HELP PLEASE!!!!
(-8,7) and (-2,-3)
Answers
Answer:
Slope is -5/3
Step-by-step explanation:
Let \((x_1,y_1)\rightarrow(-8,7)\) and \((x_2,y_2)\rightarrow(-2,-3)\):
\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-3-7}{-2-(-8)}\\ \\m=\frac{-10}{-2+8}\\\\m=-\frac{10}{6}\\ \\m=-\frac{5}{3}\)
Related Questions
what percentage of 2½ meters is 100 cm?
Answers
Answer:
100/250*100= 40%
Step-by-step explanation:
40%
Step-by-step explanation:2 1/2m = 250 cm
250cm .............100%
100cm ..................x%
x = 100cmx100%/250 cm
= 10000%/250
= 40%
Solve the following system of equations graphically on the set of axes below.
y=x+8
y=−2x−1
Answers
y
=
1
2
x
+
3
y=
2
1
x+3start color #e07d10, y, equals, start fraction, 1, divided by, 2, end fraction, x, plus, 3, end color #e07d10, and every point on the green line is a solution to
y
=
x
+
1
y=x+1start color #0d923f, y, equals, x, plus, 1, end color. So, the only point that's a solution to both equations is the point of intersection
The solution of the system of the equation is x = -3 and y = 5. And the intersecting point in the graph is solution point.
What is the system of equation?One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.
We have the system of equations:
y = x+8 equation 1
y = −2x−1 equation 2
In order to solve the problem:
Subtract the equation 2 with the equation 1,
-2x-x -1-8 = 0
-3x = 9
x = -3
And y = 5
Graphically, the intersection point of both lines is the solution of the system.
The graph is given in the attached image.
Therefore, the solution of the system of the equation is x = -3 and y = 5.
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What is the indefinite integral of 1/xlnx?
Answers
In integration the bindefinite integral of 1/xlnx is
ln(|u|)+C=ln(|lnx|)+C with the aid of using parts, we've discovered whilst the specified formula.
The vital of the 2 capabilities are taken, with the aid of using thinking about the left time period as first feature and 2nd time period as the second one feature.
This technique is referred to as Ilate rule.The vital of xlnx is same to (x2/2) lnx - x2/4 + C, wherein C is the mixing constant. We can compare this vital the usage of the technique of integration with the aid of using parts.
We have the vital:
\(∫1xlnxdx
Use substitution. Let u=lnx so that du=1xdx . Note that each of those are presently gift withinside the vital.
∫1xlnxdx=∫(1lnx)1xdx=∫1udu
This is a not unusualplace vital:
∫1udu=ln(|u|)+C
Since u=lnx :
ln(|u|)+C=ln(|lnx|)+C\)
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Assume that your parents wanted to have $160,000 saved for college by your 18 th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and eamed 9.5% per year on their Investments. a. How much would they have to save each year to reach their goal? b. If they think you will take five years instead of four to graduate and decide to have $200,000 saved just in case, how much would they have to save each year to reach their new goal?
Answers
Your parents would need to save approximately $4,467.56 each year to reach their goal of $160,000 by your 18th birthday. your parents would need to save approximately $40,079.89 each year to reach their new goal of $200,000, assuming a five-year saving period.
a. To calculate the amount your parents would have to save each year to reach a goal of $160,000 by your 18th birthday, we can use the future value of an ordinary annuity formula:
FV = P * [(1 + r)^n - 1] / r
Where:
FV = future value ($160,000)
P = annual savings amount
r = interest rate per period (9.5% or 0.095)
n = number of periods (number of years, in this case, 17 since they start saving on your first birthday until your 18th birthday)
Plugging in the values, we have: $160,000 = P * [(1 + 0.095)^17 - 1] / 0.095
Simplifying the equation and solving for P, we find: P ≈ $4,467.56
b. If your parents decide to save for five years instead of four and aim to have $200,000 saved, we can use the same formula to calculate the new annual savings amount: $200,000 = P * [(1 + 0.095)^5 - 1] / 0.095
Simplifying the equation and solving for P, we find: P ≈ $40,079.89
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3) Which equation correctly matches the graph below?
answer option:
y=5/3x +5
y= -3/5 +5
y= 5/3x +5
y=5/3x-5
Answers
an employer interviews 10 people for four openings at a company. six of the 10 people are women. all 10 applicants are qualified. in how many ways can the employer fill the four positions when the selection is random and exactly three selections are women?
Answers
The employer chooses at random, and three of the candidates are women, there are 80 possible ways to fill the four positions.
We may use the combination formula to address this issue,
which is:
nCr = n! / (r! * (n-r)!)
where r is the number of things being picked, n denotes the total number of items, and! denotes factorial, which is the sum of all positive integers up to that number. For example, 4! = 4 x 3 x 2 x 1 = 24.
Six women will be chosen, and one person will be selected from the remaining four (who must be a man). The result is:
Number of ways to choose 3 women from 6 women = 6C3 = 20
Number of ways to choose 1 man from 4 men = 4C1 = 4
Since these two numbers are independent options, we must multiply them together to determine the total number of alternatives to fill the four seats. Which is:
There are a total of four slots that can be filled, including 3 women and 1 man. = 20 * 4 = 80
Therefore, the employer chooses at random, and three of the candidates are women, there are 80 possible ways to fill the four positions.
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Pls help me no links
Answers
Here's ur perfect answer
right answer gets brainliest
Answers
Answer: (x=-19) as was on my question.
Suppose Argentina produces only two goods: corn and smartphones. The following graph shows Argentina’s current production possibilities frontiers, along with six output combinations represent by black points (plus symbols) labeled A to F.
Answers
Point A is inefficient.
Point B is efficient
Point C is efficient.
Pont D is unattainable.
Pont E is unattainable.
Point F is inefficient.
What is a production possibility frontier?The Production possibilities frontiers is a curve that shows the various combination of two goods a company can produce when all its resources are fully utilised.
Point outside the curve or to the right of the curve means that the production level is not attainable given the level of resources. Points inside the production possibilities frontier means that the nations resources are not being fully utilised. Points on the curve are efficient and attainable.
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What multiplication equattion can be used to explain the solution to 15 / 1/3
Answers
Step-by-step explanation:
15 / (1/3) is equal to 15 x 3/1 = 15 x 3 = 45
Reciprocal of 1/3 = 3/1
So, the multiplication equation that explains the solution is:
15 * (3/1) = 45
Therefore, 15 divided by 1/3 is equal to 45.
find the $1314^{\text{th}}$ digit past the decimal point in the decimal expansion of $\dfrac{5}{14}$.
Answers
The $1314^\text{th}$ digit past the decimal point is 2.
To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.
The long division of $\frac{5}{14}$ is as follows:
```
0.35 <-- Quotient
-----
14 | 5.00
4.2 <-- Subtract: 5 - (14 * 0.3)
-----
80 <-- Bring down the 0
70 <-- Subtract: 80 - (14 * 5)
-----
100 <-- Bring down the 0
98 <-- Subtract: 100 - (14 * 7)
-----
20 <-- Bring down the 0
14 <-- Subtract: 20 - (14 * 1)
-----
60 <-- Bring down the 0
56 <-- Subtract: 60 - (14 * 4)
-----
40 <-- Bring down the 0
28 <-- Subtract: 40 - (14 * 2)
-----
120 <-- Bring down the 0
112 <-- Subtract: 120 - (14 * 8)
-----
80 <-- Bring down the 0
70 <-- Subtract: 80 - (14 * 5)
-----
...
```
We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.
Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.
So, the $1314^\text{th}$ digit past the decimal point is 2.
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for the following question(s): a school counselor tests the level of depression in fourth graders in a particular class of 20 students. the counselor wants to know whether the kind of students in this class differs from that of fourth graders in general at her school. on the test, a score of 10 indicates severe depression, while a score of 0 indicates no depression. from reports, she is able to find out about past testing. fourth graders at her school usually score 5 on the scale, but the variation is not known. her sample of 20 fifth graders has a mean depression score of 4.4. suppose the counselor tested the null hypothesis that fourth graders in this class were less depressed than those at the school generally. she figures her t score to be 2.8. what decision should she make regarding the null hypothesis? group of answer choices postpone any decisions until a more conclusive study could be conducted fail to reject it there is not enough information given to make a decision reject it
Answers
Answer:
Based on the information provided, the correct choice is:
fail to reject it
Here are the key points:
• The mean depression score for the sample of 20 4th graders was 4.4.
• The counselor tested the null hypothesis that these 4th graders were less depressed than the general 4th grader population.
• The t score calculated was 2.8.
To reject the null hypothesis and conclude the sample differs from the population, we would need a high enough t score. But the t score of 2.8 is not conclusively high enough here.
Some additional considerations:
• The general 4th grader population mean is 5, so the sample mean of 4.4 is a bit lower, but not drastically. This suggests the sample may not differ hugely from the population.
• There is no information on the variation or standard deviation for either the sample or population. Without this, we can't determine if a t score of 2.8 actually signifies a statistically significant difference.
• The sample size of 20 is decent but not very large. Larger sample sizes provide more conclusive results.
• No p-value is given, making it hard to judge if the t score of 2.8 is high enough to reject the null hypothesis. By convention, p<0.05 is often used but we don't have the p-value here.
So overall, there is not enough definitive evidence provided to conclusively reject the null hypothesis. The t score of 2.8 alone is probably not high enough, given the considerations around sample size, variation, and lack of a p-value. More data and analysis would be needed to make a firm decision either way.
Therefore, the correct choice is: "fail to reject it". There is not enough information given in this question and results to conclusively reject the null hypothesis.
Step-by-step explanation:
"Belinda borrowed $18,500 at simple interest rate of 4.40% p.a.
from her parents to start a business. At the end of 3 months, she
paid them $5,200 and $3,200 at the end of 6 months. How much would
she repays
Answers
Belinda would have to pay $10,765.16 at the end of 18 months to clear the remaining balance.
To calculate the final payment, we need to consider the initial loan amount, the interest rate, and the time period. Belinda borrowed $18,500 at a simple interest rate of 4.40% per year.
She made two payments during the loan period. At the end of 3 months, she paid $5,200, and at the end of 6 months, she paid $3,200. These payments reduce the outstanding balance.
To calculate the remaining balance after the initial payments, we subtract the total amount paid from the initial loan amount:
Remaining Balance = Initial Loan Amount - Total Amount Paid
= $18,500 - ($5,200 + $3,200) = $10,100
Now, we need to calculate the interest accrued on the remaining balance for the remaining 12 months (18 months - 6 months). To calculate the interest, we use the formula: Interest = Principal * Rate * Time.
Interest = $10,100 * 0.044 * (12/12) = $443.44
Finally, we add the interest accrued to the remaining balance to find the final payment: Final Payment = Remaining Balance + Interest Accrued = $10,100 + $443.44 = $10,543.44
Therefore, Belinda would have to pay $10,543.44 at the end of 18 months to clear the balance. However, since we are using 'now' as the focal date, and 18 months have already passed, we need to account for the additional 6 months that have elapsed. Hence, the final payment becomes:
Final Payment = Remaining Balance + Interest Accrued for the additional 6 months = $10,100 + $443.44 + ($10,100 * 0.044 * (6/12)) = $10,765.16. Therefore, Belinda would have to pay $10,765.16 at the end of 18 months from 'now' to clear the balance.
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The complete question is:
Belinda borrowed $18,500 at simple interest rate of 4.40% p.a. from her parents to start a business. At the end of 3 months, she paid them $5,200 and $3,200 at the end of 6 months. How much would she have to pay them at the end of 18 months to clear the balance? Use 'now' as the focal date.
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Jorge biked a total of 42 miles in 5 days. He biked the same distance each day.
The number of miles, m, Tim biked is represented by m = 8.75d for d days.
Is each statement true or false? Choose "True" or "False" for each row in the table.
Statement
Jorge biked more miles per day than Tim biked..
The difference between the number of miles jorge and Tim biked is 0.35 mile per day.
In 5 days, the difference between the number of miles Jorge and Tim biked is 1.25 miles.
In 7 days, the difference between the number of miles Jorge and Tim would bike would be 2.45 miles.
True or False
True
False
True
False
True
False
True
False
Answers
The first and the third statements are false and second and fourth statements are true. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
Any real number can be represented using one of four basic mathematical operations, which are as follows:
1. The addition operator ('+') is used to calculate the sum of the numbers.
2. Using the "-" sign to subtract, which yields the difference between the integers.
3. When the result is the product of the numbers, multiply (×) it.
4. Division (÷), which results in the quotient of the numbers.
We are given that Jorge biked a total of 42 miles in 5 days.
The number of miles, m, Tim biked is represented by m = 8.75d for d days.
So, the number of miles, m, Tim biked in 5 days is
m = 8.75(5)
m = 43.75
Statement 1: Jorge biked more miles per day than Tim biked.
Miles per day of Jorge = 42/5 = 8.4 miles
Miles per day of Tim = 8.75 miles
The statement is false because Tim biked more miles per day than Jorge.
Statement 2: The difference between the number of miles jorge and Tim biked is 0.35 mile per day.
Difference = 8.75 - 8.4 = 0.35 miles
So, the statement is true.
Statement 3: In 5 days, the difference between the number of miles Jorge and Tim biked is 1.25 miles.
Difference = 43.75 - 42 = 1.75 miles
So, the statement is false.
Statement 4: In 7 days, the difference between the number of miles Jorge and Tim would bike would be 2.45 miles.
Miles biked in 7 days by Jorge = 8.4*7 = 58.8 miles
Miles biked in 7 days by Tim = 8.75*7 = 61.25 miles
Difference = 61.25 - 58.8 = 2.45 miles
So, the statement is true.
Hence, the first and the third statements are false and second and fourth statements are true.
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Which is an example of a statistical question?
Question 1
Question 2
Question 3
Questions
How many pets does Alisha have at home?
What is your favorite kind of pet?
Do you like having a pet?
What is Alisha's pet's name?
Question 4
question 1
question 2
question 3
question 4
Answers
Answer: How many pets does Alisha have at home?
Step-by-step explanation:
A statistical question, put simply, is something based on facts and numbers. The only option here that is not an opinion is the first option, "How many pets does Alisha have at home?"
Two of the other options have something to do with a bias or an opinion. This is stuff such as "your favorite" or "do you like." The last one has to do with a name, not a number.
Answer:
How many pets does Alisha have at home?
Step-by-step explanation:
question 1
Aisha is n years old.
a) Mohammed is 5 years older than Aisha. Write an algebraic expression
for his age.
b) Martha writes her age as 6n. Write a sentence to explain how her age
compares with Aisha's.
Answers
Answer:
Step-by-step explanation:
n x 5
All four B points are equidistant from points A and C. Are they all midpoints of AC? Justify your answer.
Answers
Answer:
No
Step-by-step explanation:
For a point to be the midpoint of a line segment, it must bisect it into two equal segments and be on the line segment (hence, colinear with the endpoints). All four B points are equidistant from points A and C, but aren’t colinear with A and C. Therefore, they aren’t all midpoints of line segment AC.
I hope this helps! :)
If x and y are two rational numbers such that x < y , then ______ is a rational number in between x and y.
Answers
Answer:
\(\dfrac{x+y}{2}\)
Step-by-step explanation:
Let first number be x and another number is y.
A rational number is a fraction that can be expressed in the form of x/y.
A rational number between x and y is given by :
\(R=\dfrac{x+y}{2}\)
So,
If x and y are two rational numbers such that x < y , then \(\dfrac{x+y}{2}\) is a rational number in between x and y.
What fraction is equivalent to 1/3?
Answers
The base of a solid is the region in the first quadrant bounded by the y-axis, the graph of y = ????????????-1x, the horizontal line y = 3 and the vertical line x = 1. For this solid, each cross section perpendicular to the x-axis is a square. What is the volume of the solid?
Answers
The volume of the solid is 9 cubic units, which is determined by the base in the first quadrant bounded by the y-axis, the graph of y = x-1, the horizontal line y = 3, and the vertical line x = 1. As the cross sections perpendicular to the x-axis are squares, the volume can be calculated.
The volume of the solid can be calculated by finding the area of the base and then multiplying it by the height of the solid. The base of the solid is in the first quadrant and is bounded by the y-axis, the graph of y = x-1, the horizontal line y = 3, and the vertical line x = 1. This region forms a trapezoid, with an area of 6. As the cross sections perpendicular to the x-axis are squares, the height of the solid is 3 units. Thus, the volume of the solid is 6 multiplied by 3, which gives us a total volume of 9 cubic units. To calculate the volume, it is important to identify the base of the solid and the shape of the cross sections perpendicular to the x-axis. This will allow us to calculate the area of the base, and multiply it by the height of the solid to determine the total volume.
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need help asap please
Answers
Your answer is C.
I hope this helps! :)
Write a function of the geometric sequence with a starting term of 6 and a common ratio of 3. Find the sixth term.
Answers
A function for the described sequence is; f(n) = 6• 3^(n-1) and the sixth term is; 1458.
What is the sixth term of the sequence?Since, it follows that the first term of the sequence is; 6 and the common ratio is 3, it follows that the recursive function that represents the sequence is; f(n) = 6• 3^(n-1).
Additionally, by substitution of 6 for n; f(6) = 1,458.
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The rent of a bowling lane is $25 for 5 minutes.
How much per minute?
Answers
Answer:
5 dollars
Step-by-step explanation:
write the standard form of the equation that is perpendicular to y = 5x + 4 and goes through point (3, -2).
Answers
Answer:
y=-1/5x-7/5
Step-by-step explanation:
y=5x+4
(y+2)=-1/5(x-3)
y+2=-1/5x+3/5
y+10/5=-1/5x+3/5
y=-1/5x-7/5
Answer: x+5y= -7
Step-by-step explanation:
Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting an orange marble.
0.27
0.33
0.40
0.67
Answers
The probability of selecting an orange marble is 0.33.
Option B is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The number of times each marble is selected.
Green = 4
Black = 6
Orange = 5
Total number of times all marbles are selected.
= 4 + 6 + 5
= 15
Now,
The probability of selecting an orange marble.
= 5/15
= 1/3
= 0.33
Thus,
The probability of selecting an orange marble is 0.33.
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is B= -3x - 7x^2 and C = -x^2 - 8 - x, find an expression that equals 3b-3c in standard form
Answers
Therefore, the expression that equals 3B - 3C in standard form is -21x² - 6x + 24.
What is expression?In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated or simplified to obtain a single value or another expression. In algebra, expressions are often used to represent mathematical relationships or formulas, and can be manipulated using various algebraic techniques such as factoring, expanding, simplifying, and solving for unknown variables. Expressions are also used in calculus, probability theory, and many other branches of mathematics to describe mathematical models and relationships.
Here,
We can start by substituting the expressions for B and C into the expression for 3B - 3C and simplifying:
3B - 3C = 3(-3x - 7x²) - 3(-x² - 8 - x)
= -9x - 21x² + 3x² + 24 + 3x
= -21x² - 6x + 24
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Please help! Worth 60 points for a super rapid reply right now-MN is the midsegment of Trapezoid ABCD. What is the length of AB?
Answers
Answer:
c) 27.9
Step-by-step explanation:
Since MN is the midsegment ,
MN = (AB + CD)/2
21.1 = (AB + 14.3)/2
21.1*2 = AB + 14.2
AB = 42.2 - 14.2
AB = 27.9
Answer:
C
Step-by-step explanation:
the midsegment is equal to half the sum of the parallel bases, that is
\(\frac{1}{2}\) (AB + CD) = MN ( substitute values )
\(\frac{1}{2}\) (AB + 14.3) = 21.1 ( multiply both sides by 2 to clear the fraction )
AB + 14.3 = 42.2 ( subtract 14.3 from both sides )
AB = 27.9 cm
Reconstruction failed to establish racial equality and black freedom. Explain how the rapid industrialization of the United States under the system of "free labor" in the years after the Civil War led to a social crisis by the end of the nineteenth century in which the traditional American values of democracy, equality, and opportunity seemed to be disappearing, and in which class conflict threatened to tear society apart. How did the capitalists and working classes attempt to enhance their own power and interests in their struggle with each other? Why was the working class unable to achieve much, despite valiant efforts? How did the middle-class respond to the struggle between labor and capital as well as the changes that American society underwent during the late nineteenth century?
Answers
The working class was unable to achieve much, despite valiant efforts, due to their lack of solidarity and the capitalist's willingness to use violence against them.The middle class responded to the struggle between labor and capital, as well as the changes that American society underwent during the late nineteenth century, by supporting a variety of social reform movements.
After the Civil War, Reconstruction failed to establish racial equality and black freedom in the United States. The rapid industrialization of the United States under the system of "free labor" in the years following the Civil War contributed to a social crisis by the end of the nineteenth century. This crisis seemed to be causing the disappearance of traditional American values of democracy, equality, and opportunity, and class conflict was threatening to tear society apart.In their struggle against each other, capitalists and working classes attempted to enhance their own power and interests. Capitalists attempted to enhance their power by instituting new labor policies, cutting wages, and lowering working conditions.
The working class was unable to achieve much, despite valiant efforts, due to their lack of solidarity and the capitalist's willingness to use violence against them.The middle class responded to the struggle between labor and capital, as well as the changes that American society underwent during the late nineteenth century, by supporting a variety of social reform movements. They sought to provide relief for the urban poor and to reform politics by promoting women's suffrage and demanding the elimination of political corruption.In conclusion, Reconstruction failed to establish racial equality and black freedom in the United States. The rapid industrialization of the United States under the system of "free labor" in the years following the Civil War contributed to a social crisis by the end of the nineteenth century. Capitalists and working classes attempted to enhance their power and interests in their struggle with each other. The working class was unable to achieve much, despite valiant efforts. The middle class responded to the struggle between labor and capital, as well as the changes that American society underwent during the late nineteenth century, by supporting a variety of social reform movements.
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Sylvia read that the height of the Empire State Building is 443.2 m and wants to build a scale model of the building in her room. She knows that the height of the ceiling in her room is 8ft. Write a scale that would allow a scale model of the Empire State Building in Slyvia's bedroom so that the top of the building would just touch her ceiling.
Answers
Answer:
\(Scale = 1ft : 55.4m\)\
Step-by-step explanation:
Given
\(Height = 443.2m\) --- Empire State Building.
\(Height = 8ft\) --- Her Room
Required
Determine the scale model
The scale model is calculated as thus:
\(Scale = Her\ Room: Empire\ Building\)
\(Scale = 8ft : 443.2m\)
Divide both ration by
\(Scale = 8ft/8 : 443.2m/8\)
\(Scale = 1ft : 55.4m\)
Hence. the scale she'll use is 1 ft her room to represent 55.4 m of the state building
Find the indicated derivative. dp/dq for p = (q^2 + 2)/(4q-4)
Answers
The indicated derivative of p with respect to q, dp/dq, can be found using the quotient rule of differentiation. Let's rewrite p as (q^2 + 2)(4q-4)^(-1). Using the quotient rule, we get dp/dq = [2q(4q-4)^(-1) - (q^2+2)(4(4q-4)^(-2))] = [2q/(4q-4) - (q^2+2)/(4q-4)^2]. We can simplify this further by factoring out a 2 from the first term in the numerator to get dp/dq = [2(q-2)/(4q-4)^(2) - (q^2+2)/(4q-4)^2]. This is our final answer.
To find the derivative dp/dq, we first rewrite p in a form that makes it easier to apply the quotient rule. We then use the quotient rule, which states that for a function f(x)/g(x), the derivative is [(g(x)f'(x) - f(x)g'(x))/(g(x))^2]. We substitute q^2+2 for f(x) and 4q-4 for g(x) and differentiate each term separately. We then simplify the result to obtain the final answer.
The indicated derivative dp/dq for p = (q^2 + 2)/(4q-4) can be found using the quotient rule of differentiation. The final answer is dp/dq = [2(q-2)/(4q-4)^(2) - (q^2+2)/(4q-4)^2].
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