XY is a diameter of a circle and Z is a point on the circle such that ZY=6. If the area of the triangle XYZ is 18 square root 3 find the length of arc XZ
Answers
4π
Step-by-step explanation:As shown in the diagram, triangle XYZ is a right triangle. Therefore, its area (A) is given by:
A = [tex]\frac{1}{2}[/tex] x b x h -------------(i)
Where;
A = 18[tex]\sqrt{3}[/tex]
b = XZ = base of the triangle
h = YZ = height of the triangle = 6
Substitute these values into equation(i) and solve as follows:
18[tex]\sqrt{3}[/tex] = [tex]\frac{1}{2}[/tex] x b x 6
18[tex]\sqrt{3}[/tex] = 3b
Divide through by 3
6[tex]\sqrt{3}[/tex] = b
Therefore, b = XZ = 6[tex]\sqrt{3}[/tex]
Now, assume that the circle is centered at O;
Triangle XOZ is isosceles, therefore the following are true;
(i) |OZ| = |OX|
(ii) XZO = ZXO = 30°
(iii) XOZ + XZO + ZXO = 180° [sum of angles in a triangle]
=> XOZ + 30° + 30° = 180°
=> XOZ + 60° = 180°
=> XOZ = 180° - 60°
=> XOZ = 120°
Therefore we can calculate the radius |OZ| of the circle using sine rule as follows;
[tex]\frac{sin|XOZ|}{XZ} = \frac{sin|ZXO|}{OZ}[/tex]
[tex]\frac{sin120}{6\sqrt{3} } = \frac{sin 30}{OZ}[/tex]
[tex]\frac{\sqrt{3} /2}{6\sqrt{3} } = \frac{1/2}{|OZ|}[/tex]
[tex]\frac{1}{12} = \frac{1}{2|OZ|}[/tex]
[tex]\frac{1}{6} = \frac{1}{|OZ|}[/tex]
|OZ| = 6
The radius of the circle is therefore 6.
Now, let's calculate the length of the arc XZ
The length(L) of an arc is given by;
L = θ / 360 x 2 π r ------------------(ii)
Where;
θ = angle subtended by the arc at the center.
r = radius of the circle.
In our case,
θ = ZOX = 120°
r = |OZ| = 6
Substitute these values into equation (ii) as follows;
L = 120/360 x 2π x 6
L = 4π
Therefore the length of the arc XZ is 4π
Related Questions
Dange measures and finds that she can do a vertical jump that is27.5 % her height f dange can jump 13.2 inches how tall is she
Answers
The height of Dange who can jump 27.5% of her height is 10.4 inches.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Dange measures and finds that she can do a vertical jump that is 27.5 % of her height f and the distance of the jump is 13.2 inches.
Therefore. (100 + 27.5)% = 127.5% of f is 13.2 inches, This can be numerically expressed as,
(127.5/100)×f = 13.2.
1.275f = 13.2.
f = 13.2/1.27.
f = 10.4 feet.
So, The height of Dange is 10.4 inches.
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3. Given: ACAN
m/ATN= (4x + 18)
Find: x so that AT is an altitude
N
Answers
Therefore , the solution of trigonometry function comes out to be tan x tan(4x+18)
What does trigonometry mean exactly?When it comes to trigonometry, the relationship between the rectangular line segment and The field is believed to have originated in the 1770s, most likely beginning in the third century through the fusion of astrophysics and mathematical sciences. Numerous mathematical equations and their possible uses in calculations are covered by precise mathematical techniques. The basis of trigonometry are the six basic trigonometric operations.
Here,
tan x tan 4x=1
cos 4X cos X - sin 4x sin x=0
cos 5x=0
5x=(n+1/2)π,n ∈ Z
x=(2n+1)/10 π,0 <x <π
π/10, 3π/10, 5π/10, 7π/10,9π/10 (5π/10 is not possible)
Thus, there are only four solutions.
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Find the theoretical probability that a 12-month calendar is turned to the month of May or the month of June. Write your answer as a fraction in simplest form.
Answers
Probability that the calendar turned to month of May or June is 1/6.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Total number of months = 12
Suppose that a calendar is turned.
Probability that the calendar turned to month of May = 1/12
Probability that the calendar turned to month of June = 1/12
Probability that the calendar turned to month of May or June = 1/12 + 1/12
= 2/12
= 1/6
Hence the probability that the calendar turned to month of May or June is 1/6.
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What are logarithms used for?
Answers
Logarithms are used for a variety of purposes in mathematics, science, engineering, and other fields. Some common uses of logarithms are mentioned below:
What are functions?A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
What are exponential function?The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, however it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.
They are used for:
Solving exponential equationsCompressing dataMeasuring the Richness of a signalComparing quantitiesSolving problems in physics and engineeringIn finance, it is used for financial modelings, such as the Black-Scholes model for pricing optionsIn computer science, it is used for information theory in the analysis of algorithms, complexity theory, and data compression.To learn more about exponential visit:
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Please answer correctly! Afterwards I’ll mark you brainlist!
Answers
Answer:
Area:80mi^2
Perimeter:40mi
Step-by-step explanation:
What is the length of the leg (b) of the triangle?
Answers
Answer:
20
Step-by-step explanation:
c² = a² + b²
25² = 15² + b²
625 = 225 + b²
b² = 625 - 225
= √400
= 20
please uhm help me heh
Answers
Answer:
d=90°
e=81°
f=99°
Step-by-step explanation:
To find f
180-81
=99
Answer:
d = 90°
e = 81°
f = 99°
Step-by-step explanation:
Have a nice day!
should I shoot my shot?
Answers
Answer:
yesssssss!!!!!!!!!!!
To determine the mean number of children per
household in a community, Tabitha surveyed
20 families at a playground. For the 20 families
surveyed, the mean number of children per
household was 2.4 .4 Which of the following
statements must be true?
A) The mean number of children per household in
the community is 2.4 .
B) A determination about the mean number of
children per household in the community should
not be made because the sample size is too small.
C) The sampling method is flawed and may
produce a biased estimate of the mean number
of children per household in the community.
D) The sampling method is not flawed and is likely
to produce an unbiased is not flawed and is likely
number of children per household in the
community.
Answers
True statement is number C.
What is biased and unbiased sample in statistics?
The method of sampling where a portion of population are given priority over the rest of the population is called biased sample.
In the unbiased sampling method almost, each population is valued, and they are given chance to be selected in the data list.
flawed sampling means the method of sampling is inappropriate such as survey works that taken in non-random way. As example, researchers start to ask people walking in the street.
Which statement is true as given in question?The survey was taken at a playground on 20 families.
the survey estimated that mean number of children per household in the community was 2.4.
The main purpose of the survey was to determine the mean number of children per household in the community.
but the survey study was held at the playground and the sample size is too small.
The above data could not give the true estimation.
So, the sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.
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i have a procrastination problem so um yay points for free #momboss
Answers
Answer:
Thanks
Step-by-step explanation:
ADDFFFG
Which of the following functions has a vertex of (-1,2)?
Choose 3.
f(x) = (x + 1)^2 + 2
g(x) = x^2 - 1x + 2
h(x) = -x^2 + 2
r(x)= x^2+2x+3
t(x) = -(x + 1)^2 + 2
Answers
Answer:
f(x) , r(x), t(x)
Step-by-step explanation:
A veterinarian weighs three cats. The
American Shorthair weighs 13.65 pounds.
The Persian weighs 13.07 pounds, and
the Maine Coon weighs 13.6 pounds.
List the cats in order from least to
greatest weight.
Answers
Answer:
Least to greatest.
Persian, Maine Coon, and American Shorthair
Refer to the equation a-6 equals b if a equals 45 what is the value of b?
Answers
Answer:
Step-by-step explanation: a=4, b=2.
Answer:
b = 39
Step-by-step explanation:
[tex]a-6=b[/tex]
if a = 45:
[tex]45-6=b\\39=b[/tex]
Hope this helps
There are 8 employees on The Game Shop's sales team.
Last month, they sold a total of g games. One of the
sales team members, Chris, sold 17 fewer games than
what the team averaged per employee.
How many games did Chris sell?
Write your answer as
an expression.
games
Answers
According to the solving the team average is g/17 and Chris sold (g/8) - 17 games.
What do you mean by average?The term "Average" refers to a value that should be used to describe the sample as a whole. The average is determined by dividing the total number of values in a set by the total number of values. also known as the arithmetic mean.
How do you calculate the mean?Average A collection of integers are added, their count is divided, and the sum is used to determine the arithmetic mean.
According to the given information:average game sold = g/8
since Chris sold 17 games less than average
hence, Chris sold games
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How can you find 50% of any number? Select all that apply.
Divide by 50
Find 1/2 of the number.
Divide the number by 2.
Divide by 100.
Answers
Austin had 1200 apples eaten in his hole life. Austin is 22 years old . how many apples did he eat per year?
Answers
Answer:
54 apples
Step-by-step explanation:
i know that he most likely didnt eat the same amount of apples per year but, if you divide the number of apples he ate overall by his age you get 54 apples.
question: 49a+26+11–3–6
Answers
Answer:
49a + 28
Step-by-step explanation:
Answer:
49a+28
Step-by-step explanation:
49a+26+11–3–6
49a+26+11-9
49a+26+2
49a+28
Brainliest!!!
Calculate the median of the following list of numbers: 3, 5, 2, 10, 6, 3, 7, 3
Answers
The median of the list of numbers is 4
How to determine the median?The numbers are given as:
3, 5, 2, 10, 6, 3, 7, 3
Sort the numbers in ascending order
2, 3, 3, 3, 5, 6, 7, 10
The median is the middle number.
The middle numbers in the above data are 3 and 5
So, the median is:
Median =(3 + 5)/2
Evaluate
Median =4
Hence, the median of the list of numbers is 4
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please help ill give 50 points
Answers
Answer:
[tex]64 m^{2}[/tex]
Step-by-step explanation:
10 x 4 = 40
8 x 3 = 24
40 + 24 = 64
Mark as brainllest
The reasons as well as the answer
Answers
Answer:
x = 46, y = 67
Step-by-step explanation:
x = ∠ AEC = 46 ( alternate angles )
Since Δ ACE is isosceles then the base angles are congruent, then
y = [tex]\frac{180-46}{2}[/tex] = [tex]\frac{134}{2}[/tex] = 67
Answer:
x=46° and y=67°
Step-by-step explanation:
triangle ACE is isosceles, meaning <A=<B=y
any triangle is add up to 180. <A+<B+<C=180
y+y+46=180
2y=180-46
2y=134
divide both sides by 2
y=134/2
y=67°
for angle x°
since AB is parallel to CD,hence
<AEC=<ECD
x=46°
What is the solution to this system of linear equations 2x 3y equals 3?
Answers
The solution to this system of linear equations is x = 3, y = 2.
2x - 3y = 3
2x = 3 + 3y
2x = 3y + 3
x = (3y + 3) / 2
x = 3/2 + 3/2y
x = 3, y = 2
This system of linear equations features two unknown variables, x and y. The equation 2x - 3y = 3 can be rearranged into 2x = 3y + 3. This equation can then be solved for x by dividing both sides by 2, resulting in x = 3y + 3/2. Since 3y + 3/2 must equal 3, this means that y must equal 2. Substituting 2 for y in the original equation yields 2x = 3 + 3(2), or 2x = 9. Dividing both sides by 2 yields x = 9/2, or x = 3. Therefore, the solution to this system of linear equations is x = 3 and y = 2.
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The solution to the system of linear equations 2x + 3y = 3 is x = 1 and y = -1/3.
1. Rewrite the equation in standard form is
2x + 3y = 3
2. Subtract 2x from both sides of the equation:
3y = 3 - 2x
3. Divide both sides by 3:
y = (3 - 2x)/3
4. Solve for x by substituting y in the original equation:
2x + 3(3 - 2x)/3 = 3
5. Simplify and solve for x:
2x + 3 - 2x = 3
x = 1
6. Substitute x into the equation y = (3 - 2x)/3
y = (3 - 2(1))/3
y = -1/3
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DEFG is a square with vertices at D(1, 1), E(1,6), F(6, 6), and G(6, 1). DEFG is reflected in the line x = 1. Find the coordinates of
D',E,F, and G'.
Answers
By considering the reflection, the coordinates of the reflected square D'E'F'G' are:
D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)
What is square?A square is a two-dimensional geometric shape that has four equal sides and four right angles. It is a type of rectangle, but with all sides equal. The opposite sides of a square are parallel and of equal length. A square can be defined by its side length or by the coordinates of its vertices.
What is reflection?Reflection is a type of transformation in geometry in which a shape is flipped over a given line, called the line of reflection. The image that is created is a mirror image of the original shape. The line of reflection can be a horizontal line, a vertical line, or any line that is not parallel to the axes. Reflecting a shape over a line involves taking the coordinates of each point of the shape and applying a specific rule (such as multiplying or adding a constant) to the x or y coordinate, depending on the line of reflection. This rule is often simple and easy to apply, such as reflecting over x = 1. The reflected shape will be in the same plane as the original shape but with a different orientation or position.
When a square is reflected in the line x=1, each of the points on the square will have their x-coordinate replaced by 1 subtracted from their original x-coordinate.
The coordinates of the reflected square D'E'F'G' can be found by applying this rule to the original coordinates of square DEFG:
D(1,1) => D'(1-1,1) => D'(0,1)
E(1,6) => E'(1-1,6) => E'(0,6)
F(6,6) => F'(6-1,6) => F'(5,6)
G(6,1) => G'(6-1,1) => G'(5,1)
So the coordinates of the reflected square D'E'F'G' are:
D'(0,1) , E'(0,6), F'(5,6) and G'(5,1)
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Find the volume of a triangular pyramid with a right triangular base that has leg lengths of 8.4 centimeters and 9.2 centimeters and a height of 6.2 centimeters.
Answers
Answer:
9.2+8.4+6.2
Step-by-step explanation:
hope that helps
Bro can someone please help me on these three questions I’ve been trying to get help on these questions for like the past 30 minutes please help me
Answers
Answer:
Step-by-step explanation:
1). By applying cosine rule in the given triangle,
cos(x°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
cos(x°) = [tex]\frac{6}{8}[/tex]
x = [tex]\text{cos}^{-1}(\frac{3}{4} )[/tex]
x = 41.41°
2). By applying cosine rule in the given triangle,
cos(x°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
cos(x°) = [tex]\frac{4}{5}[/tex]
x = [tex]\text{cos}^{-1}(0.8)[/tex]
x = 36.87°
3). By applying cosine rule in the given triangle,
cos(x°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
cos(x°) = [tex]\frac{51}{85}[/tex]
x = [tex]\text{cos}^{-1}(0.6)[/tex]
x = 53.13°
Choose all the conversion factors that relate cups to fluid ounces. 8fl oz1c 8c1fl oz 1fl oz8c 1c8fl oz 4fl oz2c
Answers
Answer:
[tex]1\ c = 8\ fl\ oz[/tex]
[tex]\frac{1}{8}\ c = 1\ fl\ oz[/tex]
[tex]\frac{1}{4}\ c = 2\ fl\ oz[/tex]
Step-by-step explanation:
The options are not properly formatted;
So, I will solve the question using general notations
Required
Conversion factors of cups and fluid ounces
Let
[tex]c = cup[/tex]
[tex]fl\ oz = fluid\ ounces[/tex]
In standard conversion
[tex]1\ c = 8\ fl\ oz[/tex]
Divide both sides by 8
[tex]\frac{1\ c}{8} = \frac{8\ fl\ oz}{8}[/tex]
[tex]\frac{1}{8}\ c = 1\ fl\ oz[/tex]
Multiply both sides by 2
[tex]2 * \frac{1}{8}\ c = 1\ fl\ oz * 2[/tex]
[tex]\frac{1}{4}\ c = 2\ fl\ oz[/tex]
Is algebra.
PLEASE HELP NO LINKS OR FILES.
I don't want links.
I don't want links.
I don't want links.
I don't want links.
Answers
Answer:
5.(x+7)(4x2+7)
6.(b−3x)(3x2−1)
6: C (b-3x)(3x^2-1)
Help!! I will give brainlest to the right one!
Answers
Easy question! Will mark brainiest if you show steps
What value of x makes this equation true?
x/3 − 3 = x/9 + 3
A. 3
B. -9
C. -1
D. 27
Answers
Answer:
D.27
Step-by-step explanation:
I took a picture of my work doing a explanation.
(sorry for the messy hand writing)
The Taylor family had a $74 dinner bill. How
much did they pay after including an 18%
tip?
Answers
Answer:
$87.82
Step-by-step explanation:
You do $74 divided by .18 which gets you $13.82. Then you add $74 and $13.82 which gives you the total, $87.82
$200 for 12 piano lessons
Answers
Answer: Is the question to find unit price, if it is, the answer is $16.77. Divide 200/12 to get the unit price. Hope this helps and good luck to having a bright future ☀️
Step-by-step explanation: