36.74098197 kg in 81 lbs. Likewise, the question how many pounds in 81 kilogram has the answer of 178.57443237 lbs in 81 kg.
What is 81 kilos in pounds?81 kg * 2.2046226218 lbs / 1 kg= 178.57443237lbs
The weight of 81 kilograms is equivalent to 178.57443237 pounds (81kg = 178.57443237lbs). It is simple to convert 81 kg to lb. Simply use our calculator above or the method to convert 81 kg to pounds. To convert 81 kg to pounds, multiply the kilogram mass by 2.2046226218. The formula for converting 81 kilograms to pounds is [lb] = 81 * 2.2046226218. Thus, 81 kilos in pounds are 178.57443237 pounds.
One pound is about equivalent to 0.45359237 kilos (kg). The pound to kilogram conversion is accomplished by multiplying the provided pound value by 0.45359237. In addition, one kilogram is about equal to 2.2046226218 pounds.
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help pls.. i am not getting the correct solution
The common chord has a length equal to 6 centimeters.
How to determine the length of a chord common to two circles
In this problem we find the case of two circles of different radii (r₁ = 5 cm, r₂ = 3 cm), whose distance between centres is equal to 4 centimeters. We are required to determine the length of the chord common to the two circles.
First, determine one angle of a triangle by law of cosine:
cos θ = [(5 in)² - (3 in)² - (4 in)²] / [- 2 · (3 in) · (4 in)]
θ ≈ 90°
Second, determine the length of the common chord:
x = 2 · (3 cm)
x = 6 cm
The length of the common chord is equal to 6 centimeters.
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The half-life of caffeine varies among individuals. For example, some medications extend the half-life to 8 hours. This means that 1/2 of the caffeine is eliminated from the bloodstream every 8 hours. Write a function for this new half-life time (assuming a peak level of 80 mg of caffeine) Determine the amount of caffeine in the bloodstream after: 1 hour? 5 hours? 10 hours? 20 hour?
The amount of caffeine in the bloodstream after different times decreases following an exponential decay pattern.
What is caffeine?Caffeine is a natural chemical with stimulant effects.
Let's call the new half-life time for an individual with extended half-life as t. The function for the amount of caffeine (C) in the bloodstream after time t can be expressed as:
C(t) = 80 * (1/2)^(t/8)
Using this formula, we can determine the amount of caffeine in the bloodstream after different times:
1 hour:
C(1) = 80 * (1/2)^(1/8) = 80 * (1/2)^0.125 ≈ 79.28 mg
5 hours:
C(5) = 80 * (1/2)^(5/8) ≈ 64.51 mg
10 hours:
C(10) = 80 * (1/2)^(10/8) ≈ 51.37 mg
20 hours:
C(20) = 80 * (1/2)^(20/8) ≈ 25.68 mg
Therefore, The amount of caffeine in the bloodstream after different times decreases following an exponential decay pattern.
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A map of a national forest has a scale in which 1 inch represents 3 miles. If two picnic areas in the national forest are actually located 15 miles apart, which of the following is true about the map?
A.
There are 5 inches between the two picnic areas on the map.
B.
There are 45 inches between the two picnic areas on the map.
C.
There are 15 inches between the two picnic areas on the map.
D.
There are 3 inches between the two picnic areas on the map.
There are 5 inches between the two picnic areas on the map. Therefore, option A is the correct answer.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
Given that, a map of a national forest has a scale in which 1 inch represents 3 miles.
If two picnic areas in the national forest are actually located 15 miles apart, then on map it is 15/3 =5 inches
Therefore, option A is the correct answer.
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Given that A, O & B lie on a straight line
segment, evaluate obtuse ZAOC.
C
A
(3x +94)
0
→ ZAOC =
(x +30)
(2x-4)
The diagram is not drawn to scale.
0°
D
B
The evaluation of obtuse angle ∠AOC is 124°.
What does "obtuse angle" mean?Any angle more than 90 degrees is deemed obtuse: A straight angle is one with a 180° measurement: A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.
3x + 94 + x + 30 + 2x - 4 = 180
Sum of angle in a triangle
6x + 120° = 180°
6x = 180° - 120°
6x = 60°
x = 10°
Now, ∠AOC = 3x + 94
3 × 10 + 94
30 + 94
124°
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All of the following are benefit of joining a profeional aociation or organization EXCEPT…\
The one which not the benefit of being a member of a professional organization is providing certificate examinations at discounted rate. The correct option is D.
Which is a benefit of joining a Professional Organization?Professional associations provide the better networking opportunities with people who are specifically in our industry. Whether we are looking to pursue employment opportunities, link with other industry professionals, or even looking for a mentor in our profession, the networking opportunities are invaluable.
Another benefits of joining in a professional organization is that it helps build the career portfolio of a professional. Organizations which can provide opportunities for speaking engagements, career specialization, publication and even scholarship and training programs abroad.
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Although part of your question is missing, you might be referring to this full question: All of the following are benefits of being a member of a professional organization, except:
A. providing a wide range of continuing education units.
B. publishing newsletters and magazines dealing with current issues and trends in healthcare.
C. providing tuition reimbursement.
D. providing certificate examinations at discounted rate.
(1.0x10^3) and 2.0x10^5
The value for (1.0x10³) / 2.0x[tex]10^5[/tex] is 0.005.
What are Exponent and Power?Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner.
For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as [tex]3^4[/tex], where 4 is the exponent and 3 is the base.
Given:
(1.0x10^3) and 2.0x10^5
We don't have any sign so we proceed with operation division
(1.0x10³) ÷ 2.0x[tex]10^5[/tex]
= (1.0x10³) / 2.0x[tex]10^5[/tex]
Suing exponents
[tex]a^m/ a^n= a^{m-n[/tex]
= 1/2 x [tex]10^{3-5[/tex]
= 0.5 x [tex]10^{-2[/tex]
= 0.5 / 10²
= 0.5 /100
= 0.005
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trevor is making a poster for his science project he decides to use 1/2 of the poster for his pictures 3/8 for his hypothesis and 1/4 for the experiment process is this possible explain why or why not
No, it's not possible for Trevor to use 1/2 of the poster for his pictures, 3/8 for his hypothesis, and 1/4 for the experiment process.
How to show it is not possibleThis is discovered by addition of fraction
= 1/2 + 3/8 + 7/8
= 7/8
The fractions 1/2, 3/8, and 1/4 add up to 7/8, which is greater than 1.
Since the fractions represent parts of a whole poster, the total must be less than or equal to 1.
Therefore, Trevor needs to adjust the fractions so that their sum is less than or equal to 1.
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Help me please
Mainsail
Headsail
Welcome to the land down under! Spend the day sailing
in Sydney Harbor! Sailboats are made up of two sails,
the mainsail and the headsail. Typically, these sails are
the shape of triangles and these two triangles are
similar. Considering the sailboat pictured below,
determine the value of x and y and the unknown side
lengths.
6+A
X-2
30 ft
5y-3
26 ft
The value of x is 15
The value of y is 7.
The unknown sides:
x = 15
5y - 3 = 33
y + 9 = 16
x - 2 = 13
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Similar triangles mean the ratios of the corresponding sides are equal.
Now,
(5y - 3)/(y + 9) = 30/x = 26/(x - 2)
Taking two ratios.
(5y - 3)/(y + 9) = 30/x
5xy - 3x = 30y + 270
Taking two ratios.
30/x = 26/(x - 2)
30x - 60 = 26x
30x - 26x = 60
4x = 60
x = 15
Now,
Substituting x = 15
5xy - 3x = 30y + 270
5 x 15 x y - 3 x 15 = 30y + 270
75y - 45 = 30y + 270
75y - 30y = 270 + 45
45y = 315
y = 7
Now,
x = 15
5y - 3 = 35 - 3 = 33
y + 9 = 7 + 9 = 16
x - 2 = 15 - 2 = 13
Thus,
x is 15 and y is 7.
The unknown sides are 15, 33, 16, and 13.
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a bin contains 5 red balls and 9 blue balls. the following experiment is repeated several times: remove a ball from the bin, observe its color, and replace it. what is the probability that the 5th ball drawn is red and the 8th ball drawn is blue?
The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
What is probability ?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.
The probability of both events happening is the product of the individual probabilities:
P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196
So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
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The probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
The probability of drawing a red ball on the 5th draw is the number of red balls divided by the total number of balls in the bin, which is 5/14. The probability of drawing a blue ball on the 8th draw is the number of blue balls divided by the total number of balls in the bin, which is 9/14.
The probability of both events happening is the product of the individual probabilities:
P(red on 5th draw and blue on 8th draw) = (5/14) * (9/14) = 45/196
So, the probability that the 5th ball drawn is red and the 8th ball drawn is blue is 45/196 or approximately 0.2307.
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find the curvature. r(t) = 9t i 7t j (2 t2) k
The curvature of a curve r(t) = 9t i 7t j (2 t2) k is 4 × ||9 i + 7 j|| / (9² + 7² + 4t²)^(3/2).
What do you mean by curvature?Curvature is a measure of the amount by which a curve deviates from being straight. It describes the degree to which a curve bends or twists at any point along its length.
In mathematics, curvature is a property of curves and surfaces that is used to describe their shape and local behavior. For example, the curvature of a circle is constant and is equal to the reciprocal of its radius. The curvature of a straight line is zero.
Curvature is a scalar quantity and is usually measured in units of inverse length, such as 1/meter. There are several ways to mathematically define and calculate curvature, including the concept of the curvature of a curve at a point, which is the rate of change of the direction of the tangent to the curve at that point.
The curvature of a curve is given by:
k(t) = ||r'(t) x r''(t)|| / ||r'(t)||³
where r'(t) is the first derivative of r(t), r''(t) is the second derivative of r(t), and || || is the magnitude or length of a vector.
Given the curve r(t) = 9t i + 7t j + (2 t²) k, we can find its first and second derivatives:
r'(t) = 9 i + 7 j + 4t k
r''(t) = 4 k
So, the curvature of the curve r(t) is:
k(t) = ||r'(t) x r''(t)|| / ||r'(t)||³ = ||9 i + 7 j|| × ||4 k|| / ||9 i + 7 j + 4t k||³ = 4 × ||9 i + 7 j|| / (9² + 7² + 4t²)^(3/2)
Since this expression depends on t, the curvature is a function of t, not a constant.
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When marginal revenue is negative for a linear (inverse) demand function, increases in output will cause total revenues to:
a. increase
b. decrease
c. remain unchanged
d. there is not sufficient information to classify the elasticity of demand
Marginal Revenue is negative, the firm should consider reducing its output to increase its total revenue.
Therefore, correct answer will be a. increase.
Marginal Revenue (MR) is a crucial concept in economics that measures the change in a firm's total revenue as a result of selling one additional unit of output. MR is used by firms to make decisions about how much output to produce and what price to charge.
In a linear (inverse) demand function, MR is negative when the elasticity of demand is less than one, meaning that the demand for a product is relatively inelastic. In other words, as the firm increases output, the price will decrease, causing total revenue to decline.
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question content area top part 1 suppose a 4×7 coefficient matrix for a system has four pivot columns. is the system consistent? why or why not?
If a 4x7 coefficient matrix has four pivot columns, the system is consistent and has exactly one solution.
A coefficient matrix is a matrix that represents a system of linear equations. In the case of a 4x7 coefficient matrix, the matrix has 4 rows and 7 columns.
When it comes to determining the consistency of a system of linear equations, the presence of pivot columns is a key factor.
A pivot column is a column that contains a leading 1 in the row reduced echelon form of the matrix. If a system has four pivot columns, this means that the system has 4 linearly independent equations, meaning that there is exactly one solution to the system.
Therefore, the system is considered consistent.
However, if the number of pivot columns is less than the number of unknowns, then the system is considered inconsistent, meaning that there is either no solution or an infinite number of solutions.
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Can anyone tell me how to do this
The required dimensions in the figure are
angle FXD = 44 degreesEG = 14angle FZG = 21How to find the required dimensionsDG = FG = EG incenters
solving for angle FXD using SOH CAH TOA
The side XG is worked using SOH CAH TOA
Sin = opposite / hypotenuse - SOH
Cos = adjacent / hypotenuse - CAH
Tan = opposite / adjacent - TOA
sin 22 = FG / XG
XG = 14 / sin 22
XG = 37.37
sin x = DG / XG = 14 / 37.37 hence x = 22
therefore angle FXD is 44 degrees
EG = DG = 14
angle FZG
< DYE + < FXD + < FZE = 180 sum of angles of a triangle
94 + 44 + < FZE = 180
< FZE = 180 - 94 - 44
< FZE = 42
< FZE = 2 * < FZG
< FZG = 42 / 2
< FZG = 21
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sketch an angle θ in standard position such that θ has the least possible positive measure, and the point \left(-2,\sqrt{3}\right) is on the terminal side of θ.
The angle has a measure of 0° and is in standard position with its vertex at the origin. On the terminal side of lies the point (-2, 3).
The vertex of an angle in standard position on a coordinate plane is at the plane's origin. The angle's terminal side is rotated anticlockwise from the starting side while the angle's initial side is on the positive x-axis. The number of degrees the terminal side has travelled away from the initial side anticlockwise is how an angle is measured in standard position. This signifies that the terminal side is exactly on the same line as the initial side because the angle has the smallest positive measure of 0°. Since the line segment from the origin to the point (-2,3) is on the terminal side of, the point (-2,3) is on that side as well.
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PLSSSS HELP IF YOU TURLY KNOW THISSS
Answer:
Step-by-step explanation:
Since the numerator is missing, you want to multiply the denominator onto the other side.
5 x 7 =35
x=35
Answer:
x=35
Step-by-step explanation:
Easy way to solve is making x/5 an improper fraction (fraction whose numerator is equal to or greater than its denominator.)
How I solved it was by multiplying 7×5=35, then I plugged the value into x making it (35/5)=7.
Now just make it a proper fraction, 35÷5=7, now we have 7=7.
:(help please..i dont understand it.
Answer:
Below
Step-by-step explanation:
A = qty 2 at 12.50 each = 25.00
B = 33.90 / 2 = 16.95 unit price
C = 31.00 / 6.20 = quantity 5
VAT is value added tax ...take the total 108.28 and multiply by 15% = 16.24
why is it impossible to convert a decimal number to binary on a digit-by-digit basis as can be done for hexadecimal?
Each decimal number has a unique bit structure that starts at 1 bit, that's why it is impossible to convert a decimal number to binary digit-by-digit as is achievable with hexadecimal.
It impossible to convert a decimal number to binary on a digit-by-digit basis as can be done for hexadecimal because each decimal number has a separate bit structure that starts at 1 bit and goes quickly, it is difficult to convert a decimal number to binary string of 4 bits digit by digit.
However, since each hexadecimal number has a width of 4 bits, this is achievable. It is relatively easy to go back and forth between binary and hexadecimal. The comparable 4-bit binary string is used to replace each hexadecimal digit in the original number.
Hexadecimal Number FD13.
1111 1101 00010011 each hexadecimal digit with its corresponding 4-bit binary value.
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A shipping company makes cube-shaped boxes. Their basic box measures 1 foot per side. They want to know how to scale the basic box to build new boxes of various volumes. If the company wants a box with a volume of 8 cubic feet, by what scale factor do they need to dilate the box?
They need to dilate the box by a scale factor of ∛8.
What is scale factor?This refers to the number/amount by which a figure is bigger or smaller than the original figure.
Solving for scale factor they need to dilate the box:
The volume of a cube with sides of length "s" is given by the formula:
V = s³.
If the basic box has a volume of 1 cubic foot (V = 1), then a box with a volume of 8 cubic feet (V = 8) can be found by scaling the basic box by a factor of ∛8.
Hence, the scale factor is ∛8.
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The table below shows that the number of miles driven by Parker is directly
proportional to the number of gallons he used.
Gallons Used Miles Driven
34
41
45
1305.6
1574.4
1728
How many miles can he travel on 44.2 gallons of gas?
The number of miles he can travel on 44.2 gallons of gas would be = 1697.28 miles
How to calculate the number of mile?The table shows that there is direct proportional relationship between the number of miles traveled and the number of gallons used by Parker. That is increase in the number of mile = increase in the number of gallons.
If 34 gallons = 1305.6 miles
44.2 gallons = X miles
Make X miles the subject of formula;
X miles = 44.2 × 1305.6/34
= 57707.52/34
= 1697.28 miles
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Which expression can be used to represent the volume of this prism?
Responses
3 × 9 × 9 units³
2 × 3 × 9 units³
2 × 3 × 9 units³
3 × 3 × 18 units³
2 × 3 × 3 units³
A rectangular prism made up of unit cubes. There are 3 layers, and each layer is 9 units long and 2 units wide.
The volume of this prism = 2 × 3 × 9 units³.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
from the given figure we get,
A rectangular prism made up of unit cubes.
There are 3 layers, and each layer is 9 units long and 2 units wide.
i.e. l = 9
w = 2
h = 3
so, the volume = V
we know, V= l.w.h
so, V = 9.2.3
Hence, The volume of this prism = 2 × 3 × 9 units³.
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for a given number of domains, which characteristic is common to every molecule?
Every molecule has a unique molecular formula.
A molecular formula is a chemical formula that represents a molecule and gives information about the number and type of atoms present in the molecule. This formula is unique to each molecule and distinguishes one molecule from another, even if they have the same number and type of atoms arranged in a different way.
For example, the molecular formula for glucose (C6H12O6) is different from that of fructose (C6H12O6), even though they have the same number and type of atoms. The molecular formula represents the actual number of atoms present in the molecule and their chemical makeup, which in turn determines the chemical properties and behavior of the molecule.
Thus, for a given number of domains, the characteristic that is common to every molecule is their unique molecular formula.
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Throughout this module, you have learned how to gather and present information to help justify your answer. You will use this skill, along with your knowledge of constructing figures in Geometry, to construct an argument in paragraph form.
Step 1: Tips on Formulating Your Argument
Here are some tips on formulating your argument:
● Think, Think, Think. Ask yourself lots of questions about each side of the topic, then answer them based on your research findings, your opinion, and your experiences with both sides of the argument.
● Think from the other side. It is impossible to refute, or prove false, someone’s claim if you don’t know what he or she is thinking ahead of time.
● Create a list of some sort that helps you organize your thoughts. The more organized you are, the more prepared you will be and the more likely you are to win a debate!
● Cite your sources when you are speaking. Citing your sources gives your arguments more credibility. For example, you might say, "According to an article in the Math Rocks Journal ..."
● Use credible sources. Credible sources are ones readers can trust and ones that can be backed up with evidence. Not all sources carry the same weight; use sources that enhance your argument. Wikipedia is not a reliable or credible source.
● Use effective speech and grammar. Remember, you are trying to get others to side with you, so speak clearly and professionally.
● Do more research. If you haven’t caught on by now, formulating your argument takes a lot of digging. Essentially, you have to prove your
points. You can even research how to debate! Take really good notes.
Step 2: The Argument
Here are the two arguments:
Argument A: There is a need for students to understand and be able to construct geometric figures using a compass and straightedge.
Argument B: There is no need for students to use a compass and straightedge, and all geometric constructions should be done using a drawing program.
There are two opposing arguments listed above. You need to choose which one you will support as your argument. Formulating an argument takes research and time to get yourself to the point where you can defend your position thoroughly.
Step 3: What to Submit
You may use any word processing program to present your argument, but you must include the following:
1. A summary of your argument. The summary should begin with the argument statement you chose. In addition, provide at least three
reasons why the method you chose is better than the other method and at least three reasons why the other method is not better. This
summary can have a lot of opinion in it and should be persuasive and argumentative. You should submit in paragraph form.
2. A list of at least two resources used. Resources may include interviews with professionals and/or URLs of websites. Remember, you may
gather ideas from research, but you must explain the ideas yourself. Copying and pasting someone else's ideas is plagiarism. Be sure to avoid plagiarism by phrasing your argument in your own words. Reach out to your teacher if you have any questions.
An argument that supports Argument A is given below:
Geometric figures play a crucial role in many areas of mathematics and science, including engineering, architecture, physics, and computer graphics.
Why is it important to understand and be able to construct geometric figures?Being able to construct these figures accurately and efficiently is therefore an important skill for students to have. By using only a compass and straightedge, students can explore and understand the properties of different shapes and their relationships with one another.
This helps them develop their spatial reasoning abilities and improves their understanding of mathematical concepts such as congruence, similarity, and symmetry.
Furthermore, this skill can be applied to solving real-world problems, such as determining the dimensions of a building or designing a circuit board.
In conclusion, the ability to construct geometric figures using a compass and straightedge is essential for students' mathematical and scientific development and should be taught as part of their education.
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Which segment of this graph shows a decreasing velocity?
A. A to B
B. B to C
C. C to D
D. D to E
E. E to F
The slope of the line below is 3. Use the coordinates of the labeled point to find a point-slope equation of the line. О A. у-8=-3(x-6) OB. y-6=-3(x-8) C. y-6=3(x-8) D. v-8 = 3(x - 6)
When the slope of the line is 3 the equation of the line using point slope formula is
D. у - 8 = 3 (x - 6)
How to fine the equation of the line using point slope formulaPoint slope formula is giving by (y - y₁) = m (x - x₁)
where
m = slope
x₂ and x₁ = points in x coordinates
y₂ and y₁ = points in y coordinates
For slope of 3, equation passing through point (5, 8)
(y - y₁) = m (x - x₁)
y - 8 = 3 (x - 6)
y - 8 = 3x - 18
y = 3x - 18 + 8
y = 3x - 10
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3/4 8 1/2 =
explain how you got the answer
Answer:
[tex]\frac{51}{8} \:or \: 6\frac{3}{8}[/tex]
Step-by-step explanation:
solution given:
[tex]\frac{3}{4} *8\frac{1}{2}[/tex]
let make mixed fraction to normal fraction
[tex]8\frac{1}{2} =\frac{8*2+1}{2} =\frac{17}{2}[/tex]
replace [tex]\frac{17}{2}[/tex]
we have
[tex]\frac{3}{4} *\frac{17}{2}[/tex]
in multplication fraction, we multiply numerator to numerator and denominator to denominator.
[tex]\frac{3}{4} *\frac{17}{2}=\frac{3*17}{4*2} =\frac{51}{8}[/tex]
again
in mixed fraction =[tex]6\frac{3}{8}[/tex]
which of the following gives the volume of the solid created by revolving a curve f(x) around the y-axis?a. V = π∫dc[f(y)]^2dyb. V = π∫dc[f(y)]dyc. V = π∫dc[f(y)]dy^2d. V = π∫dc[f]2dy
The volume of a solid rotated about the y-axis can be calculated by V = π∫dc[tex][f(y)]^{2}[/tex]dy. Option (A)
The volume of a solid rotated around the y-axis can be calculated using the "Disk Method"
The disk method is predominantly used when we rotate any particular curve around the x or y-axis.
Suppose a function x = f(y), which is rotated about the y-axis.
The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by
V = π ∫dc [tex][f(y)]^{2}[/tex]dy.
The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y)
Thus, the volume of a solid rotated about the y-axis can be calculated by V = π∫dc[tex][f(y)]^{2}[/tex]dy. Option (A)
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The volume of a solid rotated about the y-axis can be calculated by V = π∫dc [f(y)]² dy. Option (A)
The volume of a solid rotated around the y-axis can be calculated using the "Disk Method"
The disk method is predominantly used when we rotate any particular curve around the x or y-axis.
Suppose a function x = f(y), which is rotated about the y-axis.
The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by
V = π∫dc [f(y)]² dy
The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y)
Thus, the volume of a solid rotated about the y-axis can be calculated by V = π∫dc [f(y)]² dy. Option (A)
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y=1/4x+1
y=1/4x-1
How many solutions does this system
of equations have?
One solution, because the slopes
are different.
No solution, because the slopes
are the same and the y-intercepts
are different.
Infinitely many solutions, because
the slopes are the same and the
y-intercepts are the same.
Answer:
No solution, because the slopes are the same and the y-intercepts are different.
Step-by-step explanation:
The two equations are:
y = 1/4x + 1 and y= 1/4x - 1
Since the left sides are equal we can equate the right sides:
1/4x + 1 = /4x - 1
1/4x cancels out of the equation and we get the absurdity:
1 = -1
This indicates no solution to the system of equations
Answer:
No solution, because the slopes are the same and the y-intercepts are different.
We can see that the slopes are the same (1/4) and the y-intercepts are different (1 and -1)
Find the volume of the cylinder.
Either enter an exact answer in terms of \piπpi or use 3. 143. 143, point, 14 for \piπpi.
units^3
3
Answer:
4 is there answer I think
Step-by-step explanation:
Which graph is a function of x?
solve the following system x1 −3x2 4x3 = −4 3x1 −7x2 7x3 = −8 −4x1 6x2 −x3 = 7
The solution of the system of equations is [tex]$x_1 = \frac{-400}{35}$, \\$x_2 = \frac{-400}{35}$, and $x_3 = -\frac{20}{35}$.[/tex]
The given system of equations can be written in matrix form as follows:
[tex]\begin{bmatrix}1 & -3 & 4 \\ 3 & -7 & 7 \\ -4 & 6 & -1\end{bmatrix}[/tex][tex]\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}[/tex]
=[tex]\begin{bmatrix}-4 \\ -8 \\ 7\end{bmatrix}[/tex]
We can solve for the unknowns [tex]$x_1$, $x_2$, and $x_3$[/tex] by using the Gaussian elimination method. The first step is to subtract 3 times the first equation from the second equation, and the result is
[tex]\begin{bmatrix}1 & -3 & 4 \\ 0 & -10 & 15 \\ -4 & 6 & -1\end{bmatrix}\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}[/tex]
[tex]=\begin{bmatrix}-4 \\ -20 \\ 7\end{bmatrix}[/tex]
We can then subtract 4 times the first equation from the third equation, and the result is
[tex]\begin{bmatrix}1 & -3 & 4 \\ 0 & -10 & 15 \\ 0 & 18 & -5\end{bmatrix}\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}[/tex]
=[tex]\begin{bmatrix}-4 \\ -20 \\ -12\end{bmatrix}[/tex]
We can now add 10 times the second equation to the third equation, and the result is
[tex]\begin{bmatrix}1 & -3 & 4 \\ 0 & -10 & 15 \\ 0 & 0 & -35\end{bmatrix}\begin{bmatrix}x_1 \\ x_2 \\ x_3\end{bmatrix}[/tex]
=[tex]\begin{bmatrix}-4 \\ -20 \\ 20\end{bmatrix}[/tex]
We can now solve for [tex]$x_3$[/tex] by dividing the third equation by -35, and the result is = [tex]\frac{20}{-35} = -\frac{20}{35}$.[/tex]
Therefore, the solution of the system of equations is
[tex]$x_1 = \frac{-400}{35}$, $x_2 = \frac{-400}{35}$, and $x_3 = -\frac{20}{35}$.[/tex]
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