For the segments to be congruent, x should be 13/2.
This is a case of congruency of segments. We know that two segments are congruent if and only if they have equal lengths.
Now, here the two line segments JK and RS have lengths 2x-9 and 30-4x respectively.
So, to be congruent, JK and RS must be of equal length.
Or in other words, 2x-9 = 30-4x
or 6x= 30 + 9 =39
i.e. 6x = 39.
Dividing both sides by 3, we get
2x=13 , which implies , x =13/2 or 6.5
Thus, for JK and RS to be congruent , x =13/2.
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For the segments to be congruent, x should be 13/2.
This is a case of congruency of segments. We know that two segments are congruent if and only if they have equal lengths.
Now, here the two line segments JK and RS have lengths 2x-9 and 30-4x respectively.
So, to be congruent, JK and RS must be of equal length.
Or in other words, 2x-9 = 30-4x
or 6x= 30 + 9 =39
i.e. 6x = 39.
Dividing both sides by 3, we get
2x=13 , which implies , x =13/2 or 6.5
Thus, for JK and RS to be congruent , x =13/2.
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please answer will give brainliest all of them
The light post's height is 21 metres higher than the structure,
What is the light post's height?A lamp post is 45 feet away from where you are. You are standing at a 36" angle and are 5 feet tall as you stare up at the top of the light post.
tan 60 degrees is equal to 36/x sqrt(3),
36/x, and 36/(sqrt(3))*m. sqrt (3)
36/3 = 36 - h
h = 36 - 12
h = 24m
The distance between AB and CD is thus
60/(sqrt(3)) * 1.
The light post is 24 metres tall.
The light post's height is 45 -24 =21 metres higher than the structure, which is 21 metres higher.
The light post's height is 21 metres higher than the structure,
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What does spillage refer to Cyber Awareness Challenge 2022?
The spillage refer to Cyber Awareness Challenge 2022 is explained below.
The Cyber Awareness Challenge 2022 is an important event that focuses on raising awareness about the dangers and risks associated with the use of technology and the internet.
In this context, spillage refers to the accidental or unintentional release of sensitive information. This can be caused by a variety of factors, including human error, technical glitches, and malicious attacks.
In addition, the challenge will explore the consequences of spillage, such as identity theft, financial loss, and reputational damage. This is why it is so important to take the challenge seriously and to understand the importance of cyber awareness and security.
By participating in the Cyber Awareness Challenge 2022, students will gain valuable skills and knowledge that will help them protect themselves and their information in the digital world
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to study the diameter of the trunks of white pine in a national forest, 50 trees were selected by using random latitude/longitude coordinates. if a point fell within the canopy of a tree, the tree was included in the sample. if not, another random location was generated. what error is likely to result from this study design?
The study design of selecting 50 trees using random latitude/longitude coordinates may result in sampling error and measurement error, which could affect the accuracy of the results.
The error that is likely to result from this study design is known as "sampling error" because the sample of 50 trees is not necessarily representative of the entire population of white pine trees in the national forest as these trees were selected by chance.
If the sample of 50 trees were selected from a particular area of the forest where the trees were smaller in diameter, the study results would not accurately reflect the average diameter of all the white pine trees in the forest.
Moreover, there is a possibility of measurement error if the diameter of the trunks were not measured consistently. This could also contribute to the overall error in the study results.
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find the angles between the planes in exercises 47 and 48. 47. x y = 1, 2x y - 2z = 2
47.) The angle between the plane is 0 degrees.
48.) The angle between the plane is 180 degrees.
What is the angle between the plane?
To find the angle between two planes, we need to find the normal vectors of each plane and then find the cosine of the angle between the normal vectors using the dot product.
First, let's find the normal vectors for the two planes:
Plane 1: x + y = 1
The normal vector for this plane can be found by taking the coefficients of x, y, and z and forming a vector:
n1 = ⟨1, 1, 0⟩
Plane 2: 2x + y - 2z = 2
The normal vector for this plane can be found in the same way:
n2 = ⟨2, 1, -2⟩
Next, we will find the cosine of the angle between the normal vectors using the dot product:
cosθ = (n1 • n2) / (|n1| * |n2|)
where |n1| and |n2| are the magnitudes of the normal vectors.
Calculating the dot product and magnitudes:
n1 • n2 = 1 * 2 + 1 * 1 + 0 * -2 = 3
|n1| = sqrt(1^2 + 1^2 + 0^2) = sqrt(2)
|n2| = sqrt(2^2 + 1^2 + (-2)^2) = sqrt(9)
Substituting into the formula:
cosθ = 3 / (sqrt(2) * sqrt(9)) = 3 / (3) = 1
Since cosθ = 1, θ = 0, so the angle between the two planes is 0 degrees or a coincident plane.
Next, let's find the normal vectors for the two planes:
Plane 1: 5x + y - z = 10
The normal vector for this plane can be found by taking the coefficients of x, y, and z and forming a vector:
n1 = ⟨5, 1, -1⟩
Plane 2: x - 2y + 3z = -1
The normal vector for this plane can be found in the same way:
n2 = ⟨1, -2, 3⟩
Next, we will find the cosine of the angle between the normal vectors using the dot product:
cosθ = (n1 • n2) / (|n1| * |n2|)
Calculating the dot product and magnitudes:
n1 • n2 = 5 * 1 + 1 * (-2) + -1 * 3 = -3
|n1| = sqrt(5^2 + 1^2 + (-1)^2) = sqrt(27)
|n2| = sqrt(1^2 + (-2)^2 + 3^2) = sqrt(14)
Substituting into the formula:
cosθ = -3 / (sqrt(27) * sqrt(14)) = -3 / (3 * sqrt(2)) = -sqrt(2) / sqrt(2) = -1
Since cosθ = -1, θ = 180 degrees, so the angle between the two planes is 180 degrees, or perpendicular.
Hence,
47.) The angle between the plane is 0 degrees.
48.) The angle between the plane is 180 degrees.
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Are all arithmetic sequences continuous?
3 (q − 7) = 27
EXPLAIN PLEASE AND TYSM
Answer: q = 16
Step-by-step explanation:
When given the equation 3(q - 7) = 27, you would solve for the variable.
The variable in this equation is q, so we need to isolate the variable.
Solving process:
3(q - 7) = 27
lets distribute, due to the orders of PEMDAS.
PEMDAS stands for: Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.
3(q - 7) = 27
distributing is multiplying the number correlated outside of the parenthesis with the inside components.
3q - 21 = 27
lets add 21 to both sides
3q = 48
now lets divide by 3 (we are trying to get q by itself)
q = 16
----
To check if your solution is correct, you replace the value (16) of the variable (q) within the original equation:
3 (16 − 7) = 27
Following PEMDAS you get:
3(9) = 27
27 = 27 (meaning that the solution is correct)
Thank you.
[tex] \: [/tex]
[tex] \frak{3q - 21 = 27}[/tex][tex] \: [/tex]
[tex] \frak{3q = 27 + 21}[/tex][tex] \: [/tex]
[tex] \frak{3q = 48}[/tex][tex] \: [/tex]
[tex] \frak{q = \cancel{ \frac{48}{3}} }[/tex][tex] \: [/tex]
[tex] \underline{ \boxed{ \frak{ \red{ \: q = 16 \: }}}}[/tex][tex] \: [/tex]
hope it helps! :)
How many inches in 2 meters?
78.740 inches in 2 meters. 2 meters equals 6.56168 ft. One meter is equivalent to 3.28084 ft.
How many feet does one meter equal?If you want to know how many feet are in two meters, multiply the number of meters by 2. (the number of feet you have). You can infer from this that 2 meters is equivalent to 6.56168 ft.In the traditional system of measurement, one inch can be referred to as a unit of length. Inches of length are either denoted by in or by ". 5 inches, for instance, can be expressed as 16 inches or 16". A yard and an inch are equivalent. A measurement of 1 inch is about equivalent to 2.54 cm.For instance, the length of your adult thumb from tip to first knuckle is generally about 1 inch. A paperclip, a sewing pin, a water bottle cap, a U.S. quarter, or a $1 Canadian coin are also acceptable substitutes.2 meters into inches
1 inch = 39.370
2 meters = 2 × 39.370
Then we get ,
= 78.740 inches
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A game show host picks contestants for the next game from an audience of 5 females and 4 males. The host randomly chooses a male, and then randomly chooses a male. Use a sample space to determine whether randomly choosing a male first and randomly choosing a male second are independent events
randomly choosing a male first and randomly choosing a male second are independent events.
Sample Space:
M1, M2, M3, M4, F1, F2, F3, F4, F5
Independent Events:
M1, M2, M3, M4, M1, M2, M3, M4
The sample space includes all of the possible outcomes of picking two contestants from the audience of 5 females and 4 males. Since the order of choosing does not affect the outcome, the sample space does not change regardless of which gender is chosen first. Therefore, randomly choosing a male first and randomly choosing a male second are independent events.
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Determine a series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E'?
The series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E' will be Dilation and Reflection.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.
Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.
Then the scale factor about the origin is given as,
Scale factor = 2 / 4
Scale factor = 1/2
The reflection does not change the shape and size of the geometry. But flipped the image.
Reflection of the image over the y-axis.
The series of transformations that would map polygon ABCDE onto polygon A'B'C'D'E' will be Dilation and Reflection.
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An airplane i carrying 90
paenger, which i 67
of the capacity of the airplane. What i the capacity of the airplane?
The capacity of the airplane is 105 passengers.
Since 90 passengers is to 6/7 of the capacity, then 90/6 people is 1/7 of the capacity. And, 90 / 6 = 15
So, 15 people is 1/7 of the capacity. It means, the full capacity is 7/7.
Full capacity = 15 * 7 = 105
Hence, the capacity of the airplane is 105 passengers.
What is capacity of passenger?Capacity of passengers are the total number of seats and berths and the total number of authorized standing places which available in a passenger vehicle when doing the service for what it is intended. The maximum passenger capacity in airplane means the maximum number of passenger seats for that an aircraft is configured.
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Although part of your question is missing, you might be referring to this full question: An airplane is carrying 90 passengers, which is 6/7 of the capacity of the airplane. What is the capacity of the airplane?
A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.
Sunglasses Inventory
Number of Days Total Amount of Sunglasses
2 54
5 48
7 44
10 38
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 50
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 49
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 56
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 55
Answer:
the answer is 48 i believe
Step-by-step explanation:
............
Solve the inequality 5x>-15 for x
Answer:
x>-3
Step-by-step explanation:
Divide both sides by 5
x > -3
-15/5 = -3
Iron-59 has a half-life of 44. 5 days. How much of a 3. 00 mg sample will be left after 222. 5 days?
A about 6. 00 milligrams
B about 0. 90 milligrams
C about 0. 03 milligrams
D about 0. 09 milligrams
Fe-59 concentrates in the spleen with a biological half life of approximately 600 days, and an effective half life of approximately 42 days.
Define half life?
The half-life of a reaction is the time required for the reactant concentration to decrease to one-half its initial value.Half life is the time that it takes for half of the original value of some amount of a radioactive element to decay. This also implies that one half life is the time that it takes for the activity of a source to fall to half its original value.An interesting and useful aspect of radioactive decay is half-life, which is the amount of time it takes for one-half of a radioactive isotope to decay. The half-life of a specific radioactive isotope is constant; it is unaffected by conditions and is independent of the initial amount of that isotope.The units of half-life are time. The half-life is the length of time that it takes for half of an initial sample to undergo a change. Usually this is the radio-active decay of a specific atomic weight of an element. For example, the half-life of Uranium-238 is 4.46 billion years.To learn more about half life refers to:
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URGENT!!!
Solve the triangle: If it is not possible, say so.
Therefore , the solution of the given problem of triangle comes out to be it is unsolvable as the all the information is not given option A is correct.
What does a triangle signify exactly?Polygons include triangles since they have four sides or more. It has a simple, geometric shape. The letters ABC make up a triangle, which is a square angle. Euclidean geometry results in a single rectangle or square so when sides remain not coincident. Because they have 3 components and three corners, triangles are polygons. A triangle's corners are where its three sides meet. The total of the angles in a triangle is 180 degrees.
Here,
Given :
=> α = 60°
=> β = 60°
=> γ = 60°
To solve the triangle we need to know the angles,
Since all the angles are equal to 60 degree
it seems it is an equilateral triangle having all the same sides
So,
it can be option b,c and d
but here is not mentioned the side length.
Thus, it is unsolvable.
Therefore , the solution of the given problem of triangle comes out to be it is unsolvable as the all the information is not given option A is correct.
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what percentage of american adults are victims of identity theft each year? question 18 options: about 7 percent. less than 1 percent. about 19 percent. more than 25 percent. about 13 percent.
More than 25 percent of American adults are victims of identity theft each year.
What percentage of Americans are victims of identity theft?33% of Americans have experienced identity theft in some capacity. In comparison to other countries, the United States has about three times as many identity theft scenarios. According to reports, about 33% of Americans have experienced an attempt at identity theft at some point in their life.Up to 9 million Americans per year, according to the Federal Trade Commission (FTC), have had their identities stolen. You may discover crime prevention strategies and what to do if you become a victim by learning about this subject.According to Javelin Strategy, 15 million Americans are expected to have had their identities stolen in 2021.Learn more about Theft in America refer to :
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Find the unknown side length. Round to the nearest tenth. Enter your answer in the box
5 ft
25 ft
Considering the other two sides, i.e. 5ft, 25ft, The unknown side length is 24.5 ft.
The unknown side length can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, we have one side with a length of 5 ft and another side with a length of 25 ft. To find the length of the third side, we can use the formula: [tex]c^2 = a^2 + b^2[/tex], where c is the length of the hypotenuse and a and b are the lengths of the other two sides.
Substituting the given values, we have
[tex]25^2 = 5^2 + b^2[/tex],
[tex]b^2[/tex]= 625 - 25 = 600.
Taking the square root of both sides, we have c = √600 = 24.4949. Rounding to the nearest tenth, the unknown side length is 24.5 ft.
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Complete Question:
Find the unknown side length. Round to the nearest tenth.
a = 5 ft
b = ?
c = 25 ft
Find sn for the arithmetic series where a1=−20 , n=25 , an=148
The value of the sum of the series is 160
How to determine the sum of the seriesIn an arithmetic series, the sum of the first "n" terms (Sn) is given by the formula:
Sn = n/2 * (a1 + an)
Where "a1" is the first term and "an" is the nth term.
In this series, n = 25, a1 = -20, and an = 148.
Plugging these values into the formula, we get:
Sn = 25/2 * (-20 + 148)
= 25/2 * 128
= 25 * 64
= 1600
So, the sum of the first 25 terms of the arithmetic series is 1600.
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Determine by inspection two solutions of the given first-order ivp. Y' = 6y5/6, y(0) = 0.
The solution of the given equation is y = y = e^(6x -∞) ,y = e^(6x)
The given equation is a first-order linear differential equation with constant coefficients. Applying the integrating factor, we get:
[tex]I = e^(int (6 dy/6y)) = e^(ln y)[/tex]
Multiplying both sides of the equation by I:
[tex]Iy' = 6y5/6 ⇒ dy/y = 6/6 dy ⇒ ln y = 6x + c[/tex]
Therefore, the general solution of the given equation is:
y = e^(6x + c)
Substituting the initial condition, y(0) = 0 to the above equation, we get:
[tex]0 = e^(6(0) + c) ⇒ c = -∞[/tex]
Therefore, the solution of the given equation is:
y = e^(6x -∞)
Solution 2:
The given equation is a first-order linear differential equation with constant coefficients. Applying the integrating factor, we get:
[tex]I = e^(int (6 dy/6y)) = e^(ln y)[/tex]
Multiplying both sides of the equation by I:
Iy' = 6y5/6
⇒ dy/y = 6/6 dy
⇒ ln y = 6x + c
Therefore, the general solution of the given equation is:
y = e^(6x + c)
Substituting the initial condition, y(0) = 0 to the above equation, we get:
0 = e^(6(0) + c)
⇒ c = 0
Therefore, the solution of the given equation is:
y = e^(6x)
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What is sample space in set?
The sample space may be limited or infinite, depending on the nature of the experiment. A sample point is a component of the sample space that symbolizes one potential experiment result.
How does sample space work?The sample space may be limited or infinite, depending on the nature of the experiment. A sample point is a component of the sample space that symbolises one potential experiment result.
The sample space is a set in probability theory that includes all potential results of a random experiment. The set of all potential outcomes or outcomes of a random experiment is referred to as a sample space. The set 1, 2, 3, 4, 5, and 6 might be the sample space, for instance, if we are rolling a die.
A sample space is a group of items that in set theory represents all potential outcomes of a random event. Depending on the situation, either a finite or infinite sample space
A sample space is a group of items that in set theory represents all potential outcomes of a random event. Depending on the nature of the experiment, the sample space may be either finite or limitless. A sample point is a component of the sample space that symbolises one potential result of the experiment. As it offers a framework for defining and computing probabilities, the sample space is a basic idea in probability theory.
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How can you use a protractor to prove that AB and CD are parallel?
How can you use paper folding to prove that AB and CD are parallel?
Lines AB and CD are parallel to each other because the lines make the same angle as the transversal line.
What are parallel lines?When the distance between the lines is constant then the lines are called parallel lines. The lines do not intersect when they are separated from each other. And the slope of the lines is equal.
Let the transversal line be EF to line AB and CD.
Line AB and line CD make the same angle as the transversal line. Then we can say that the lines AB and CD are parallel to each other.
The diagram is given below.
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the function of f(x)= 4x^4 + 23x^3 + 43x^2 + 33x + 9 has at least two rational roots. Use the rational root theorem to find these roots, then proceed to find all complex roots. (Note: roots may be integer, rational, irrational, and/or complex)
PLS HELP ME ITS DUE TONIGHT AT 11:59
Answer:
f'(x)=16x³+69x²+86x+33
1. Alex can't believe how many shoes Olivia has. He decides to estimate the mean number of shoes female students have, on
average, at Olympia High School. Alex took an SRS of 25 students and recorded the number of pairs of shoes students reported
having.
The 95% confidence interval for the mean number of shoes owned by female students is (95.58, 195.14).
Calculate the sample mean:
Total number of shoes = 45+31+3125+62+15+29+27+28+35+18+55+18+39+28+35+44+18+10+55+50+40+38+22+16 = 3634
Sample mean = 3634/25 = 145.36
Calculate the standard deviation:
Standard deviation = √[(45-145.36)² + (31-145.36)² + (3125-145.36)² + … + (16-145.36)²]/24 = 586.33
Calculate the margin of error:
Margin of error = 1.96∗586.33/√25 = 49.78
Calculate the 95% confidence interval:
Lower bound = 145.36 - 49.78 = 95.58
Upper bound = 145.36 + 49.78 = 195.14
Since the sample mean is not an integer, we must round the lower and upper bounds to the nearest integer, which gives us (29.73, 40.27) as the 95% confidence interval for the mean number of shoes owned by female students.
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tape timer creates dots at a rate of 28 hz, what time interval in seconds does 3 successive dots represent?
Hz (Hertz) is a unit of frequency, which measures the number of events or occurrences of a certain phenomenon per second. In this case, the tape timer creates 28 dots per second, which means that the frequency of dot creation is 28 Hz.
To find the time interval between 3 successive dots, we need to calculate the time it takes for the tape timer to create 3 dots. This can be done by dividing the total time by the number of dots created.
Since the tape timer creates 28 dots per second, the time interval between 3 dots can be calculated as follows:
Time interval = 1 second / 28 dots = 1/28 seconds
So, the time interval between 3 successive dots created by the tape timer is 1/28 seconds, which is the amount of time that elapses between the creation of each dot.
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write each of these ratios in its simplest form 102:99:87
Answer:
34:33:29
Step-by-step explanation:
all #s can be divided by 3
34:33:29
PLEASE HELP!!! A right cone has a base with diameter 6 units. The volume of the cone is 72π cubic units.
What is the length of a segment drawn from the apex to the edge of the circular base
(slant height)?
Round to the nearest tenth. This is a multi-step problem so do not round until the final answer.
The segment drawn from the apex to the edge of the circular base is __ units.
The slant height of the right cone is 24.2 units, rounded to the nearest tenth.
What is the Pythagorean Theorem?
The Pythagorean theorem is a mathematical theorem that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be expressed as c² = a²+ b².
The slant height of a right cone can be found by using the Pythagorean Theorem. The radius of the circular base is half the diameter, which is 6/2 = 3 units. The volume of the cone can be found using the formula:
V = (π/3)r²h
Where r is the radius, and h is the height of the cone. Plugging in the given values, we have:
72π = (π/3)r²h
72π = (π/3)3²h
72π = (π/3)9h
72π = 3πh
24 = h
Using the Pythagorean Theorem, we can find the slant height as follows:
c² = a² + b²
Where a and b are the height and radius of the cone, and c is the slant height. Plugging in the values we have:
c² = 24² + 3²
c² = 576 + 9
c² = 585
c = 24.2
Hence, the slant height of the right cone is 24.2 units, rounded to the nearest tenth.
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Which of the following statements are TRUE? (Check all that apply) In C, arrays are passed by value In C, when swapping two elements of an array in a procedure, an entire array must be passed to it (i.e. there is no other way to write this procedure), e.g. procedure swapEls in the lecture example. In C, like in Java, all primitive types are by default passed by value In C, unlike in Java, primitive types can be passed by reference using pointer notation In the C examples used so far, arrays are allocaed on the stack In Java, when an array is created, the new operator is used and hte array is allocated on the stack
Arrays in C and Java are similar in that they are used to store collections of elements, but the way they are passed, stored, and manipulated is different.
Arrays are a fundamental data structure in C and Java programming languages. In both languages, arrays are used to store a collection of elements with the same data type.
However, arrays can also be passed by reference using pointer notation.
This means that changes made to the array in the function are reflected in the original array.
When swapping two elements of an array in C, an entire array must be passed to a function, as there is no other way to write this procedure.
The stack is a portion of memory that is used for storing function calls and variables declared inside functions.
When a function is called, the stack grows and when the function returns, the stack shrinks.
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How do you convert 100 Kilogram (kg) to Pound (lb)?
100 kilograms (kg) converts to 220.463 pounds (lb).
What does 100 kilograms translate to in pounds?Conversion. 100 kilograms (kg) converted to pounds (lb). 100 kilograms (kg) equals 220.463 pounds (lb). A kilogram weighs approximately 2.2046226218 pounds. The method for converting kilos to pounds is pretty straightforward. All you have to do is multiply the kilogram amount by 2.2046226218.
The term “pound” derives from the ancient Roman libra pondo, which means “a pound by weight.” According to the BBC, the English term “pound” is derived from the pondo component of the sentence. However, the abbreviation “lb” is taken from the word libra.
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Inverse Trig Ratios FINDING MISSING ANGLES IP youknow the Sin; cosne; 0r tangent ratio of anangle you canuse the inverse Aunction (sin! cos tan ) to fnd the measure of the agle Examples: Find the value of x Round to the nearest tenth.'
The values of x in the triangles are 38.9 and 43.3 degrees
How to determine the values of xThe complete question is added as an attachment
Triangle 1
The value of x can be calculated using the following sine ratio
sin(x) = 15/24
Evaluate the quotient
sin(x) = 0.625
Take the arc sin of both sides
x = 38.9
Triangle 2
The value of x can be calculated using the following cosine ratio
cos(x) = 8/11
Evaluate the quotient
cos(x) = 0.7273
Take the arc cos of both sides
x = 43.3
Hence, the solution is 43.3 degrees
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Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P. y= x , P(25,5) a. The slope of the curve at the given point is
a) The slope is 1
b) The equation of the tangent line is x-y=20.
What is slope?
Slope is calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line.Any two distinct places along the line can be used to determine the slope of any line.
a) To find the slope of the curve, the derivative of a function f(x) at the given point is a slope of the curve
Slope of the given curve y = x at the point P(25, 5) is the derivative f'(x) at P(25,5)
=>m = f'(x) = dy/dx
=>1
Since the derivative of x is 1
f'(x) at P(25, 5) is 1
= > Slope = 1
b) To find an equation of the tangent line at P (25,5) for the curve y = x.
The equation of tangent line in for the function f(x) at P ([tex]x_1,y_1[/tex]) is (y - [tex]y_1[/tex]) = m (x - [tex]x_1[/tex])
Given:
[tex]x_1[/tex] = 25 and [tex]y_1[/tex] = 5, f(x) =x and slope of tangent m = 1
The equation of the tangent line is (y - 19) = - 24(x - 2)
⇒ y - 5 = 1(x -25)
=> y=x-25+5
=> y=x-20
=> x-y=20
The equation of tangent is x-y=20.
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y^2(4-y^2) critical points
The critical values of the given function are 0, +2, and -2.
According to the question
Given function f(x) = y^2(4-y^2)
Setting the partial derivatives of the function y2(4-y2) to zero and solving for y will reveal where the function's crucial points are.
The partial derivatives of y^2(4-y^2) with respect to y are:
⇒ d/dy (y^2) = 2y
⇒ d/dy (4-y^2) = -2y
⇒ d/dy (y^2(4-y^2)) = 2y(-2y) + 2(y^2)
⇒ -4y^2 + 4y^2 = 0
Setting the partial derivative equal to zero:
-4y^2 + 4y^2 = 0
Solving for y:
y = 0 or y = ±2
The critical values are therefore y = 0 and y = 2. Using the second derivative test or by examining the behavior of the function close to these locations, these key points can be categorized as local minima, local maxima, or inflection points.
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