We have to find solutions for the given differential equation when
y = 0, y = 1/(k-x) and y(a) = b using ordinary differential equations.
We have dy / dx = y^2
a. let's define the given y = 1/(k-x)
derive the above equation with respect to x :
dy / dx = y' = 1/(k-x)^2
So this is the general solution.
b) We would want a singular solution that is not included in the general form. Here we could use y = 0
dy / dx = 0 = 0^2
so,this is a trivial singular solution.
c) If we have y(a) = b,
then, y = 1(k-a) = b
To find the value of k we use the other condition: y'(^2) = 4 x y(2)
1/(k-a)^2 = 4 x 1/(k-a)
k - 2 = 1/4
therefore, k = 9/4
hence we got, y = 1/(9/4 - a) = b
So the points (a, b) are of the form: (a, 1/(9/4 - a))
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The complete question is :
Find a general solution of the differential equation dy/dx=y2
b. Find a singular solution that is not included in the general solution.
c. Inspect a sketch of typical solution curves to determine the points (a,b) for which the initial value problem (y′)2=4y,y(a)=b
find the measurements of the angles
all the mentioned angles have been found.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The sum of all angles of triangle = 180
∠ICA =180-20 =160
∠EAF = 20
∠ICB =180
∠GAF = 120 -20 =100
∠CAB= 180-80=100
∠HAG=180-120 =60
∠CBA=180-120=60
∠HAC.= 20
Hence all the mentioned angles have been found.
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find the y intercepts of the graph shown. (5.6,0) (-3.3,0) (0.4) (-5,0)
A's x- intercept is 3 and y-intercept is 5. Both are favourable.
How can you determine a graph's y-intercept?shown. (5.6,0) (-3.3,0) (0.4) (-5,0) (-5,0)Finding the value of y at x=0 on a graph will reveal the y-intercept. At this location, the graph passes across the y-axis.The slope (m) and the y-intercept (b) of a line are highlighted in the slope-intercept form of linear equations (y=mx+b).I Plotting point A (5.6,0)(0.4) (-5,0) (-5,0)In this instance, A's x-coordinate is 3 and y-coordinate is 5. Both are favourable. As a result, the point A (0.4) is in quadrant I.ate is 3 and y-coordinate is 5. Both are favourable. As a result, the point A (-5,0) is in quadrant I. begin at the beginning. Along the x-axis, move three units to the right. Then, turn, travel parallel to the Y-axis by 5 units, and mark point A.To learn more about y intercepts refer to:
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Please I can't seem to get this. It's really hard
The number of notepads per department used in the Southeast location is given as follows:
6.
How to obtain the number of notepads per department?The number of notepads per department is obtained applying the proportions in the context of this problem, considering the graph.
The number of departments of the Southeast location is given as follows:
6.
Which is given from the table given in the second image for this problem.
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What is a perimeter of a rectangluar drive way measuring 20 feet long and 15 feet wide?
find the unit vector orthogonal to the plane through the points p, q and r which has a positive y-component.
The unit vector orthogonal to the plane can be found by taking the cross product of the vectors p-q and p-r. The vector should have a positive y-component if the cross product points in the positive y direction.
To find a unit vector orthogonal to the plane through the points p, q, and r, with a positive y-component, we will use the cross product of two of the vectors. The cross product of two vectors is a vector perpendicular to both of them. First, we will create vector p-q, which is a vector from point p to point q. We can do this by subtracting the coordinates of point q from the coordinates of point p. Next, we will create vector p-r, which is a vector from point p to point r. We can do this by subtracting the coordinates of point r from the coordinates of point p. Finally, we will take the cross product of the two vectors. This will give us a vector orthogonal to the plane through the three points. If the vector has a positive y-component, then it is the unit vector orthogonal to the plane that we are looking for.
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the school marching band has 328 members. Can the band members march in 8 lines, with an equal numberof band members in each line with no members left over? Explain
Answer:
Yes
Step-by-step explanation:
328/8 = 41
Thus if 41 members are in each line, there should be no members left without a spot and it should be equal all across
Estimate the distance in feet that your car travels on the entrance ramp to a freeway as it accelerates from 30 mph to the freeway speed of 70 mph. During this motion what is the average acceleration of the car?
The Average Acceleration of the car will be 14.67 ft/[tex]s^{2}[/tex].
What is Acceleration?
The rate at which an object's velocity with respect to time changes is referred to as acceleration in mechanics. Any procedure where the velocity varies is referred to as acceleration. There are only two ways to accelerate: changing your speed or changing your direction, or changing both. This is because velocity is both a speed and a direction.
Formula: a = (v(final) - v(initial))/t
In the given formula, it is given that:
v(initial) = 30mph = 44 ft/s
v(final) = 70mph = 102.67 ft/s
t(time) = 4s
Putting these values in our formula, we get:
a(acceleration) = (102.67 - 44)/4
a = 14.67 ft/[tex]s^{2}[/tex].
Therefore as per the given problem, the acceleration of the given car is 14.67 ft/[tex]s^{2}[/tex].
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If Y is a random variable with moment-generating function m(t) and U is given by U = aY + b, a) Show that the moment-generating function of U is e tbm(at). b) If Y has mean µ and variance σ 2 , use the moment-generating function of U to derive the mean and variance of U. c) Suppose that the moment-generating function of a normally distributed random variable, Y , with mean µ and variance σ 2 is m(t) = e µt+(1/2)t 2σ 2 . Derive the moment-generating function of X = −3Y + 4. What is the distribution of X? Why?
a) E(e^(taY)) = m(at), then the moment-generating function of U is e^(tb)m(at).
b) µ is the mean of Y and σ^2 is the variance of Y.
c) the moment-generating function of X =e^((−3µ + 4)t + (9/2)σ^2t^2) and The distribution of X is normal.
a) If Y is a random variable with moment-generating function m(t), and U is given by U = aY + b, then the moment-generating function of U is e^(tb)m(at). This can be shown by using the definition of a moment-generating function:
E(e^(tU)) = E(e^(taY + tb)) = E(e^(taY)e^(tb)) = e^(tb)E(e^(taY))
Since E(e^(taY)) = m(at), then the moment-generating function of U is e^(tb)m(at).
b) To find the mean and variance of U using the moment-generating function, we can take the first and second derivatives of e^(tb)m(at) and set t = 0. The first derivative with respect to t evaluated at t = 0 is:
(d/dt)e^(tb)m(at) = be^(tb)m(at) + ae^(tb)m'(at)
Setting t = 0, we get the mean of U:
E(U) = be^(0)m(a0) + ae^(0)m'(a0) = b + a*(m'(0)) = b + a*µ
Where µ is the mean of Y.
The second derivative of e^(tb)m(at) is:
(d^2/dt^2)e^(tb)m(at) = b^2e^(tb)m(at) + 2abe^(tb)m'(at) + a^2e^(tb)m''(at)
Setting t = 0, we get the variance of U:
Var(U) = b^2e^(0)m(a0) + 2abe^(0)m'(a0) + a^2e^(0)m''(a0) = b^2 + 2ab*(m'(0)) + a^2*(m''(0)) = b^2 + 2abµ + a^2σ^2
Where µ is the mean of Y and σ^2 is the variance of Y.
c) If the moment-generating function of a normally distributed random variable Y with mean µ and variance σ^2 is m(t) = e^(µt + (1/2)t^2σ^2), then the moment-generating function of X = −3Y + 4 is e^((−3µ + 4)t + (1/2)(−3)^2σ^2t^2) = e^((−3µ + 4)t + (9/2)σ^2t^2)
The distribution of X is normal with mean (-3µ + 4) and variance (9/2)σ^2. This can be deduced by the fact that if Y is normally distributed, then a linear transformation of Y (such as X = aY + b) is also normally distributed with mean aµ + b and variance a^2σ^2.
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Find the average of the following set of integers. −20,−54,−93,37,45
The average of given set of integers is -17.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
The given set of integers are -20, -54, -93, 37 and 45.
Here, average = Sum of all the observations/Number of observations
= (-20-54-93+37+45)/5
= -85/5
= -17
Therefore, the average of given set of integers is -17.
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given that 15^5x=8 solve for x
Answer:
Step-by-step explanation:
The value of x for the given expression will be x = 0.1535.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is [tex]15^{5x}=8[/tex]. The expression will be solved as below,
[tex]15^{5x}=8[/tex]
Take log on both the sides and solve for the value of x.
5x = 3log₁₅(2)
x = (3/2)log₁₅(2)
x = 0.1535
Hence, the value of x will be 0.1535.
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Convert 4/15 to a decimal and a percent.
The percentage and decimal values of the given fraction are 26.67% and 0.267 respectively.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given a fraction number 4/15
To convert it into decimals we need to divide 4 by 15
Thus, the Decimal value = 0.2666...
the Decimal value = 0.267
To convert it into a percentage we need to multiply it with 100
So,
The percentage values of the given fraction = 4/15 * 100
The percentage values of the given fraction = 26.67%
Therefore, the percentage and decimal values of the given fraction are 26.67% and 0.267 respectively.
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Can any anyone explain X^3=-125 ?
This is solving polynomial equations.
The value of x in the equation, X^3= -125 is -5.
How do we arrive at the solution for x?To find x in the above polynomial equation, we need to collect like terms and equate the expression to 0. To begin we can arrange the expression this way:
x^3 + 125 = 0
This means that we should find the figure which when multiplied three times would equate to 125. This figure is -5. So, when solved, we have:
-5³ + 125 = 0
-125 +125 = 0
So, the value for x in the equation above is -5.
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Work with a partner. Baby manatees are about 4 feet long at birth. They
grow to a maximum length of 13 feet.
a. Which of the following can represent a baby manatee's growth?
What does x represent? Explain your reasoning.
x + 4 < 13
x + 4 ≤ 13
x-4> 13.
x-4 ≥ 13
An equation which can represent a baby manatee's growth include the following: B. x + 4 ≤ 13.
The variable x represent the baby manatee's growth after birth.
How to write and solve the required inequality?In order to write and solve an inequality that represents a baby manatee's growth, we would take note of the following important information;
The maximum length is equal to 13 feet.Baby manatees are typically about 4 feet long at birth.Let the variable x represent the baby manatee's growth after birth.Now, we can write an inequality that represents the value of x for which a baby manatee's growth as follows;
x + 4 ≤ 13
By subtracting 4 from both sides of the inequality, we have the following:
x + 4 - 4 ≤ 13 - 4
x ≤ 11
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2 x – 3 y = 7 –4 x + y = –5 What is the x -value of the solution to this system of equations?
The value of x which holds true for the given system of equations as required is; x = 4 / 5.
What is the value of x which holds true for the system of equations?It follows from the task content that the value of x which holds true for the given system of equations be determined.
Since the given system is;
2x - 3y = 7........(i)
-4x + y = -5........(ii)
The value of x which holds true for the given system of equations can be determined by making y the subject of the formula in (ii) and substitution into (i) as follows;
y = 4x - 5.
Therefore;
2x - 3 (4x - 5) = 7
2x - 12x + 15 = 7
-10x = -8
x = 4/5
Ultimately, the value of x which holds true for the given system of equations is; x = 4 / 5.
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2 x – 3 y = 7 –4 x + y = –5 Wh
Rewrite this number in appropriate scientific notation:
459,000
Answer:
4.59 × 10^(5)
Step-by-step explanation:
Answer: 4.59 x 10^5
Step-by-step explanation:
If we move the decimal place over 5 times in the answer we get 459,000.
I hope this was able to help you :D
When assessing schedule feasibility, a systems analyst must consider the interaction between time and costs.true or false
True, When assessing schedule feasibility, a systems analyst must consider the interaction between time and costs.
When assessing the viability of scheduling a project, an organisation determines the anticipated completion time. The feasibility analysis assists in identifying any potential obstacles the proposed project may encounter, such as: Internal project constraints, including those related to technology, finances, and resources
The expansion and acceptance of project management training have undergone significant changes over the past few years, and it is projected that these developments will continue and accelerate. And as project management becomes more popular, feasibility studies become more important. It may be exhilarating to begin a difficult, extensive project that will have a significant influence on your organization.
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Consider the following frequency table representing the scores on a test.
Scores on a TestClass Frequency
30–46
10
47–63
3
64–80
13
81–97
12
98–114
12
Step 3 of 5 :
Determine the class width of each class.
The class width of each class is 17.
What is the class width?Class width is the distance between a class's upper and lower bounds (category). It may also refer to one of the following more precisely, depending on the author:
the difference between the upper and lower limits of two (nearby) consecutive classes, or the lowest and higher limits of two classes.
The width of each class in a frequency distribution table must be the same. Due to the fact that you are only working with a single width, this makes calculating the class width relatively simple (as opposed to varying ones).
To find the class width in this, we subtract the lower limits of two consecutive class. i.e.
47 - 30 = 17
64 - 47 = 17
81 - 64 = 17
98 - 81 = 17
So that, The class width of each class is 17.
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the following question is from the four steps of statistical inference. if you respond with a summary of all four steps, you will receive no credit on this problem:
One of the steps in statistical inference, to check the claim is hypothesis testing. In this method, we determine whether to reject or accept the null hypothesis.
Hypothesis testing is the procedure in statistical inference that helps to decide whether the result of the research study supports a particular hypothesis when applied to a population. This helps to test the relationship between two statistical variables.
This includes two types null and alternate hypotheses. If the results say that there is no relationship seen between the two variables, then the null hypothesis is accepted. But if the results so there is a relationship seen between two variables, then an alternate hypothesis is accepted. So to check our claim, we do hypothesis testing.
The complete question is -
The following question is from the four steps of statistical inference. If you respond with a summary of all four steps, you will receive no credit on this problem:
What do we do to check a claim?
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Mathematical 8. PRACTICE Model Math Christy purchased 6.75 pounds of licorice. How much licorice does she need to put in each bag if she divides the total amount into 10 equal-sized bags?
Answer:i think it is yes! this )--89+98
Step-by-step explanation:
ANYONE GOOD IN MATH PLEASE HELP!
Answer: 15
Step-by-step explanation:
The range is the set of all Y values, in this question -8 is the minimum and +7 is the maximum, therefore the range is (-8-7) = -15, but range is not negative so we get 15
32.- The high costs of the California real estate market have caused families who cannot afford to buy larger houses to consider backyard sheds as an expansion option. Many are using their patio structures to build their studios, art rooms, and hobby areas, as well as for additional storage. The median price for a custom-built backyard clapboard frame is $3,100 (Newsweek, September 29, 2003). Assume that the standard deviation is $1,200.
The z-score for a backyard structure costing $2300 is -0.67.
How to calculate the z score?The standard score in statistics is the amount of standard deviations that a raw score deviates from or exceeds the mean of the phenomenon being observed or measured. Standard scores are positive for raw scores above the mean and negative for raw scores below the mean.
The Z-score quantifies the deviation between a given value and the standard deviation. The Z-score, also known as the standard score, indicates how many standard deviations a given data point deviates from the mean. In essence, standard deviation represents the degree of variability present in a given data set.
The z score will be:
= (2300 - 3100) / 1200
= -0.67.
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The high costs in the California real estate market have caused families who cannot afford to buy bigger homes to consider backyard sheds as an alternative form of housing expansion. Many are using the backyard structures for home offices, art studios, and hobby areas as well as for additional storage. The mean price of a customized wooden, shingled backyard structure is $3100 (Newsweek, September 29, 2003). Assume that the standard deviation is $1200.
a. What is the z-score for a backyard structure costing $2300?
The scatterplot shows the relationship between the number of yards allowed by teams in the National Football League and the number of wins for that team in a recent season, along with the least-squares regression line. Computer output is also provided.
2 Calculate and interpret the residual for the Seattle Seahawks, who allowed 4668 yards and won 10 games.
If the residual is negative, it means the observed number of wins is lower than the predicted number of wins, indicating that the team performed worse than expected based on their yards allowed.
What is the interpret the residual for the Seattle sea hawks?The residual for a data point in a regression analysis represents the difference between the observed response (number of wins) and the predicted response (value on the regression line).To calculate the residual for the Seattle Sea hawks, we need to find the value of the regression line at the number of yards allowed (4668), then subtract the observed number of wins (10).Interpretation of the residual: if the residual is positive, it means the observed number of wins is greater than the predicted number of wins, indicating that the team performed better than expected based on their yards allowed. If the residual is negative, it means the observed number of wins is lower than the predicted number of wins, indicating that the team performed worse than expected based on their yards allowed.To learn more about interprets refer:
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The distance between -19 and 12 is
Answer:
The distance between -19 and 12 is 31.
Step-by-step explanation:
write the word sentence as an equation: 5 is one-forth of a number c
(don't solve. just write an equation)
The equation of the word sentence, "5 is one-fourth of a number c" is: 5 = 1/4c.
How to Write a Word Sentence as an Equation?To write a word sentence as an equation, you need to identify the variables and the operations being described in the sentence, and then use mathematical symbols to represent them.
For example, we are given the sentence "5 is one-fourth of a number c,", in this case, the variable is "c" and the operation is "one-fourth of," which is represented by the fraction 1/4 or the multiplication by 1/4.
Therefore, the equation would be:
5 = 1/4c.
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36% of the people did not vote for the candidate. 5400 people voted. How many did not vote for the candidate?
To go on a summer trip, Charlie borrows $700. He makes no payments until the end of 4 years, when he pays off the entire loan. The lender charges simple
interest at an annual rate of 4%.
Answer the following questions. If necessary, refer to the list of financial formulas.
(a) How much total interest will Charlie have to pay?
(b) What will the total repayment amount be (including interest)?
$0
X
Ś
a) The total interest that Charlie, who borrows $700 at a simple interest rate of 4% per annum, will pay after 4 years is $112.
b) The total repayment amount after 4 years, including interest, is $812.
What is simple interest?The simple interest system is one that does not add interest to the principal before calculating subsequent years' interest.
The simple interest system is different from compound interest.
The simple interest formula is given as Principal x Time x Rate.
Principal loan = $700
Loan period = 4 years
Annual interest rate = 4%
Interest system = Simple Interest
Simple interest after 4 years = $112 ($700 x 4% x 4)
Amount to be repaid = Principal + Interest
= $812 ($700 + $112)
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Exercise 5 The table shows the number of registered electric cars in Norway in the period 2016-2021.
Number of
year electric cars
2016 - 97,532
2017 - 138,983
2018 - 195,351
2019 - 260,692
2020 - 337,201
2021 - 455,277
Task A: Create an exponential model for the development in the number of electric cars for the years 2016-2021.
Task B: Use the model from task a to estimate the number of electric cars in 2025.
An exponential model has the formula A is A0(b)t/c, so, we get 1071371.
How Do You Create a Model of Exponential Growth?The formula for exponential growthOne plus the growth rate r is added. Find the growth rate, replace it with the appropriate value in the formula, and then add one.Raise the product of one and r to the power of x. Identify the period of time during which population increase takes place.multiply by the starting point.Analyze the outcomes.An exponential model has the formula A = A0(b)t/c, where A0 is the starting quantity of the thing being modeled.t is the amount of time that has passed.A is equal to the sum at time t.B is the growth factor, and c is the amount of time it takes for it to manifest.A = A0(b)t/c,
97532 ( 455277)1/ 41446 = 1071371.
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Can someone help me thank you
EASY just say THANK YOU!!!
Answer:
1. 3 ones
2. 3
3. 3 tens
4. 3
5. 3 hundreds
6. 3
7. 3 halves
8. 3 (not 3/2)
9. 3 fourths
10. 3
11. 3
12. 2
13. 1/2
14. 3
15. 5/2
16. 3/4
17. 3
18. 3/2
19. 3/4
20. 7/2
21. 2/3
22. 4/11
NOTE: Read the step-by-step explanation on how we arrive on these final answers. Don't just copy-paste it and try to understand the concept so that next time you already know how to solve this type of expressions.
Step-by-step explanation:
This is a simple mathematic problem which requires basic strategies to be solved. People should already know on how to calculate these simple mathematic tasks. Most especially to the first 7 items, we will just use division to get the final answer (numerator/denominator).
[tex]\frac{9}{3}[/tex] = 3 or
9 ÷ 3 = 3
Similar, with the rest of items that includes fractions. We will just reciprocate the denominator and multiply it to the numerator to get the final answer.
Example was the item 8:
= [tex]\frac{9}{2}[/tex] ÷ [tex]\frac{3}{2}[/tex]
= [tex]\frac{9}{2}[/tex] x [tex]\frac{2}{3}[/tex]
= [tex]\frac{18}{6}[/tex]
= 3
the triangle below js equilateral. find the length of side x in the simplest radical form with a rational denominator
The length of side x is given as follows:
[tex]x = \frac{11\sqrt{3}}{3}[/tex]
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the opposite side.For this problem, we have that:
The angle is of 60º.The adjacent side is of x.The opposite side is of 11.Applying the tangent, the length x is obtained as follows:
tan(60º) = 11/x
x = 11/tan(60)º
[tex]x = \frac{11}{\sqrt{3}}[/tex]
[tex]x = \frac{11\sqrt{3}}{3}[/tex]
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help pls now now pls
The change in the function per unit over a specific period of time is the average rate of change. Between x is 5 and x is 7, the average rate of change is -4.
What is a specific period of time is the average rate of change?The y = f graph
The points on f(x) that connect x = 5 to x = 7 are in the attachment. A green line serves as the line segment's representation.
The following values can be used to calculate the line segment's average rate of change.
If x = 5, then y = 8.
Y Equals 0 when x = 7
Consequently, the typical rate of change (m) is
(Delta*y/(Delta*x)) = m
Where:
Delta*y equals y 2 - y 1.
Sigma*y = 0 to 8
Delta*y equals -8
Delta*x equals x 2 - x 1.
x = 7 - 5 for delta.
x*Delta = 2
We therefore have:
(Delta*y/(Delta*x)) = m
m = - 8/2 m = - 4
Hence, the average rate of change from x = 5 to 7 is -4
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