To find the coordinates of the points on the curve r = 1 + cos(θ) where the tangent line is vertical or horizontal on the interval [0, 2π), follow these steps:
1. Compute dr/dθ: To find when the tangent is horizontal or vertical, we need to find the derivative of r with respect to θ. Start by differentiating r = 1 + cos(θ) with respect to θ:
dr/dθ = -sin(θ)
2. Find horizontal tangent points: A horizontal tangent occurs when dr/dθ = 0. In this case, -sin(θ) = 0. Solve for θ:
θ = nπ, where n is an integer
Since we're only considering the interval [0, 2π), we have two values of θ: 0 and π. Now, find the corresponding r-values for these points:
r(0) = 1 + cos(0) = 1 + 1 = 2
r(π) = 1 + cos(π) = 1 - 1 = 0
So, the coordinates for horizontal tangents are (2, 0) and (0, π).
3. Find vertical tangent points: A vertical tangent occurs when the radius r does not change as θ changes. Since dr/dθ = -sin(θ), we are looking for values of θ where sin(θ) is undefined. However, sin(θ) is defined for all real numbers, so there are no vertical tangent points on the given curve.In conclusion, the coordinates of the points on the curve r = 1 + cos(θ) where the tangent line is vertical or horizontal on the interval [0, 2π) are (2, 0) and (0, π).
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Please help me im struggling sm
The measurements are x = 7 and ∠NJK = 51°
Given is a rectangle, we need to find the asked measurement,
So,
Since we know that the diagonals of a rectangle bisect each other,
So,
JN + JN = JL
4x+4+4x+4 = 5x+29
8x+8 = 5x+29
3x = 21
x = 7
And,
The vertex angle is 90° so,
∠NMJ + ∠NML = 90°
∠NML = 51°
Also,
∠NML = ∠NJK because they are alternate angles,
So, ∠NJK = 51°
Hence x = 7 and ∠NJK = 51°
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On Friday, Jacob planted a pinto bean in science class. When he returned to school on Monday, the bean had sprouted a stem that was 3 millimeters long. At the end of the week, Jacob's bean sprout had a stem that was 42 millimeters long. How many centimeters did Jacob's bean sprout grow during the week?
Jacob's bean sprout grew 3.9 centimeters during the week.
What is measurements?
Measurements in math involve the assignment of numerical values to physical quantities, such as length, area, volume, mass, time, temperature, and so on. Measuring objects or events allows us to compare and quantify them, and is an essential part of mathematical problem-solving, as well as many other fields of study
Jacob's bean sprout grew 42 millimeters - 3 millimeters = 39 millimeters during the week.
To convert millimeters to centimeters, we need to divide by 10 since there are 10 millimeters in 1 centimeter.
So, the growth in centimeters is 39 millimeters ÷ 10 = 3.9 centimeters.
Therefore, Jacob's bean sprout grew 3.9 centimeters during the week.
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My office is 10 ft by 12 ft. I want to buy border for the top of my wall. I have a 3ft door on a 10 ft wall and a 3 ft window directly across from it. How much wallpaper border should I buy?
a. 24
b. 44
c. 38
You should buy 38 feet of wallpaper that cover the border for the top of the wall using the perimeter of the room. Thus, option C is correct.
Length of office = 10 feets
width of office = 12 feets
Door length = 3 feet
Wall length = 10 feet
Window length = 3 feet
To estimate the length of the wallpaper border needed, we need to calculate the perimeter of the room that needs the bordering of wallpaper. It is given that only the top of the roof needs bordering.
We need to add the lengths of all 4 sides of the walls and subtract the lengths of the door and window.
Mathematically,
The perimeter of the room =(sum of the length of sides of the room) - (length of the window) - (length of the door)
Perimeter of room = (10 + 12 + 10 + 12) - 3 - 3
Perimeter of room = 38 ft
Therefore, we can conclude that we need to buy 38 feet of the wallpaper border.
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Suppose a 4 is rolled on a number cube with sides numbered 1, 2, 3, 4, 5, and 6. The
complement of this event would be rolling a 1, 2, 3, 5, or 6. What is the probability of the
complement, written as a fraction in simplest form?
The probability of rolling any number other than 4 on a number cube with sides numbered 1, 2, 3, 4, 5, and 6 is 5/6, which can be written as a fraction in simplest form.
The complement of rolling a 4 on a number cube with sides numbered 1, 2, 3, 4, 5, and 6 is rolling any number other than 4, which includes rolling a 1, 2, 3, 5, or 6.
To find the probability of the complement, we need to add up the probabilities of rolling each of these numbers.
Since each number has an equal chance of being rolled, we can find the probability of rolling each number by dividing 1 by the total number of possible outcomes (which is 6, since there are six sides on the cube).
Then, we can add up the probabilities of rolling each of the five numbers in the complement:
P(rolling a 1, 2, 3, 5, or 6) = P(rolling a 1) + P(rolling a 2) + P(rolling a 3) + P(rolling a 5) + P(rolling a 6)
P(rolling any number other than 4) = 1 - P(rolling a 4)
P(rolling any number other than 4) = 1 - 1/6 = 5/6
Therefore, the probability of rolling any number other than 4 on a number cube with sides numbered 1, 2, 3, 4, 5, and 6 is 5/6, which can be written as a fraction in simplest form.
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If (x+1/x)² = 3, find x³+1/x³.
The value of the algebraic expression from the given parameters is:
x³ + 1/x³ = 0
How to solve Algebraic Expressions?The given problem is simply based on the expansion.
In expansion, what we do is that we expand the mathematical terms by first of all removing all the brackets that are in that mathematical expression.
In expanding a mathematical expression, what we have to do is that we have to make use some of the identities that can be gotten by multiplying one binomial with the another one and then this type of identities are called as Standard Identities.
For example:
(x + a)(x + b) = x² + (a + b)x + ab
Thus:
(x + 1/x)² = 3
x + 1/x = √3
(x+1/x)³ = x³ + (1/x)³ + 3(x)(1/x) (x + 1/x)
√3³ = x³ + 1/x³ + 3(√3)
x³ + 1/x³ = 3√3 - 3√3
x³ + 1/x³ = 0
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Fries 420 grams = $2.77
How much if its 1kg?
At the Fisher farm, the weights of zucchini squash are Normally distributed. Which standardized weight represents the top 10% of the zucchinis?
Find the z-table here.
–1. 64
–1. 28
1. 28
1. 64
The standardized weight which represents the top 10% of the zucchinis from the z-score for the fisher farm the weights of zucchini squash are Normally distributed is 1.28.
Standardized normal distribution = Z given by ,
Z = (X - μ)/σ
Here, X is sample, is μ mean and is σ standard deviation.
At the Fisher farm, the weights of zucchini squash are Normally distributed.
For the normal distribution,
The value mean be 0 and standard deviation be 1.
Z = (X - μ)/σ
μ = 0 , σ = 1
Z = (X -0)/1
Z = X
For the top 10% of the zucchinis, the value of α is 0.9. From the table for this value the z score is,
Z = X
Z = 1.28
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Find the surface area of the triangular prism. The base of the prism is an isosceles triangle.
The surface area of the triangular prism is 3152 square cm if the base of the prism is an isosceles triangle.
What exactly is a triangular prism?
When a prism has three rectangular sides and two triangular bases, the prism is said to be triangular. It's a pentahedron. A right triangular prism has two faces and three rectangular sides. Bases refers to the triangle faces, whereas laterals refers to the rectangular sides.
We have a triangular prism, is showing in the picture:
Here a = 25
b = 25
c = 14
h = 44
The surface area of the triangular prism is given by
A = ah + bh + ch + 1/2√-a⁴ + 2(ab)² + 2(ac)² + -b⁴ + 2(bc)² - c⁴
Plug all the values in the formula we get:
A = 3152 square cm
Thus, the surface area of the triangular prism is 3152 square cm if the base of the prism is an isosceles triangle.
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MAKRING BRAINLIST ^_^
"Twisted till" and "claw curled" are example of what poetic device
1) Repetition
2) Alilteration
3) Ryhme
4) Onomatopoeia
Author repeats "hands folded in as if he wished for something" because it
1) Encourages the readers to save a creature
2) Exaggerates the praying mantis's movement
3) Compares the author to the praying mantis
4) Makes the praying mantis seem more human
"Twisted till" and "claw curled" are examples of alliteration, which is a poetic device that involves the repetition of consonant sounds at the beginning of words.
The author repeats "hands folded in as if he wished for something" to exaggerate the praying mantis's movement and make it seem more human.
This repetition is a literary technique used to emphasize the mantis's behavior and draw the reader's attention to it.
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In ΔGHI, h = 9. 6 cm, g = 9. 3 cm and ∠G=109°. Find all possible values of ∠H, to the nearest 10th of a degree
Using the Law of Sines and Cosines, we get all possible values of ∠H are approximately 60.6° and 69.0°.
We can use the Law of Cosines to find the length of side GH
GH² = g² + h² - 2gh cos(G)
GH² = (9.3)² + (9.6)² - 2(9.3)(9.6)cos(109°)
GH ≈ 3.585 cm
Next, we can use the Law of Sines to find the measure of angle H
sin(H)/GH = sin(G)/HI
sin(H)/3.585 = sin(109°)/HI
sin(H) ≈ 3.585(sin 109°)/HI
H ≈ arcsin[3.585(sin 109°)/HI]
Since we do not know the length of side HI, we cannot determine the exact value of angle H. However, we can find the possible range of angle H by assuming that HI is the longest side of the triangle (making angle H the smallest) and the shortest side of the triangle (making angle H the largest).
If HI is the longest side, then H ≈ arcsin[3.585(sin 109°)/9.3] ≈ 60.6°
If HI is the shortest side, then H ≈ arcsin[3.585(sin 109°)/9.6] ≈ 69.0°
Therefore, the possible values of angle H are between approximately 60.6° and 69.0°.
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Kate surveyed 16 politicians from her state about their views on certain issues. is this sample of citizens of the state likely to be representative?
The representativeness of a sample depends on how it is selected and whether it accurately reflects the characteristics of the larger population. Without more information about the sampling method used, it is difficult to determine if the sample of 16 politicians is likely to be representative of the citizens of the state.
If the sample was selected randomly from a diverse pool of politicians that accurately represents the political landscape of the state, there is a higher likelihood that the sample would be representative. However, if the sample was obtained through convenience sampling or if it disproportionately represents certain political affiliations or demographics, it may not be representative of the entire population of citizens in the state.
To assess the representativeness of the sample, it is important to consider factors such as the sampling method, sample size, diversity of the sample, and the specific characteristics being studied.
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Molly has a rectangular piece of cardboard. If the length of the cardboard can be modeled by 3x - 1 and the width of the cardboard can be modeled by 2x + 5, which polynomial models the area of her piece of cardboard? *
The polynomial that models the area of Molly's cardboard is 6x^2 + 13x - 5.
How can the area of Molly's cardboard be modeled with a polynomial?
First, we were given that the length of the cardboard can be modeled by 3x - 1 and the width can be modeled by 2x + 5. To find the area, we use the formula:
Area = length x width
So, we substitute the expressions for the length and width:
Area = (3x - 1) x (2x + 5)
Next, we use the distributive property of multiplication to expand the expression:
Area =[tex]6x^2 + 15x - 2x - 5[/tex]
Simplifying, we get:
Area = [tex]6x^2 + 13x - 5[/tex]
Therefore, the polynomial that models the area of Molly's piece of cardboard is [tex]6x^2 + 13x - 5.[/tex]
This polynomial gives us a way to calculate the area of the cardboard for any value of x. For example, if we know that the length of the cardboard is 5 units, we can substitute x = 2 into the polynomial to find the area:
Area =[tex]6x^2 + 13x - 5[/tex]
Area =[tex]6(2)^2 + 13(2) - 5[/tex]
Area = 24 + 26 - 5
Area = 45
So, the area of the cardboard when x = 2 (and the length is 3x - 1 = 5) is 45 square units.
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If there were eight equal pieces and seven of them were gone how many would there be in angle measurement
If there were eight equal pieces and seven of them were gone, there would be 45 degrees in angle measurement.
When the circle is divided into eight equal pieces, each piece has an angle of 360°/8 = 45°. If seven of these pieces are gone, only one piece is remaining, which is equivalent to 45 degrees in angle measurement. Therefore, the answer is 45 degrees.
Alternatively, we can use the formula for finding the angle of a sector of a circle. The formula is given as Angle = (θ/360) x 2πr, where θ is the central angle in degrees, and r is the radius of the circle. In this case, the radius of the circle is not given, but we know that there were eight equal pieces initially.
Therefore, the central angle for one piece is 360°/8 = 45°. So, the angle of the remaining piece is (45/360) x 2πr = (1/8) x 2πr = π/4 radians or 45 degrees.
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The function R = 73. 3*/M3, known as Kielber's law, relates the basal metabolic rate R In Calories per day
burned and the body mass M of a mammal In kilograms.
a. Find the basal metabolic rate for a 180 kilogram lion. Then find the formula's prediction for a 80
kilogram human. If necessary round down to the nearest 50 Calories.
b. Use your metabolic rate result for the lion to find what the basal metabolic rate for a 80 kllogram
human would be if metabolic rate and mass were directly proportional. Compare the result to the result
from part a.
a. Kleiber's law for lion
Calories
Kleiber's law for humans
Calories
b. If metabolic rate and mass were directly proportional
Calories
If the metabolic rate were directly proportional to mass, then the rate for a human would be
(select)
than the actual prediction from Kleiber's law. Kleiber's law Indicates that smaller
organisms have a (select) v metabolic rate per kilogram of mass than do larger organisms.
The basal metabolic rate for a 180-kilogram lion is approximately 766.4 Calories per day.
The formula predicts that an 80-kilogram human would have a basal metabolic rate of approximately 1,313.9 Calories per day.
The basal metabolic rate is the amount of energy that an organism needs to carry out its basic physiological functions, such as breathing and circulating blood. In this case, Kielber's law is expressed as:
R = 73 [tex]\sqrt[4]{M^3}[/tex]
Let's use this function to find the basal metabolic rate for a 180-kilogram lion. To do this, we simply substitute M = 180 into the equation and solve for R:
R = 73 [tex]\sqrt[4]{180^3}[/tex]
R = 73 [tex]\sqrt[4]{5832}[/tex]
R ≈ 766.4
Now, let's find the formula's prediction for an 80-kilogram human. Again, we simply substitute M = 80 into the equation and solve for R:
R = 73[tex]\sqrt[4]{80^3}[/tex]
R = 73[tex]\sqrt[4]{512}[/tex]
R ≈ 1,313.9
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Complete Question:
The function R = 73 [tex]\sqrt[4]{M^3}[/tex], known as Kielber's law, relates the basal metabolic rate R In Calories per day burned and the body mass M of a mammal In kilograms.
Find the basal metabolic rate for a 180-kilogram lion. Then find the formula's prediction for an 80-kilogram human. If necessary round down to the nearest 50 Calories.
a rectangular prism’s base has an area of 80 square inches and a width of 18 square inches. What is the prism’s height?
The height of the rectangular prism is 4.4 inches
How to determine the areaThe formula for calculating the area of a rectangular prism is expressed with the equation;
A = wh
Such that the parameters of the formula are given as;
A is the area of the rectangular prismw is the width of the rectangular prismh is the height of the rectangular prismFrom the information given, we have that;
Area of the prism = 80 square inches
width of the rectangular prism = 18 square
Now, substitute the value, we have
80 = 18h
Divide both sides by the coefficient of the variable h, we have;
h = 80/18
divide the values
h = 4. 4 inches
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A normal distribution curve, where x = 70 and o = 15,
was created by a teacher using her students' grades.
What information about their performances can be obtained by analyzing the curve?
The normal distribution curve gives useful information regarding the distribution of students' grades, such as the average grade, the dispersion of grades, the likelihood of receiving a specific grade, and the presence of any outliers.
Obtainable Information's from the Distribution Curve?The normal distribution curve generated by the educator offers multiple insights into the distribution of academic achievement among her pupils. The analysis of the curve yields various informative data such as:
The parameter of central tendency for this distribution is represented by the mean, denoted as x=70, signifying that the students' mean grade is at 70.The normal distribution's degree of dispersion is represented by the standard deviation, denoted by o=15 in this context, conveying the extent of variability among grades. In this particular instance, the presence of a higher standard deviation denotes a greater degree of variability in the distribution of grades from the central tendency.Probability theory allows for the utilization of the normal distribution curve to determine the likelihood of a student achieving a particular grade. An illustration of this notion can be depicted by estimating the likelihood of an individual receiving a marks within the range of 55 and 85 through the computation of the region beneath the curve that occupies those particular values.The utilization of the normal distribution in statistical analysis is instrumental in recognizing any possible outliers within the dataset. An outlier refers to a data point that deviates considerably from the rest of the data. In the present scenario, grades whose values extend beyond two standard deviations from the mean, calculated as 70 + 215 = 100 or 70 - 215 = 40, may be considered as outliers.Learn more about distribution curve here: https://brainly.com/question/23418254
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The relative frequency table describes the relationship between students who completed an exam review and their performance on the exam. Passed exam Did not pass exam Row Totals Completed exam review 55% 10% 65% Did not complete exam review 20% 15% 35% Column Totals 75% 25% 100% Part A: What is the percentage of students who passed the exam, given that they completed the exam review? Round to the nearest percentage. (2 points) Part B: What is the percentage of students who passed the exam, given that they did not complete the exam review? Round to the nearest percentage. (2 points) Part C: Is there an association between passing the exam and completing the exam review? Justify your answer. (2 points
The values on the relative frequency table indicates;
Part A; 55%
Part B; 20%
Part C; There is an association between passing the exam and completing the exam review
What is a relative frequency table?The relative frequency table shows the mode of a dataset, from the sample obtained from a population.
The data in the table can be expressed as follows;
[tex]{}[/tex] Passed exam Did not pass exam Row totals
Completed exam review [tex]{}[/tex] 55% 10% 65%
Did not completed exam review[tex]{}[/tex] 20% 15% 35%
Column Total [tex]{}[/tex] 75% 25% 100%
Part A; The above table indicates that the percentage who passed the exam given that they completed the exam review is 55%
Part B; The percentage that passed the exam given that they did not complete exam review is 20%
Part C; The conditional percentages of passing the exam and completing the exam review are very different indicating that there is an association between passing the exam and completing exam review
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Need help with this question
Answer:
11
Step-by-step explanation:
23-12=11
The perimeter of a semicircle is 35. 98 millimeters. What is the semicircle's radius Use 3. 14 for a. Millimeters Submit explain
If the perimeter of a semicircle is 35. 98 millimeters, 7 mm is the semicircle's radius.
A semi-circle refers to half of the circle. The circle is cut along the diameter to form a semi-circle.
A diameter is a line segment that passes through the center of the circle and touches the boundary of the circle from both ends.
The perimeter of the semi-circle is the sum of the length of the diameter and the circumference of the semi-circle.
P = 2r + πr
where P is the perimeter
r is the radius
P = 35.98 mm
35.96 = 2r + 3.14r
35.96 = 5.14r
r = 7 mm.
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Which is a solution to 2n = 16?
Answer:
3
Step-by-step explanation:
2x2=4
4x2=8
8x2=16
The radius of a circle is 15 ft. Find its area in terms of pi
Answer:
A= 225π ft²
Step-by-step explanation:
A = π r²
A= π 15²
A= 225π ft²
Answer:
706.86
Step-by-step explanation:
1. A=πr^2 : The formula to find the area of a circle.
2. A = π15^2 : Substitute the given radius value into the equation.
3. Insert equation into calculator
706.86 (Rounded to the nearest hundredth)
Please help it would be amazing if you knew this
The solution of the function (f - g)(x) is 17x + 7.
How to solve composite function?A function relates input and output. A composite function is generally a function that is written inside another function.
Therefore, let's solve the composite function as follows:
f(x) = 10x + 3
g(x) = -7x - 4
Therefore, let's find (f - g)(x)
Hence,
(f - g)(x) = f(x) - g(x)
Therefore,
f(x) - g(x) = 10x + 3 - (-7x - 4)
f(x) - g(x) = 10x + 3 + 7x + 4
f(x) - g(x) = 17x + 7
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A phone company set the following rate schedule for an m-minute call from any of its pay phones.what is the cost of a call that is under six minutes?
For calls that are 6 minutes less, the rate is $0.70 per minute.
To find the cost of a call that is under 6 minutes, we simply need to use the first part of the rate schedule.
Let's say the call lasts for m minutes. Since m is less than or equal to 6, we can use the first part of the rate schedule, which gives us
c(m) = $0.70 per minute
So the cost of the call is simply the rate per minute times the number of minutes
c(m) = $0.70 × m
For example, if the call lasted 4 minutes, the cost would be
c(4) = $0.70 × 4 = $2.80
Therefore, the cost of a call that is under 6 minutes is simply $0.70 per minute.
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--The given question is incomplete, the complete question is given
" A phone company set the following rate schedule for an m-minute call from any of its pay phones.
c(m)=
{0.70 when m≤6
0.70+0.24(m−6) when m>6 and m is an integer
0.70+0.24([m−6]+1) when m>6 and m is not an integer }
what is the cost of a call that is under six minutes?"--
3.
Noah is playing a game where he must spin two wheels, each with 9 equal slices. There are 3 red slices, 3 green slices, 2 blue slices and 1 yellow slice on each wheel. If Noah spins and lands on a yellow slice on both wheels he wins, but if he lands on any other color, he loses. This information was used to create the following area model.
Is this a fair game? Why or why not?
No, the game is not fair because Noah does not have equal probabilities of winning or losing.
No, the game is not fair because Noah has equal probabilities of winning or losing.
Yes, the game is fair because Noah has equal probabilities of winning or losing.
Yes, the game is fair because Noah does not have equal probabilities of winning or losing
The answer to whether it is this a fair game is: No, the game is not fair because Noah does not have equal probabilities of winning or losing. Therefore, the correct option is 1.
The reason why it is not a fair game is as follows.
There are 9 slices on each wheel, so the total possible outcomes when spinning both wheels are 9 x 9 = 81.To win, Noah needs to land on a yellow slice on both wheels. There's only 1 yellow slice on each wheel, so the probability of this happening is 1/9 (for the first wheel) multiplied by 1/9 (for the second wheel), which is 1/81.The probability of losing is the opposite, meaning he doesn't land on a yellow slice on either wheel. The probability of not landing on a yellow slice on one wheel is 8/9. So, the probability of losing is 8/9 (for the first wheel) multiplied by 8/9 (for the second wheel), which is 64/81.Since the probabilities of winning and losing are not equal (1/81 vs 64/81), the game is not fair. Therefore, the correct answer is option 1.
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Sketch the region enclosed by x + y² = 2 and x + y = 0. Decide whether to integrate with respect to x or y, and then find the area of the region. The area is ...
The area of the region enclosed by x + y² = 2 and x + y = 0 is 4/3 + 4√2/3 square units.
How to find limits of integration?To find the limits of integration, we need to solve for the intersection points of the two curves.
x + y² = 2x + y = 0Substituting x = -y from the second equation into the first equation, we get:
(-y) + y² = 2y² - y + 2 = 0Using the quadratic formula, we get:
y = [1 ± √(1 - 8)]/2y = [1 ± i√7]/2Since we're dealing with a real-valued area, we can discard the complex solution. The two intersection points are:
(-1 - √2, 1 + √2)(-1 + √2, 1 - √2)We can see from the graph below that the region we're interested in is the one enclosed by the curves, which lies to the left of the y-axis.
The limits of integration for the area are y = 0 (the x-axis) and y = 1 + √2.
Since the curves intersect at right angles, we can integrate with respect to either x or y. However, since the region is easier to express in terms of y, we'll integrate with respect to y.
The equation for the curve x + y² = 2 can be rearranged as:
x = 2 - y²The area of the region is given by:
A = ∫[0, 1+√2] (2 - y²) dyA = 2y - (1/3)y³ |[0, 1+√2]A = 2(1+√2) - (1/3)(1+√2)³ - 0A = 2(1+√2) - (1/3)(3+2√2)A = 4/3 + 4√2/3Learn more about Limits of integration
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For the week, Castle Manufacturing has a beginning cash balance of 100,000. They spend 99,000 on direct materials, 19,000 on direct labor, and 29,000 on manufacturing overhead. They also have cash sales of 10,000, accounts receivable collections of 220,000 and asset sales of 30,000. They also purchased assets in the amount of 20,000 and had sales commissions and other administrative expenses in the amount of 40,000. What was Castle Manufacturing cash balance at the end of the week?
Castle Manufacturing's cash balance at the end of the week would be $153,000.
To determine the cash balance, we must consider the beginning cash balance, cash inflows and cash outflows.
Beginning cash balance: $100,000
Cash inflows:
- Cash sales: $10,000
- Accounts receivable collections: $220,000
- Asset sales: $30,000
Total cash inflows: $260,000
Cash outflows:
- Direct materials: $99,000
- Direct labor: $19,000
- Manufacturing overhead: $29,000
- Purchase of assets: $20,000
- Sales commissions and administrative expenses: $40,000
Total cash outflows: $207,000
Ending cash balance: Beginning cash balance + Total cash inflows - Total cash outflows
= $100,000 + $260,000 - $207,000
= $153,000
Therefore, Castle Manufacturing's cash balance at the end of the week would be $153,000.
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which function is shown in the graph below
Answer: y=log 3 x
Step-by-step explanation:
A cable hangs between two poles 12 yards apart. The cable forms a catenary that can be modeled
by the equation y = 12 cosh(x/12) - 5 between x =- 6 and x = 6. Find the area under the
12 catenary.
Round your answer to four decimal places.
The area under the catenary between the two poles is approximately 51.3224 square yards.
To find the area under the catenary between two poles 12 yards apart, with the equation y = 12cosh(x/12) - 5 between x = -6 and x = 6.
We can find the area by using integration.
The equation for the catenary.
y = 12cosh(x/12) - 5
Set up the integral to find the area under the curve between x = -6 and x = 6.
Area = ∫ (-6 to 6)[12cosh(x/12) - 5]dx
Integrate the function with respect to x.
Since we are dealing with the hyperbolic cosine function, we know that the integral of cosh(x/12) is 12sinh(x/12).
Therefore, the integral becomes:
Area = [12 (12sinh(x/12)) - 5x] evaluated from -6 to 6
Evaluate the integral at the bounds.
At x = 6: 12 (12sinh(6/12)) - 5(6) = 12 (12sinh(0.5)) - 30
At x = -6: 12 (12sinh(-6/12)) - 5(-6) = 12 (12sinh(-0.5)) + 30
Subtract the lower bound result from the upper bound result.
Area = [12(12sinh(0.5)) - 30] - [12(12sinh(-0.5)) + 30]
Calculate the numerical values and round to four decimal places.
Area = 51.3224
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Quadrilateral abcd is inscribed in this circle.
find the measure of angle a and angle b if
m&c = 121-and m&d=93°
а
d
b.
121°
с
The measure of angle a is 59 degrees and the measure of angle b is 87 degrees. Based on the information given, we know that angles a and b are opposite angles of the quadrilateral abcd,
So they are supplementary (their sum is 180 degrees).
We also know that angles c and d are opposite angles of the quadrilateral abcd, and they are given in the problem. Using the fact that angles on the same side of a chord are equal, we can say that angles a and d are equal, and angles b and c are equal.
Therefore, we can set up the following equation:
a + d = 180 (because they are supplementary)
d = 121
a = d (because they are opposite angles of the quadrilateral)
b = c (because they are opposite angles of the quadrilateral)
c + d = 180 (because they are supplementary)
c = 93
Substituting the known values, we get:
a + 121 = 180
a = 59
b + 93 = 180
b = 87
Therefore, the measure of angle a is 59 degrees and the measure of angle b is 87 degrees.
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please help!
Given YZ tangent to ⊙J at point Y and m∠WYZ = 104, what is mWXY?
The measure of the angle WXY is 152 degrees
Calculating the measure of the angle WXY?From the question, we have the following parameters that can be used in our computation:
Line segment YZ tangent to J at point Y The measure of m∠WYZ = 104,Using the above as a guide, we have the following:
m∠MYW = 104 - 90
m∠MYW = 14
The inscribed angle opposite to the same arc is half of the external angle
So, we have
mw = 2 * m∠MYW
mw = 2 * 14
mw = 28 degrees
Also, we have
my = 180 degrees
So, we have
Angle WXY = 180 - 28
Evaluate the difference
Angle WXY = 152
Hence, the measure of the angle is 152 degrees
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