Answers
The solution of the equation for all real values of x is πk, π/6.
How to solve the equation for all real values of x?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, specifically right triangles.
3 tan²x = √3 tan x
Divide both sides by 3tan x:
tan x = (√3)/3
x = tan⁻¹((√3)/3)
x = 30°
x = π/6 radian
Note: multiply 30° by π/180 to convert to radian. 180° = π radian
Since π/6 (i.e. 30°) falls between 0 and 180°.
Thus, the solution of the equation for all real values of x is πk, π/6. We can choose πk, π/6.
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Related Questions
Let f(x)= x^2 + 7 and g(x)= x^2+2. Find the following functions, and simplify each as much as possible: your final answer should be a polynomial with only one term in each power of x. (a) f(x) + g(x) = (b) f(x) - g(x) = (c) f(x).g(x)= (c) f(x)/g(x)= (For part (d), you need not simplify as you did in (a)-(c).)
Answers
For function f(x)= x² + 7 and g(x)= x² + 2,
a) f(x) + g(x) = 2x² + 9
b) f(x) - g(x) = 5
c) f(x) . g(x) = x⁴ + 9x² + 14
d) [tex]\frac{f(x)}{g(x)} =\frac{x^2 + 7 }{ x^2+2}[/tex]
Consider given functions f(x)= x² + 7 and g(x)= x² + 2
a) To find addition of functions: f(x) + g(x)
f(x) + g(x)
= (x² + 7) + (x² + 2)
= x² + x² + 7 + 2 .............(associative property of addition)
= 2x² + 9 ................(combine like terms)
b) to find subtraction of functions : f(x) - g(x)
f(x) - g(x)
= ( x² + 7 ) - (x² + 2)
= 7 - 2
= 5
c) To find multiplication of functions: f(x).g(x)
f(x) . g(x)
= ( x² + 7 ).(x² + 2)
= x² (x² + 2) + 7(x² + 2)
= x⁴ + 2x² + 7x² + 14
= x⁴ + 9x² + 14 ................(combine like terms)
d) To find division of functions: f(x)/g(x)
[tex]\frac{f(x)}{g(x)}\\\\ =\frac{x^2 + 7 }{ x^2+2}[/tex]
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at a certain high school, the distribution of backpack weight is approximately normal with mean 19.7 pounds and standard deviation 3.1 pounds. a random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded.
Answers
A sample of 5 backpacks will be chosen from a population of backpacks whose weights are normally distributed with mean 19.7 pounds with a 3.1-pound standard deviation. Each backpack's weight will be noted.
A sample of 5 backpacks will be chosen from a population of backpacks whose weights are normally distributed with mean 19.7 pounds with a 3.1-pound standard deviation. Each backpack's weight will be noted.. The weight of each backpack will be recorded in order to calculate the mean and standard deviation of the sample. To calculate the mean, the total weight of the five backpacks will be added together and then divided by the number of backpacks in the sample (5). To calculate the standard deviation, the weight of each backpack will be subtracted from the mean and the resulting difference will be squared. All of the squared differences will then be added together, divided by the number of backpacks in the sample (5), and the square root of this result will be taken. This will give us the standard deviation of the sample. These calculations will provide us with valuable information about the weights of the backpacks in the sample, which can then be compared to the weights of the backpacks in the population.
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Use the graphs of f and g to evaluate g(f(2))
I have added the photo of the graphs.
When I answered it the first two times I put -2 and then for the second time I put 4 and I got both of them wrong
Answers
Answer:
1
Step-by-step explanation:
We have g(f(2))
Working from the inside out, we start with f(2)
So we go to the f(x) graph and find where X is 2. We get to the point (2, -2). f(2) is pretty much asking for the Y value at 2. On this graph the y value is -2
Now that we know f(2) is -2, we can plug that into g(f(2)), giving us g(-2)
Now we can go to the other graph, g(x) and find where X is -2.
That's where we find the point (-2,1)
Like last time, g(2) is asking for that Y value at that point of -2. On this graph, it's 1
Now we can conclude g(f(2)) = 1
Using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.
What is the graph?
A graph is a visual representation of data or information, often used in mathematics and science to depict relationships between variables. Graphs can take many forms, including line graphs, bar graphs, scatter plots, and pie charts.
To evaluate g(f(2)), we need to first find the value of f(2) using the graph of f. From the graph, we can see that f(2) is approximately 4. So, g(f(2)) = g(4).
Then, using the graph of g, we can see that g(4) is approximately 3. So, g(f(2)) = 3.
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A 20.00 g milk chocolate bar is found to contain 12.00 g of sugar.
A) How many milligrams of sugar does the milk chocolate bar contain?
B) What will be the amount of sugar in milligrams if the size of the milk chocolate bar is reduced from 20.00 g to 3.000 g?
Answers
The amount of sugar present in the milk chocolate bar is, 12000 milligrams.
Given,
Amount of milk chocolate bar = 20.00 grams
Amount of sugar = 12.00 grams
The conversion used for grams to milligram is :
1 gram = 1000 milligram
As per question we are given that, 12 grams of sugar
As, 1 gram of sugar = 1000 milligram of sugar
So, 12.00 grams of sugar = (12/1) x 1000
= 12000 milligrams of sugar
Therefore, the amount of sugar present in the milk chocolate bar is, 12000 milligrams.
(b) THe reduced size is 3 g
3 g bar has 12x3/20 g of sugar
i.e 7.2 g
hence , he amount of sugar in milligrams if the size of the milk chocolate bar is reduced from 20.00 g to 3.000 g is 7200mg.
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row reduce the matrices in exercises 3 and 4 to reduced echelon form. circle the pivot positions in the final matrix and in the original matrix, and list the pivot columns.
Answers
Reduced matrix to its reduced echelon form Original Matrix:
[tex]$$ \begin{bmatrix}1 & -1 & 2 & -1 & 3 \\2 & -2 & 3 & 0 & 4 \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]
Pivot Positions (Original): (1,1), (2,2), (3,4)
Pivot Columns (Original): 1, 2, 4
Reduced Echelon Form:
[tex]$$ \begin{bmatrix}1 & 0 & \frac{2}{3} & 0 & \frac{11}{3} \\0 & 1 & \frac{1}{3} & 0 & \frac{2}{3} \\0 & 0 & 0 & 1 & -2\end{bmatrix} $$[/tex]
Pivot Positions (Reduced): (1,1), (2,2), (3,4)
Pivot Columns (Reduced): 1, 2, 4
To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:
1. Divide row 1 by 1 to get the leading 1 in the first column
2. Subtract two times row 1 from row 2 to get the leading 1 in the second column
3. Subtract three times row 1 from row 3 to get the leading 1 in the fourth column
4. Divide row 2 by 3 to get the coefficient 2/3 in the third column
5. Subtract row 2 from row 1 to get the coefficient 11/3 in the fifth column
6. Subtract row 2 from row 3 to get the coefficient 2/3 in the fifth column
Exercise 4:
Original Matrix:
[tex]$$ \begin{bmatrix}1 & 2 & -3 & 1 & 5 \\2 & 4 & -6 & 2 & 8 \\-1 & -2 & 3 & -1 & -4\end{bmatrix} $$[/tex]
Pivot Positions (Original): (1,1), (2,2), (3,3)
Pivot Columns (Original): 1, 2, 3
Reduced Echelon Form:
[tex]$$ \begin{bmatrix}1 & 0 & 0 & \frac{2}{3} & \frac{11}{3} \\0 & 1 & 0 & \frac{-1}{3} & \frac{1}{3} \\0 & 0 & 1 & \frac{2}{3} & \frac{5}{3}\end{bmatrix} $$[/tex]
Pivot Positions (Reduced): (1,1), (2,2), (3,3)
Pivot Columns (Reduced): 1, 2, 3
To reduce this matrix to its reduced echelon form, I used the following series of elementary row operations:
1. Divide row 1 by 1 to get the leading 1 in the first column
2. Subtract two times row 1 from row 2 to get the leading 1 in the second column
3. Subtract row 1 from row 3 to get the leading 1 in the third column
4. Divide row 2 by 3 to get the coefficient -1/3 in the fourth column
5. Add row 2 to row 1 to get the coefficient 2/3 in the fourth column
6. Divide row 3 by 3 to get the coefficients 2/3 and 5/3 in the fourth and fifth columns respectively
7. Add row 3 to row 1 to get the coefficient 11/3 in the fifth column
8. Add row 3 to row 2 to get the coefficient 1/3 in the fifth column
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42. HOW DO YOU SEE IT?
Write an expression in rational
exponent form that represents
the side length of the square.
Area:
x in.²
Answers
The exponent form that represents the side length of the square is √x
How to determine the side length of the square.From the question, we have the following parameters that can be used in our computation:
Area = x in.²
The area of a square is calculated as
Area = Side length²
substitute the known values in the above equation, so, we have the following representation
Side length² = x
Take the square root of both sides
Side length = √x
Hence, the expression is √x
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E.
Carry out the following operations to the proper number of significant figures:
1. 212.45 +5.61-37.9
2. 89.001+2.50-91.50
3. 400+125= 500
4. 73.35-3.65-69.70
5. (81.7-23.456)+(78.44+2.72) =
Answers
By adding (81.7-23.456)+(78.44+2.72), we get 139.404
How does one determine the number of significant figures?Use the three rules below to calculate the number of significant figures in a number:
Non-zero digits are always meaningful.
Any zero between the first and second significant digits is significant.
Only the last zero or trailing zeros in the decimal section are important.
Numbers Have Rules INCLUDING a Decimal Point
START COUNTING FOR SIGNIFICANT FIGURES. On the very first non-zero digit.
STOP COUNTING FOR SIGNIFICANT FIGURES.
Non-zero numbers are ALWAYS meaningful.
After the first non-zero digit, any zero is still relevant. The zeroes preceding the first non-zero digit are unimportant.
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Transistors are used to build computer chips. The size of the earliest transistors was about 1 x 10* micrometers. Today, transistors can measure smaller than 1 × 10-2 micrometer. The size of the earliest transistors is about how many times as great as the size of transistors today?
Answers
IIn a case whereby Transistors are used to build computer chips and the size of the earliest transistors was about 1 x 10* micrometers and today, transistors can measure smaller than 1 × 10-2 micrometer the numbert of times the old is as great as the size of transistors today is 1 × 10^6.
How can the size of transistors be known?The concept that will be use here is division. One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things. It is a mathematical operation used for equal distribution and equal grouping. In this post, let's study more about the division operation in math.
We were told that the side of the earliest form of transistors for computer was 1 × 10⁴.
In another sentence, we were told that the size of the transistor today is expressed as 1 × 10^-2
We can then know the difference in size will which will be
= 1 × 10^4 / 1 × 10^-2
= 1 × 10^6
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complete question:
Transistors are used to build computer chips. The size of the earliest transistors was about 1 x 10^4 micrometers. Today, transistors can measure smaller than 1 × 10-2 micrometer. The size of the earliest transistors is about how many times as great as the size of transistors today?
Laurie, who is 5 feet tall, notices that she casts an 8-foot shadow. If Laurie is standing 90 feet away from the base of a building, what is the height of the building? Show your work.
Answers
The height of the building that cast the shadow 98 feet will be 61.25 feet.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Laurie, who is 5 feet tall, notices that she casts an 8-foot shadow. If Laurie is standing 90 feet away from the base of a building.
Let 'h' be the height of the building. Then the equation is given as,
h / (90 + 8) = 5 / 8
h / 98 = 5 / 8
h = 98 x 5 / 8
h = 12.25 x 5
h = 61.25 feet
The height of the building that cast the shadow 98 feet will be 61.25 feet.
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What should go into the leaves for 11?
answer asap!!!!
Answers
0
3
4
At the leaves section always 1 digit no.
because of the enormity of the viewing audience, firms that advertise during the super bowl create special commercials that tend to be quite entertaining. thirty-second commercials cost over $5 million for the 2017 game. a random sample of people who watched the game were asked how many commercials they watch in their entirety. Do these data allow us to inter that the mean number of commercials watch is greater than 15?
Answers
No, these data do not allow us to infer that the mean number of commercials watched is greater than 15.
To make such an inference, we would need to know the population mean number of commercials watched, along with the population standard deviation. We can use the sample data to calculate the sample mean and sample standard deviation. The sample mean (X) is the sum of the data values divided by the number of observations. The sample standard deviation (s) is calculated using the equation s = √(sum of (x-X)² / (n-1)) , where n is the number of observations. With the sample mean and standard deviation we can then use a t-test to determine if the population mean is significantly greater than 15.
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find the equation of a line (or a set of lines) passing through the terminal point of a vector a and in the direction of vector b.
Answers
The equation of a line passing through the terminal point of a vector a and in the direction of vector b is r = a + λb.
In math the equation of a straight line is y = m x + c
where m is the gradient and c is the height at which the line crosses the y -axis, also known as the y -intercept.
Here we need to find the equation of a line (or a set of lines) passing through the terminal point of a vector a and in the direction of vector b.
Based on the general form of the equation of the line, the vector form of the equation of a line passing through a point having a position vector a, and parallel to a vector line b is written as,
=> r = a + λb.
Where λ refers the constant term.
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on yellow, P(not yellow).
0.325
0.625
0.750
0.875
Answers
Answer:
0.750
Step-by-step explanation:
Yellow sections: section 2 and section 3
Number of yellow sections: 2
Number of non yellow sections: 6
Total sections: 8
p(not yellow) = 6/8 = 0.75
Answer:
0.750
Step-by-step explanation:
you take a quarter and then you divide and think
Find the product of the binomial factors using the appropriate special product (difference of two squares, square of a binomial sum, or square of a binomial difference).
(x+8)2
Answers
The product of the binomial factors is x² + 16x + 64
How to determine the product of the binomial factorsfrom the question, we have the following parameters that can be used in our computation:
(x+8)2
Express properly
So, we have
(x+8)²
Using the square of a binomial sum, we have
(x+8)² = x² + 2 * x * 8 + 8²
Evaluate
(x+8)² = x² + 16x + 64
Hence, the solution is x² + 16x + 64
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Points A and B are 10 units apart. Points B and C are 4 units apart. Points C and D are 3 units apart. If A and D are as close as possible, then the number of units between them is
A. 0 B. 3 C. 9 D. 11 E. 17
Answers
A perimeter longer than 50 for any point, C satisfies the area requirement.
Consequently, we have a base-10 triangle whose area is 100. Since the area is equal to half the product of base and height, the object's height is then 20.
The next two sides. If one of the sides is exactly 20 inches tall (when it coincides with the height, forming a right triangle), the other side must be strictly greater than 20 inches tall (being the hypotenuse), in which case the perimeter must be greater than 50.
Alternately, both sides could be longer than 20 because neither side is a height. Once more, the perimeter exceeds 50.
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The full question
In a given plane, points A and B are 10 units apart. How many points C are there in the plane such that the perimeter of triangle ABC is 50 units and the area of triangle ABC is 100 square units?
Two fractions with the same denominator that have numerators 5 and 7 what would the denominator be?
Answers
The denominator could be any real value
How to determine the possible denominatorFrom the question, we have the following parameters that can be used in our computation:
Fraction = same denominator
Such that the numerators are 5 and 7
This means that the fractions can be represented as
Fractions = 5/x and 7/x
There is no restriction on the possible value of x
hence, the denominator is any value
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match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. enter the appropriate letter (a,b,c,d, or e) in each blank.
Answers
Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials.
Trigonometric expressions are mathematical functions that use the ratios of the sides of a right triangle to calculate angles. These functions are often used in applications such as navigation and surveying, as they allow us to calculate angles and distances in the real world. Examples of trigonometric functions include sine, cosine, tangent, cotangent, secant, and cosecant. Non-trigonometric functions are mathematical functions that do not use the sides of a triangle to calculate angles, but rather use other mathematical operations such as exponentials, logarithms, and polynomials. These functions are often used in engineering and scientific applications, as they allow for more precise calculations than trigonometric functions. Examples of non-trigonometric functions include polynomial functions, exponential functions, logarithmic functions, and hyperbolic functions. In each case, the function being used must be appropriate for the type of problem being solved. By understanding the differences between trigonometric and non-trigonometric functions, it is possible to choose the right function for the right problem.
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find the domain of each expression
1. y ^2+1)/(y^2-2y),
2. 25(y-9),
3. 32/y - (y+1)/Y+7)
Answers
The domain of each expression is given as follows:
1. All real values except y = 0 and y = 2.
2. All real values.
3. All real values except y = 0 and y = -7.
How to obtain the domain of the expressions?The domain of an expression is composed by the set of all the possible input values that the expression can assume.
For an expression that is a fraction, the denominator cannot be zero, hence:
Item 1: y² - 2y = 0 -> y(y - 2) = 0, hence the domain is all real values except y = 0 and y = 2.Item 3: y = 0 and y + 7 = 0 -> y = -7, hence the domain is all real values except y = 0 and y = -7.For item 2, the function is a multiplication, which has no restrictions on the domain, and thus the domain is composed by all real values.
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Can someone help me?
Answers
Answer: Maybe if you post the question
Step-by-step explanation:
Determine the number of lines of symmetry for the figure.
The figure has ✓line(s) of symmetry.
Select the angles of rotation, if any, that map the figure onto itself.
O 30°
O 90°
☐ 180°
dh
O 45°
O 120°
Answers
Answer:
The figure has 4 lines of symmetry.Rotating through angles 90° or 180° will map the figure to itself.Step-by-step explanation:
You want the number of lines of symmetry of the 4-leaved rose shown in the figure.
Lines of symmetryThe figure is symmetrical about a line through opposite petals. It is also symmetrical about a line through the space between petals. The attachment shows the 4 lines of symmetry.
Rotational symmetryThe petals have the same geometry, but are rotated 90° from each other. That means any rotation that is a multiple of 90° will map the figure to itself. (180° is a multiple of 90°)
The figure maps to itself when rotated 90° or 180°.
is there a value of a that makes the statement |a| = - 2 true ? Explain your reasoning.
Answers
Answer:
No, there is no value of a that makes the statement |a| = -2 true.
Step-by-step explanation:
The absolute value of a number is the distance of that number from zero on the number line. It is always non-negative, so it can't be -2. The absolute value of a number is denoted by two vertical lines on either side of the number like this |a|.
For example, the absolute value of -5 is 5 and the absolute value of 5 is 5. In both cases, the distance from zero is 5.
In the statement |a| = -2, the absolute value of a is -2, which is impossible as the absolute value can't be negative. Therefore, there is no value of a that makes the statement true.
Answer:
no
Step-by-step explanation:
You want to know if there's any value of the variable 'a' that would make its absolute value be -2.
Absolute valueThe absolute value of a number is always positive. There is no such thing as a number whose absolute value is negative, not -2 or any other negative number.
such a value of 'a' Does Not Exist (DNE)
The vertices of triangle xyz are x=(-2,6), y=(4,10), and z=(14,6). Find the coordinates of the centroid of triangle xyz
Answers
The centroid of the given triangle is =(5.3 , 7.3)
What is Centroid of triangle?The centroid is the term for the object's geometric centre. We apply the centroid formula to find the triangle's centroid's coordinates. The intersection of a triangle's three medians yields the centroid, or centre, of the triangle. All of the medians are divided by the centroid of a triangle in a 2:1 ratio.
The centroid formula of a given triangle can be expressed as,
C = ((x1+x2+x3)/3 , (y1+y2+y3)3/3)
where,
C denotes the centroid of a triangle
x1,x2,x3 are the x-coordinates of the 3 vertices.
y1,y2,y3 are the y-coordinates of the 3 vertices
To find: Centroid of a triangle.
We are taking the Cordinates of the traiangle XYZ
as x1,y1,x1,y2,x3,andy3
so,Given parameters are,
(x1,y1)=(-2,6)
(x2,y2)=(4,10)
(x3,y3)=(14,6)
Using centroid formula,
The centroid of a triangle = ,
=-2+4+14/3 6+10+6/3
=5.3 7.3
The centroid of a triangle is ==(5.3 and 7.3)
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Please help!! It’s due in 10 minutes!!! Also please explain how you got the answer!
Answers
Answer: 22 vaccines
Step-by-step explanation:
first, reduce the amount that doctors leave out from the total amount of a vial
6 - 0.5 = 5.5
next divide 5.5 by the amount that is given to each person, which will give you the number of vaccinations the doctor can give
5.5/ 0.25 = 22 vaccines
7. Is this a leap year?
FEBRUARY
Answers
answer
no
steps
February ends on the 28th this year 2023
leap year February ends on the 29th
Please please please please help
Answers
Translate this polygon six units to the left and two units upward:
Answers
The image that gives the translation of the polygon six units to the left and two units upward is given as follows:
The fourth graph.
(which is the third graph if we consider that the first is the original image).
What is a translation?A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.
The translations are represented as follows:
Left a units: x -> x - a.Right a units: x -> x + a.Up a units: y -> y + a.Down a units: y -> y - a.For the translation 5 units left, we have that:
The bottom segment of x = 1 to x = 4 will assume coordinates of x = -5 to x = -2.
For the translation 2 units up, we have that:
The vertical segment from y = 1 to y = 3 will assume coordinates from y = 3 to y = 5.
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Josh is thinking of two numbers. Their sum is -10 and their difference is -2. Which system of equations represents the situation? Group of answer choices
(1)x + y = -2
x - y = -10
(2) x - y = -10
x + y = 2
(3) x + y = -10
x - y = -2
(4) x = -2
y = 5
Answers
Answer: The answer is 3
Step-by-step explanation:
find the coordinates of point $p$ along the directed line segment $ab$ , from $a\left(-3,\ 2\right)$ to $b\left(5,-4\right)$ , so that the ratio of $ap$ to $pb$ is $2$ to $6$ . the coordinates are $p\text{(}$ , $\text{)}$ .
Answers
The coordinates of point p along the directed line segment ab are [tex]$p(-1,-2)$[/tex]
Let the coordinates of point p be (x,y)
The ratio of ap to pb is 2 to 6, so we have [tex]$$\frac{|ap|}{|pb|} = \frac{2}{6}$$[/tex]
We can calculate the distances between points $a$ and $p$ and points $p$ and $b$ using the distance formula as follows:
[tex]$$|ap| = \sqrt{(x+3)^2+(y-2)^2}$$$$|pb| = \sqrt{(5-x)^2+(y+4)^2}$$[/tex]
We can use the ratio of the distances to set up a proportion to solve for $x$ and $y$:
[tex]$$\frac{|ap|}{|pb|} = \frac{2}{6} \implies \frac{\sqrt{(x+3)^2+(y-2)^2}}{\sqrt{(5-x)^2+(y+4)^2}} = \frac{2}{6}$$\\[/tex]
Solving for $x$ and $y$, we get $x = -1$ and $y = -2$.
Therefore, the coordinates of point $p$ along the directed line segment $ab$ are [tex]$p(-1,-2)$[/tex]
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Time to walk 3 1/3 miles on Saturday and 2 4/5 mile on Sunday how much farther does Tonya walk on Saturday then on Sunday
Answers
The distance that Tonya walk on Saturday more than on Sunday would be = 8/15 miles
What is distance?Distance is defined as the quantity that describes the space that exists between two locations in a field.
The number of miles Tonya covered on Saturday = 3 ⅓ miles
The number of miles that Tonya covered on Sunday = 2 ⅘
Therefore the distance that Tonya walk on Saturday more than on Sunday would be the difference between the distance covered in Saturday and Sunday.
That is; 3⅓ - 2⅘ ( change to single fraction form)
= 10/3 - 14/5
= 50-42/15
= 8/15
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In circle I, IJ = 2 and the area of shaded sector = . Find the length of JLK.
Express your answer as a fraction times T.
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Answers
Given that IJ = 2, we know that IJ is the radius of the circle.
The area of the shaded sector is given as . Since the area of a sector is given by (angle of sector/360) * pi * r^2, we can set up the equation:
(x/360) * pi * 2^2 =
Solving for x:
x = (180/pi)*
We know that the arc JLK corresponds to the angle x, thus the length of JLK is (x/360)2pi*IJ = (x/180)*IJ * T = (180/pi) * T.