Find the area of the shaded region between x=y^(2)-7 y=1 x=e^y y=-1
Answers
The area of the shaded region between x=y^(2)-7 y=1 x=e^y y=-1 is e + 1/e + 12 square units.
To find the area shaded region, we need to first graph the curves and determine the boundaries of the region.
The given equations are:
x = y^2 - 7 (equation 1)
y = 1 (equation 2)
x = e^y (equation 3)
y = -1 (equation 4)
From equation 2, we know that the line y = 1 is a horizontal line passing through (0, 1).
From equation 4, we know that the line y = -1 is a horizontal line passing through (0, -1).
To graph equation 1, we can rewrite it as x + 7 = y^2 and complete the square:
x + 7 = (y - 0)^2 + 0
(y - 0)^2 = x + 7
This is the equation of a parabola with vertex at (-7, 0) and axis of symmetry parallel to the y-axis. Since the parabola opens to the right, we only need to graph the part of the parabola to the right of the vertex.
To graph equation 3, we note that e^y is always positive, so the curve will be to the right of the y-axis. Also, since e^y increases rapidly as y increases, the curve will approach the x-axis asymptotically.
The shaded region is bounded by the curves x = y^2 - 7, x = e^y, y = 1, and y = -1. We can find the boundaries of the region by finding the intersection points of the curves.
To find the intersection of equations 1 and 2, we substitute y = 1 into equation 1:
x = 1^2 - 7 = -6
So the point of intersection is (-6, 1).
To find the intersection of equations 1 and 4, we substitute y = -1 into equation 1:
x = (-1)^2 - 7 = -6
So the point of intersection is also (-6, -1).
To find the intersection of equations 2 and 3, we substitute y = 1 into equation 3:
x = e^1 = e
So the point of intersection is (e, 1).
Therefore, the boundaries of the shaded region are x = -6, x = e, and the curves y = 1 and y = -1.
We can now set up the integral to find the area of the shaded region:
A = ∫[-1,1] ∫[-6,e^y] dx dy
Integrating with respect to x first, we have:
A = ∫[-1,1] (e^y + 6) dy
Integrating with respect to y, we have:
A = [e^y + 6y]_[-1,1]
A = (e + 6) - (1/e + (-6))
A = e + 6 + 1/e + 6
A = e + 1/e + 12
Therefore, the area of the shaded region is e + 1/e + 12 square units.
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Related Questions
промінь ділить розгорнутий кут на два кути. знайди ці кути, якщо один з них на 20градусів більший за другий
Answers
Answer:
write it in English so I can understand
QuestionReflect (4,5) in the x-axis followed by the y-axis. QuestionReflect (4,5) in the x-axis followed by the y-axis
Answers
The resulting reflection will be (4,-5) and will be followed by (-4,-5).
What is coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space. The ordinate is the distance of a point from the x-axis scaled with the y-axis. Coordinates are the abscissa and ordinate combined. A series of data indicating a precise position. On graphs, it is typically represented by a pair of numbers: the first number represents the distance along, while the second number represents the distance up or down. For instance, the point (12,5) is 12 units long and 5 units high.
Here,
given coordinates=(4,5)
Firstly, reflecting across x axis, point (x,y) turns to (x, -y).
=(4,-5)
Secondly, reflecting (x,-y) across y-axis, point (x,-y) turns to (-x,-y).
=(-4,-5)
The resultant reflection will lead (4,-5) followed by (-4,-5).
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Can someone answer this
Answers
Answer:
16
Step-by-step explanation:
g(x)=-5x+1
g(-3)
x=-3
-5(-3) +1
15+1
16
Answer:
See below.
Step-by-step explanation:
For this problem, we are asked to find the value of g(-3).
We are given a Linear Function.
What is a Linear Function?A Linear Function is a Polynomial Function that is commonly graphed. This function most of the time will simply be represented as a straight line when graphed.
For this problem;
\(g(x)=-5x+1 \ Find \ g(-3).\)
We simply need to substitute -3 in for x.
\(g(-3)=-5(-3)+1\)
Simplify:
\(g(-3)=16.\)
Our final answer is g(-3) = 16.
Here are the first four terms of an arithmetic sequence 6 10 14 18 write an expression in terms of n for the nth term of this sequence
Answers
Answer:r:4(n-1) + 6 Step-by-step explanation:So, as you can see, the sequence seems to be increasing by 4 each time.So, start by finding n = 0.
Step-by-step explanation: Write an expression , in terms of n, for the nth term of this sequence. The nth term of a different arithmetic sequence in 3n + 5. (b) is 108 a term of this ...
I-Ready Solve Problems with Percent - Instruction - Level F • Noah is taking an online survey. After answering 16 questions, he has completed 80% of the survey. Noah wants to know the total the survey. What is the unknown in the problem? ) the total number of questions on the survey, t 16 = 80% t Write the percent as a rate per 100. 16 t 100
Answers
20 questions make up the entire survey. With regard to those facts, Noah has responded to 16 out of the total of 80 questions.
Suppose there are x total questions.
Now, 80% of x=16
\(\frac{80}{100}\) × \(x = 16\) (The word 'of' means multiplication)
0.8x=16
x = \(\frac{16}{0.8}\)
x=20
So, a survey has a total of 20 questions.
To determine the percentage, divide the value by the total value and divide the outcome by 100. The percentage is determined by employing the equation (value/total value)100%.
The value of either a number out of 100 is what is known as that of the percentage of that number. To use the equation (part/whole) 100, it is determined. 26 boys and 24 girls, for instance, make up a class. In those other words, 52 boys out of 100 make up 52% of the class, or 26/(26+24) 100 = 26/50 100.
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provide an appropriate response. the mean age of professors at a university is greater than 58.3 years. if a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
Answers
If a hypothesis test is performed on the mean age of professors at a university and the decision rejects the null hypothesis, it provides evidence to support the alternative hypothesis
If a hypothesis test is performed and the decision rejects the null hypothesis, it means that the evidence provided by the data supports the alternative hypothesis.
In the context of the mean age of professors at a university being greater than 58.3 years, rejecting the null hypothesis suggests that there is sufficient evidence to conclude that the mean age of professors is indeed greater than 58.3 years.
It indicates a statistically significant result and supports the claim that the mean age is higher than the specified value.
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Which answer best describes the system of equations shown in the graph?
A. NoSolution. B. One Solution
C. Infinitely Many Solutions
Answers
I NEED HELP ASAPPP NO LINKS PLSS
Answers
Answer:
heyy! im reaaally sorry if its wrong but I think its c, f, d
brainliest? :)
Step-by-step explanation:
Answer:
7= D
8= F
9= C
Step-by-step explanation:
7. x - 3 \(\leq\) 7
+3 +3
x \(\leq\) 10
8. 3b < 18
/3 /3
b < 6
9. \(\frac{y}{3}\) > 9
*3 *3
y > 27
10- 12 I am so sorry, but I don't understand these functions lol
Answer the following questions about group G with order 77. (1) Show that there are normal subgroups H and K of the group with order 7 and 11, respectively. (2) Show that HK={hk|h=H, kEK) is an Abelian subgroup of group G. (3) Show that HK-G. (4) Show that G is a cyclic group.
Answers
To answer the questions about group G with order 77: (1) Show that there are normal subgroups H and K of the group with order 7 and 11, respectively.
Since the order of G is 77, by the Sylow theorems, there exist Sylow 7-subgroups and Sylow 11-subgroups in G.
Let H be a Sylow 7-subgroup of G and K be a Sylow 11-subgroup of G. Since Sylow subgroups are conjugate to each other, H and K are both normal subgroups of G.
(2) Show that HK={hk|h∈H, k∈K} is an Abelian subgroup of group G.
Since H and K are normal subgroups of G, we have that HK is a subgroup of G. To show that HK is an Abelian subgroup, we need to prove that for any elements hk and h'k' in HK, their product is commutative.
Let hk and h'k' be arbitrary elements in HK. Since H and K are normal subgroups, we have that h'khk' = kh'h. Thus, the product hk h'k' is equal to kh'h, which implies that HK is an Abelian subgroup.
(3) Show that HK=G.
To show that HK=G, we need to prove that every element g in G can be expressed as a product hk, where h∈H and k∈K.
Since H and K are normal subgroups of G, their intersection H∩K is also a normal subgroup of G. By Lagrange's theorem, the order of H∩K divides both the order of H (which is 7) and the order of K (which is 11). Since 7 and 11 are coprime, the only possible order for the intersection is 1.
Thus, H∩K={e}, where e is the identity element of G. This implies that every element g in G can be uniquely expressed as g = hk, where h∈H and k∈K. Therefore, HK=G.
(4) Show that G is a cyclic group.
Since HK=G, and HK is an Abelian subgroup, we have that G is an Abelian group. Every Abelian group of prime order is cyclic. Since the order of G is 77, which is not prime, G cannot be cyclic.
Therefore, G is not a cyclic group.
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To answer the questions about group G with order 77: (1) Show that there are normal subgroups H and K of the group with order 7 and 11, respectively.
Since the order of G is 77, by the Sylow theorems, there exist Sylow 7-subgroups and Sylow 11-subgroups in G.
Let H be a Sylow 7-subgroup of G and K be a Sylow 11-subgroup of G. Since Sylow subgroups are conjugate to each other, H and K are both normal subgroups of G.
(2) Show that HK={hk|h∈H, k∈K} is an Abelian subgroup of group G.
Since H and K are normal subgroups of G, we have that HK is a subgroup of G. To show that HK is an Abelian subgroup, we need to prove that for any elements hk and h'k' in HK, their product is commutative.
Let hk and h'k' be arbitrary elements in HK. Since H and K are normal subgroups, we have that h'khk' = kh'h. Thus, the product hk h'k' is equal to kh'h, which implies that HK is an Abelian subgroup.
(3) Show that HK=G.
To show that HK=G, we need to prove that every element g in G can be expressed as a product hk, where h∈H and k∈K.
Since H and K are normal subgroups of G, their intersection H∩K is also a normal subgroup of G. By Lagrange's theorem, the order of H∩K divides both the order of H (which is 7) and the order of K (which is 11). Since 7 and 11 are coprime, the only possible order for the intersection is 1.
Thus, H∩K={e}, where e is the identity element of G. This implies that every element g in G can be uniquely expressed as g = hk, where h∈H and k∈K. Therefore, HK=G.
(4) Show that G is a cyclic group.
Since HK=G, and HK is an Abelian subgroup, we have that G is an Abelian group. Every Abelian group of prime order is cyclic. Since the order of G is 77, which is not prime, G cannot be cyclic.
Therefore, G is not a cyclic group.
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using 2 jugs of size 100 and 98 gallons, can we measure 3 gallons of water? why? can we measure 4 gallons of water?
Answers
No, we cannot measure 3 gallons of water using 2 jugs of size 100 and 98 gallons. But, we can measure 4 gallons of water using these jugs.
Let's call the two jugs A and B, with A being the 100-gallon jug and B being the 98-gallon jug.
To measure 3 gallons of water, we need to have one jug that is smaller than 3 gallons and another jug that is larger than 3 gallons.
However, both of these jugs are larger than 3 gallons.
This means that it is impossible to measure 3 gallons of water using these jugs.
To measure 4 gallons of water, we can follow these steps:
Fill jug A to the top with water.
Pour the water from jug A into jug B until jug B is full.
This will leave 2 gallons of water in jug A.
Pour the water from jug B down the drain, then pour the 2 gallons from jug A into jug B.
Fill jug A to the top with water.
Pour the water from jug A into jug B until jug B is full.
This will leave 96 gallons of water in jug B, with 4 gallons of water in jug A.
Thus, we can measure 4 gallons of water using these jugs.
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Which of the following statements is true? Los enlaces sencillos se forman compartiendo dos electrones Single bonds are made by sharing two electrons. Un enlace covalente se forma a través de la transferencia de electrones de un átomo a otro. A covalent bond is formed through the transfer of electrons from one atom to another. No es posible que dos átomos compartan más de dos electrones, formando enlaces multiples. It is not possible for two atoms to share more than two electrons, in a multiple bond. Un par de electrones involucrados en un enlace covalente a veces se conocen como "pares solitarios A pair of electrons involved in a covalent bond are sometimes referred to as "lone pairs."
Answers
The statement "Single bonds are made by sharing two electrons" is true.
In a covalent bond, atoms share electrons to achieve a stable electron configuration. A single bond is formed when two atoms share a pair of electrons. This means that each atom contributes one electron to the shared pair, resulting in a total of two electrons being shared between the atoms.
The statement "A covalent bond is formed through the transfer of electrons from one atom to another" is false. In a covalent bond, there is no transfer of electrons between atoms. Instead, the electrons are shared.
The statement "It is not possible for two atoms to share more than two electrons, in a multiple bond" is also false. In a multiple bond, such as a double or triple bond, atoms can share more than two electrons. In a double bond, two pairs of electrons are shared (four electrons in total), and in a triple bond, three pairs of electrons are shared (six electrons in total).
The statement "A pair of electrons involved in a covalent bond are sometimes referred to as 'lone pairs'" is true. In a covalent bond, there are two types of electron pairs: bonding pairs, which are involved in the formation of the bond, and lone pairs, which are not involved in bonding and are localized on one atom. These lone pairs play a role in the shape and properties of molecules.
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Goal: Gather and organize statistical data in frequency distribution table.
Role: Statistician, Data Analyst
Audience: Math Teacher, Adviser
Situation: Your Math Teacher asked your class to conduct a simple survey to
determine the number of learners who are using gadgets in your school.
Product/ Performance:
You were asked to look for at least 15 individuals among your friends within
your school and construct a frequency distribution table on each category:
A. gender
B. preferred distance learning modality (online, modular, blended)
C. available gadget used in distance learning (smartphone, laptop,
tablet, desktop, or none)
I'm looking for a serious answer. I need to pass this on monday. Thank you.
Answers
Frequency distribution tables are a tool for organizing data and obtaining additional information.
What is the frequency distribution?The frequency distribution is a term to refer to a type of tables that are used in the area of statistics to organize data.
In the frequency distribution tables, the different variables are arranged by rows. The columns show the number of occurrences for each value, percentages, among others. These types of tables are an ideal tool to analyze data and obtain specific information.
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A ∆ has Č = 90°, Â = 26° and = 30, Find the Angle BC, Side AB and BC.
Answers
Answer:
B = 64°
AB = 33.378
BC = 14.632
Step-by-step explanation:
Given the right angled triangle ;
Angle B = 180 - (90 + 26) (sum of angles in a triangle)
Angle B = 180 - 116
Angle B = 64°
Side AB = c
Using trigonometry :
Sin B = opposite / hypotenus
Sin 64 = 30/AB
AB = 30 / Sin64
AB = 33.378
Side BC ;
Sin A = BC / AB
Sin 26 = BC / 33.378
BC = 33.378 * Sin 26
BC = 14.632
professor doner asked you to interpret a gamma of 1.3. you told doner: group of answer choices it indicated a positive relationship. it indicated an exceedingly strong relationship. it indicated a moderate relationship. it indicated an error in calculations
Answers
The correct option told to Doner is (D) it indicated an error in calculations.
Gamma is a metric of association for variables with ordinal values. Gamma lies between -1.00 and 1.00. Once more, a Gamma of 0.00 indicates there is no correlation, a Gamma of 1.00 indicates a perfect positive relationship between the variables, and a Gamma of -1.00 indicates a perfect perfect negative relationship.
Use the measure of association from the lowest level of measurement whenever there are different levels of measurement. Use lambda, for instance, if you are analyzing a nominal and ordinal variable. Use gamma when analyzing an ordinal and scale pair.
Hence, gamma lies between -1 to 1.
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Can someone please help with this question? I’ll give brainliest
Answers
Answer:
1,and 4
Step-by-step explanation:
Answer:
the first one
Step-by-step explanation:
Because an expression to be equivalent they should both have same sign and Variables
if his conclusion is correct, which substance could he have been observing and why?
Answers
Answer:
The answer is B, baking soda and vinegar.
Original price
$7.00
Markdown
55%
•$3.15
•$3.40
•$3.55
•none of above
Help please and no links
Answers
What is the x-coordinate of the solution to the system of equations?
3x + 5y = 10
1x + 5y = 2
Answers
Answer:
x = 4
Step-by-step explanation:
Use elimination method.
-----------------
3x + 5y = 10
-(1x + 5y) = -1(2)
-1x -5y = -2
------Simiplify------
2x = 8
x = 4
Write an equation in point-slope form for the given point and slope: (-3, 6) and slope 8
Answers
y-y0=m(x-x0)
y+6=8(x-3)
How can you tell from the prime factorization of the of two numbers if their LCM is the product of the two numbers
Answers
To determine if the LCM of two numbers is the product of the two numbers using their prime factorization, you need to check if the numbers are coprime.
Coprime numbers have no common prime factors except for 1. If the numbers are coprime, their LCM will be equal to the product of the two numbers.
To tell if the LCM of two numbers is the product of the two numbers, you need to compare the prime factorization of the two numbers. If the prime factors of both numbers are unique (meaning they do not share any common factors), then the LCM will be the product of the two numbers. However, if the two numbers share some common prime factors, then the LCM will have to include those factors at their highest power. So, to find the LCM of the two numbers, you need to take the highest power of each prime factor that appears in either number and multiply them together. If the product of these highest powers matches the product of the two numbers, then the LCM is equal to the product of the two numbers.
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El peso de un objeto en le polo norte es 0.53% mayor que en el ecuador.cuanto pesa en el polo norte un objeto de 50 libras en el ecuador?
Answers
Answer:
Step-by-step explanation:
el awnser es 0.265 libras mas
if one root is the square of the other in the equation 8+mx+27x²=0,find the value of m
Answers
Answer:
The value of \(m\) is -30.
Step-by-step explanation:
Let \(27\cdot x^{2}+m\cdot x +8 = 0\), we notice that expression is a second order polynomials. We can rearrange the polynomial and use factorization to calculate all roots:
\(x^{2}+\frac{m}{27}\cdot x + \frac{8}{27} = 0\) (1)
\(-x^{2}-x = \frac{m}{27}\) (2)
\(x^{3} = \frac{8}{27}\) (3)
From (3) we find the least root:
\(x = \sqrt [3]{\frac{8}{27}}\)
\(x = \frac{2}{3}\)
By (2) we have the value of \(m\):
\(m = -27\cdot (x^{2}+x)\)
\(m = -30\)
A gardening store ordered 657,230 potted plants last year. This year, the store ordered 10% fewer potted plants. How many potted plants were ordered this year?
Answers
Potted plants ordered last year = 6,57,230 (Indian Place Value System)
Pecentage of plants deducted = 10%
10% of 6,57,230 = 10/100 × 6,57,230
or, it can also be written as -
10/10 × 65,723
or,
65,723
Therefore, potted plants odered this year is 65,723
By the way, I'm an Indian : )
a freight train left a station at 12 noon g . 4. , o~g north at a rate of 50 miles per hour. at 1:00 p.m. a passenger train left the same station, going south at a rate of 60 miles per hour. at what time were the trains 380 miles apart?
Answers
The trains will be 380 miles apart at 3:00 PM, which is 4 hours after the freight train leaves the station at 12 noon.
How to solve the problem for distance and time?We can use the formula d = rt (distance = rate x time) to calculate the distance each train has traveled during this time:
Let's call the time elapsed from 12 noon until the trains meet as t hours.
During this time, the freight train has traveled at a rate of 50 mph for t hours and the passenger train has traveled at a rate of 60 mph for (t-1) hours (since it started one hour after the freight train).
Distance traveled by freight train = 50t
Distance traveled by passenger train = 60(t-1)
The total distance between the two trains at time t is the sum of these distances, which we can write as:
Total distance = 50t + 60(t-1)
We want to find the time t at which the total distance is 380 miles. So we can set up the equation:
50t + 60(t-1) = 380
Simplifying this equation, we get:
110t - 60 = 380
110t = 440
t = 4
Therefore, the time elapsed from 12 noon until the trains meet is 4 hours. Since the passenger train left one hour after the freight train, it has been traveling for 3 hours.
So the time at which the trains are 380 miles apart is 3:00 PM (12 noon + 4 hours).
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An exterior angle of a triangle is 124°. If the non-adjacent angles are congruent, then what are the measures of all of the interior angles of the triangle?
Answers
Answer:
62 degrees
Step-by-step explanation:
Let x be the measure of each non-adjacent interior angle.
By the remote interior angle theorem, the two angles mentioned add up to the exterior angle 124
x+x = 124
2x = 124
2x/2 = 124/2
x = 62
So we have two interior angles of 62 degrees each. The third interior angle is 180-124 = 56 degrees. You can also find this by solving x+x+y = 180 for y Please brainliest
NO LINKS PLSSSSS!!!!! Which of the following equations is linear?
O x^2 + 5 = y
O y=|x|
O y= 2^x
O y=1/3x
Answers
Answer:
Y=1/3x
Step-by-step explanation:
Degree follows linear rule
X+y=150/2
x+y=75 find the solution using cramers rule
Answers
Answer:
I didn’t know if I was solving for x or for y but I believe that the answer is x=75-y
Step-by-step explanation:
Solve by simplifying both sides of the equation, then isolating the variable.
Liliana wants to find the area of a polygon. First, she breaks apart the polygon into two trapezoids. What is Liliana's next step?
Answers
Liliana's next step is to find the area of each of the two trapezoids.
How to determine her next stepFrom the question, we have the following parameters that can be used in our computation:
Liliana wants to find the area of a polygon. First, she breaks apart the polygon into two trapezoids.Given that she has broken the polygon into two trapezoids, the next step ti so calculate the area of each trapezoid
This is done using
Area = 1/2 * (sum of parallel sides) * height
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Nelda baked two kinds of pasta in pans. Each pan was the same size. She sliced one pan of pasta into 4 equal pieces. She sliced the other pan into 6 equal pieces. How can the pans of pasta now be sliced so that both pans have the same-sized pieces? If Nelda has served 8 pieces from 1 pan so far, what fraction of 1 pan has she served?
Answers
Answer:
6 equal parts; 8 equal parts
Both those will go into 24.
Step-by-step explanation: Each of six slices of the first pasta has the area 1%2F6 of the entire pan.
Each of eight slices of the second pasta has the area 1%2F8 of the original pan.
Nelda will cut each 1%2F6 in 4 equal pieces to get 1%2F24.
She also will cut each 1%2F8 in 3 equal pieces to get 1%2F24.
Guys I need help on this please
Answers
Answer:
The correct answer should be the first option.
Step-by-step explanation:
Answer:
First option. The graphs domain is -∞<x<∞ and its range is -5 ≤ y < ∞
Step-by-step explanation:
I graphed this function
Domain: x ∈ R
Range: y ∈ [-5, + ∞
Minimum (1, -5)
Verticle intercept (0, -4)