values of x where
–6 < x < –2.
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.
the interval, the function returns zero (-6,-2) –6 < x < –2
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.
The given f(x) = (x + 2)(x + 6)
In this function, a quadratic equation is represented (vertical parabola open upward)
The vertex stands for a minimum.
the use of a graphing tool
view the attached image
x=-6 and x=-2 are the x-intercepts.
Point: the y-intercept
The point is called the vertex.
The range ——-> is the domain. (-∞,∞) (All real numbers) (All real numbers)
The range is in the range [-4,].
x -6 or x > -2 make the function positive.
For the interval, the function returns zero (-6,-2) –6 < x < –2
Hence, the interval, the function returns zero (-6,-2) –6 < x < –2
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Determine if the statement below is true or false.
If BCA, then AUB=A.
Is the statement true or false?
O False
O True
The statement If B ⊂ A, then A U B = A is true.
How to determine the truth value of the statement?From the question, we have the following parameters that can be used in our computation:
If BCA, then AUB=A.
When the above statement is represented properly, we have the following representation
If B ⊂ A, then A U B = A
The statement If B ⊂ A means that
The set B is a subset of the set A
In other words, the whole of set B is in set A
If this is true, then the union of both sets represented by A U B is set A
Hence, it is true that If B ⊂ A, then A U B = A
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What is the value of n in this equation 3n 8 32?; What is equation in math?
The value of n in the equation, 3n - 8 = 32 - n will be 10. The value is obtained by rearranging the equation and adding the like term.
the equation is :-
3n-8=32-n
take all the values of n one side-
3n+n = 32+8
4n = 40
n = 40/4
n = 10
so the value of the n in the equation is 10.
What is the equation?
An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
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The universities budget covers cost for nine months what is Amy’s monthly budget for textbooks in course supplies? What is her monthly budget for rent on utilities and food? What is your monthly budget for a personal and miscellaneous cost? what is her total monthly budget?
Amy’s monthly budget for textbooks in course supplies is $900.00
Amy's monthly budget for rent, utilities and food is $12,798.
Her monthly budget for a personal and miscellaneous cost is $2,259.
Her total monthly budget equals $15,957.
What does Budget mean?A budget is best defined as estimation of the revenue and expenses over a specified future period of time and is usually compiled and re-evaluated on a periodic basis.
Budget for textbooks:
= $900.00
Budget for rent, utilities and food:
= $12,798.
Budget for personal and miscellaneous cost:
= $2,259.
Total monthly budget:
= $900 + $12,798 + $2,259
= $15,957.
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In the xy-plane, what is the y-coordinate of the y-intercept of the graph of the equation
Answer: -6
Step-by-step explanation:
(0,y)
at y intercept, x is 0. therefore sub x with 0 and solve
y= 3(0)-12/0+2
= -12/2
=-6
An office is divided into 8 cubicles. How many of the cubicles are painted if only 1/8 of the cubicles are painted?
A) 2 B) 4
C) 8 D) 1
Answer:
D) 1
Step-by-step explanation:
(1/8) x 8= 1
Hope this helps!
Simplify completely.
(h12/h4)3
Enter your answer in the box.
After solving the given expression using exponents properties, the resultant answer is h²⁴.
What are exponents?Exponentiation is a mathematical process that involves the base b and the exponent or power n.
It is represented as bⁿ and is pronounced as "b to the n."
Positive, negative, zero, and rational exponents are the four different categories. Positive exponents indicate the number of times a base should be multiplied by itself.
So, we have:
(h¹²/h⁴)³
Now, solve as follows using properties:
(h¹²/h⁴)³
(h¹²)³/(h⁴)³
h³⁶/h¹²
h³⁶⁻¹²
h²⁴
Therefore, after solving the given expression using exponents properties, the resultant answer is h²⁴.
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Change the circle equation into standard form then answer the following questions:
Coordinates of the center?
Coordinates of the vertices?
How long is the radius?
Domain?
Range?
X²+ Y²-6X-2Y+6=0
The circle equation in standard form is (X - 3)² + (Y - 1)² = 2²
How to change the circle equation into standard form?
We must transform the current polynomial to circle standard form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We will do so by completing the square, which produces a perfect square trinomial that can be factored into a square binomial in the form of the circle standard form.
According to the given question:
Equation of circle in polynomial form is X²+ Y²- 6X - 2Y + 6 = 0
Converting to standard form using completing the square method
X²+ Y²- 6X - 2Y + 6 = 0
(X² - 6X) + (Y² - 2Y) = -6
(X² - 6X + 9) + (Y² - 2Y + 1) = -6 + 9 + 1
(X - 3)² + (Y - 1)² = 4
(X - 3)² + (Y - 1)² = 2²
The circle is now in standard form.
Coordinates of the center (h,k) = (3, 1)
Coordinates of the vertices = (3, 1), (3, -6), (2, -4), (8, -1)
Domain = [2, 8]
Range = [-6, 1]
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what is 258 divided by 4?
The quotient of 258 divided by 4 is calculated to be 64.5
Division is considered to be one of the four basic operations of arithmetic. The other three are multiplication, addition, and subtraction, and they can be defined as how numbers are combined to make new numbers.
Out of the four basic operations, division is the process of splitting an amount or a number into equal parts.
In division, the numerator is the top number of a fraction, and on the other hand, the denominator is the bottom number of a fraction and the result of division is called the quotient
In this case, 258 is the numerator and 4 is the denominator;
258 / 4 = 64.5
Therefore the quotient of this division is calculated to be 64.5
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The students calculate a chi-squared value of 92.86 and compare it with a critical value of 7.82. Which of the following best completes the chi-square good The null hypothesis cannot be rejected, and the students should conclude that the data fit a model of independent assortment. The null hypothesis cannot be rejected, and the students should conclude that the data may have resulted from genetic linkage. The null hypothesis can be rejected, and the students should conclude that the data fit a model of independent assortment The null hypothesis can be rejected, and the students should conclude that the data may have resulted from genetic linkage.
The students should draw the conclusion that the data might have been caused by the genetic connection if the null hypothesis is rejected.
Given information;
The students determine a crucial value of 7.82 and compare it to a chi-squared value of 92.86.
Which of the following results in the chi-square goodness-of-fit test being most complete?
The null hypothesis can be rejected, and the students should conclude that the data may have resulted from the genetic linkage.
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Please help! I’ll mark the brainliest please!
A salon wants to conduct a survey in order to study the consumption pattern of its consumers. The population mean spending on visiting salon per month is unknown with the population standard deviation is assumed to be $200. A random sample of 55 customers is selected and the sample mean spending on visiting salon per month is $800.
(a) Construct a 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month.
(b) It is suggested to do the second round inspection. This time, the sample size is 120. What is the sampling error at 95% confidence level?
a) The 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month is given as follows:
(747, 853).
b) The sampling error at the 95% confidence level is of: 35.8.
How to obtain the confidence interval?We have the standard deviation for the population is known, hence the z-distribution is used to calculate the confidence interval.
The equation that gives the bounds of the confidence interval is presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The remaining parameters are given as follows:
[tex]\overline{x} = 800, \sigma = 200, n = 55[/tex]
Then the lower bound of the interval is calculated as follows:
800 - 1.96 x 200/square root of 55 = 747.
The upper bound of the interval is calculated as follows:
800 + 1.96 x 200/square root of 55 = 853.
For a sample size of n = 120, the sampling error is obtained as follows:
Sampling error = 1.96 x 200/square root of 120 = 35.8.
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Show a free-body diagram. For each: a. Redraw the diagram. b. Identify the direction of the acceleration vector and show it as a vector next to your diagram. Or, if appropriate, write . c. If possible, identify the direction of the velocity vector and show it as a labeled vector. d. Write a short description of a real object for which this is the correct free-body diagram. Use Examples and 5.6 as models of what a description should be like.
A) Acceleration Direction
The net force is acting down the surface, as seen in the figure. As a result, the acceleration vector should likewise be directed down the surface.
Labeling the vector of acceleration
The acceleration vector is depicted below:
B) Determine the velocity vector
According to the free-body diagram, an item should be on an inclined surface with a tension force pulling it down. When a kinetic frictional force is directed up to the surface, the item is said to be sliding down the slope. As a result, the velocity vector should be oriented upside down.
Determine the direction of the velocity vector
The velocity vector is indicated in the picture below:
C) Describe a real-world thing
The diagram shows an item on an inclined surface, with the kinetic force directed up to the surface. As a result, the item may be thought of as a box being pulled down by a rope down an inclined slope.
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Full Question
Problems 35 through 40 show a free-body diagram. For each:
a. Redraw the diagram
b Identify the direction of the acceleration vector and show it as a vector next to your diagram. Or, if appropriate, write
c. If possible, identify the direction of the velocity vector and show it as a labeled vector.
d Write a short description of a real object for which this is the correct free-body diagram. Use Examples 5.4, 5.5, and 5.6 as models of what a description should be like.
f(x)=-3x+3; Find f(8)
Answer:
f(8)= - 3 × 8 + 3
f(8) = - 21......
Which of the following can be a representation of a function?
All of the above can be a representation of a function:
A graph can be used to visualize a function.A table can be used to show input and output values.An equation can be used to express the relationships between the inputs and the outputs.Which of the following can be a representation of a function?Option D. All of the aboveA function can be represented in a variety of ways, such as:
A graph is a useful tool for visualizing the relationship between inputs and outputs of a function. A table can be used to represent the inputs and outputs of a function.An equation can be used to express the relationship between the inputs and outputs.All of these methods are valid representations of a function and can be used to explore and better understand the function.
Since the question is not complete, here's the full task:Which of the following can be a representation of a function?
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I need help with this please help me
suppose man paints on a she paper 25 in wide by 15 in high. He then places this sheet on a mat so that a uniform wide strip of the mat shows all around the picture. The perimeter of the mat is 96 in How wide is the strip of the mat showing around the picture?
When the mat's perimeter is 96 inches, the strip that shows around the picture is 4 inches broad.
What is perimeter?The perimeter of a shape is the distance around its edge. The perimeter of a form is the length of its contour. To calculate the perimeter of a rectangle or square, sum the lengths of all four sides. The perimeter of a shape is the distance around its exterior. Perimeter is calculated by summing the lengths of all the sides of a form.
Here,
length of paper, l=25 inch
width of paper, w=15 inch
perimeter=96 inch
Let x be the strip of mat,
l=25+2x
w=15+2x
perimeter=2(l+w)
96=2*(25+2x+15+2x)
48=40+2x
2x=8
x=4 inch
The strip of the mat showing around the picture is 4 inch wide when the perimeter of the mat is 96 inch.
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An airplane is flying on a compass heading (bearing) of 170° at 460 mph. A wind is blowing with the
bearing 200° at 80 mph.
a. Find the component form of the velocity of the airplane.
b. Find the actual ground speed and direction of the airplane
(a) The component form of the velocity of the airplane is (-453.01 i + 79.88 j) mph.
(b) The actual ground speed and direction of the airplane is 392.76 mph and 30 degrees respectively.
What is the component form of the velocity of the airplane?
The component form of the velocity of the airplane is calculated as follows;
Vy = V sinθ
Vx = V cosθ
where;
Vy is the vertical component of the velocity of the airplaneVx is the horizontal component of the velocity of the airplaneV is the speed of the airplaneθ is the angle of the speedVy = 460 mph x sin (170 - 90) = 79.88 mph
Vx = 460 mph x cos (170) = -453.01 mph
The bearing of the two speeds forms a triangle and the angle of the triangle is calculated as follows;
θ = θ₁ + θ₂
θ = (180⁰ - 170⁰) + (200⁰ - 180⁰)
θ = 30⁰
The resultant speed of the airplane is calculated as follows;
Vr² = V₁² + V₂² - 2(V₁)(V₂) cos(θ)
Vr² = (460²) + (80²) - 2(460 x 80) x cos(30)
Vr² = 154,260.53
Vr = √(154,260.53)
Vr = 392.76 mph
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Please help me on this.
the measure of the value a is 24°
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angles of triangle = 180
Here given 3 angles are 2a, 3a and a+36°
So the sum of all the angles should be 180°
⇒2a+ 3a +a+36° = 180
⇒6a = 180-36
⇒a = 144/6= 24
Hence the measure of the value a is 24°
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hypothesis testing is used to reject the notion that chance alone can explain the results of a study involving a random sample.
Hypothesis testing is the process used to evaluate the strength of evidence from sample and provides a framework for making determinations related to the population i.e. it provides a method for understanding how reliably over can extrapolate observed findings in a sample under study to the larger population from which the sample was drawn.
After a performing a test, scientist can: Reject the null hypothesis or Fail to reject the null hypothesis.
Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter.Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data. Such data may come from a larger population, or from a data-generating process.
The null hypothesis is usually a hypothesis of equality between population parameters. Hypothesis testing is a procedure, based on sample evidence and probability, used to test claims regarding a characteristic of a population.
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Write an equation to represent the relationship. Then solve the equation.
Six times a number plus 4 is the same as the number minus 11.
Answer:
-3
Step-by-step explanation:
6x + 4 = x - 11
6x - x = -11 - 4
5x = -15
5/5 x = -15/5
x = -3
Suppose four treatments are being compared with an ANOVA F test at the 5% level for equality of means. There are 6 replicate within each treatment. How many confidence intervals or hypothesis tests would need to be done to make significance statements for each pair-wise comparison? O 2 O 4 O 6O 8O 15
Six (6) confidence intervals or hypothesis tests would need to be done to make significant statements for each pair-wise comparison.
In an ANOVA F test, the null hypothesis is that the means of all the treatments are equal, and the alternative hypothesis is that at least two of the means are different. If the null hypothesis is rejected at the 5% significance level, this means that the differences between the means are statistically significant and the treatments can be considered different.
Since there are four treatments, there are 6 possible pairs of treatments. These tests would determine whether the means of each pair of treatments are significantly different from each other.
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4x + 19 = 8x please help
Answer:
x=4.75
Step-by-step explanation:
4x+19=8x
-4x -4x
19 = 4x
Divide 4 on each side
4.75=x or x=4.75
Tell Emily safe for trip look back over her spending habits on this page and page 9 what changes do you think she should make to save enough money for her trip explain your answer?
The total amount Emily spent each month for 20 days will be $142.
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.
In this situation, Emily spends $4.85 on a latte and $2.25 on a scone. The total amount spent for 20 days will be:
= (4.85 + 2.25) × 20
= 7.1 × 20.
= 142
The amount is $142.
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Last week,Barry's Swimwear sold/15 of its bathing suits in stock .Philip's Sun Wear sold 5 out of 72 of its bathing suits in stock. Which store sold a greater fraction of the bathing suits in stock?
Answer: Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.
Step-by-step explanation:
Barry's Swimwear sold 15 out of an unknown number of bathing suits in stock, so we can express this fraction as 15/x, where x is the total number of bathing suits in stock at Barry's Swimwear. Similarly, Philip's Sun Wear sold 5 out of 72 bathing suits in stock, so we can express this fraction as 5/72.
To compare these two fractions, we need to express them with a common denominator. One way to do this is to find the least common multiple of the two denominators, which in this case is 72. To express 15/x with a denominator of 72, we can multiply both the numerator and the denominator by a factor of 72/x. This results in the fraction 15*(72/x)/72 = 15/x. Similarly, we can express 5/72 with a denominator of 72 by multiplying both the numerator and the denominator by a factor of 72/72, which results in the fraction 5*(72/72)/72 = 5/72.
Now that we have both fractions expressed with a common denominator of 72, we can compare them directly. 15/x is greater than 5/72 as long as x is less than 72. This means that Barry's Swimwear sold a greater fraction of the bathing suits in stock as long as the store had fewer than 72 bathing suits in stock.
CAN SOMEONE HELP WITH THIS QUESTION?✨
The value of [tex]sin^{-1}[/tex](- [tex]\frac{\sqrt{2} }{2}[/tex]) in radians is [tex]-\frac{\pi }{4}[/tex]
The value of [tex]sin^{-1}[/tex](1) in radians is [tex]\frac{\pi }{2}[/tex]
The value of [tex]sin^{-1}[/tex](- 1/2) is [tex]-\frac{\pi }{6}[/tex]
What are trigonometric ratios?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
[tex]sin^{-1}[/tex](- [tex]\frac{\sqrt{2} }{2}[/tex]) is -45 in degress
but [tex]\pi[/tex] rad = 180°
so that - 45° in rad is [tex]\pi[/tex] x - 45/180 which is - [tex]\frac{\pi }{4}[/tex]
[tex]sin^{-1}[/tex](1) = 90°
but [tex]\pi[/tex] rad = 180°
so that -90° in rad is [tex]\pi[/tex] x 90/180 which is [tex]\frac{\pi }{2}[/tex]
[tex]sin^{-1}[/tex](- 1/2) = -30°
but [tex]\pi[/tex] rad = 180°
so that - 30° in rad is [tex]\pi[/tex] x - 30/180 which is - [tex]\frac{\pi }{6}[/tex]
In conclusion then values of the sine inverse of the functions are - [tex]\frac{\pi }{4}[/tex], [tex]\frac{\pi }{2}[/tex], and - [tex]\frac{\pi }{6}[/tex]
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in each of the following cases, you are given a set of numbers. in each case, determine whether this set of numbers can be a domain of convergence for a power series. if it cannot, explain why it cannot. if it can, give an example of a power series that has this set as its domain of convergence.
a. [-1,3)
b. (-1,3)
c. (-1,3]
d. [-1,3]
The possible domain of the convergence are b. (-1,3) and c. (-1,3]
Domain of convergence.
In statistics, domain of the convergence also known as interval of convergence means an interval associated with a given power series such that the series converges for all values of the variable inside the interval and diverges for all values outside it.
Given,
Here we need to identify in which of the options are domain of convergence.
As per the definition of domain of convergence, the interval of the convergence is (-∞ , ∞).
So, the possible convergence in the given options are (b) and (c).
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The National Weather Service keeps track of the temperature for a given day in a given city. It also keeps track of this information at certain times during a given day. The following temperatures were recorded on a January day in New York City.
Time of Day
10 AM
12 Noon
2 PM
4 PM
6 PM
8 PM
10 PM
Temperature ((Degrees Fahrenheit))
30
35
36
36
34
30
28
What is the average rate of change of temperature with respect to time over the evening hours from 6 PM to 10 PM? Interpret this value in a complete sentence.
a.
6 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 6 degrees per hour from 6 PM to 10 PM.
b.
Negative 6 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 6 degrees per hour from 6 PM to 10 PM.
c.
Negative 1.5 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour from 6 PM to 10 PM.
d.
1.5 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour from 6 PM to 10 PM.
The average rate of change of the temperature from 6 to 10 pm is given as -1.5. Option C is correct
How to solve for the rate of changeFrom 6 pm to 10 pm we have a total of 4 hours that is in between this period of time.
From the table the temperature at 6 pm is 34, the temperature at 10 pm is 28 degrees
Such that we would have:
[tex]\frac{28-34}{4}[/tex]
= -6 / 4
= - 1.5
Hence we would have that Negative 1.5 degrees Fahrenheit degrees per hour; The temperature drops at an average rate of 1.5 degrees per hour from 6 PM to 10 PM.
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two equilateral triangles are contained in a square whose side length is $2\sqrt{3}$. the bases of these triangles are opposite sides of the square, and their intersection is a rhombus. the area of the rhombus can be expressed in the from $a b\sqrt{c}$ for integers $a,b,$ and $c$ such that $c$ square-free. determine $-a b c$.
The area of the rhombus inside a square formed by two equilateral triangles is 1.856 cm².
Here we have to find the area of the rhombus.
Data given:
sides of a square = 2√3 cm
Let ABCD be a square whose sides are 2√3 cm.
As two triangles are inscribed in a square so ABE and CDG be equilateral triangles in square ABCD.
The altitude of the equilateral triangle ABE and CDE = 2√3 sin 60°
= 2√3 × √3/2
= 3cm
The diagonal EG of the rhombus EFGH = 2√3 - 2(2√3 - 3)
= 2.535 cm
The diagonal FH of the rhombus, EFGH = 2√3 - 2(√3tan 30°)
= 1.464 cm
The formula for the area of the rhombus = d1 × d2 / 2
where d1 and d2= diagonal of a rhombus
Now the area of the rhombus EFGH = EG × FH / 2
= 2.535 × 1.464 / 2
= 1.856 cm².
Therefore the area of the rhombus is 1.856 cm².
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