Answers
(x - h)^2 + (y - k)^2 = r^2
Where (h, k) represents the center of the circle and r represents the radius.
In this case, the center of the circle is given as (0, 9), and it passes through the point (15/2, 5).
First, we need to find the radius of the circle. The radius can be calculated using the distance formula between the center and any point on the circle.
Using the distance formula:
r = √[(x2 - x1)^2 + (y2 - y1)^2]
Let's substitute the values into the formula:
r = √[(15/2 - 0)^2 + (5 - 9)^2]
r = √[(15/2)^2 + (-4)^2]
r = √[225/4 + 16]
r = √[225/4 + 64/4]
r = √[289/4]
r = 17/2
Now that we have the radius, we can write the equation of the circle in standard form:
(x - 0)^2 + (y - 9)^2 = (17/2)^2
Simplifying:
x^2 + (y - 9)^2 = 289/4
Multiplying through by 4 to eliminate the fraction:
4x^2 + 4(y - 9)^2 = 289
Therefore, the equation of the circle in standard form is 4x^2 + 4(y - 9)^2 = 289.
I hope this helps! :)
Related Questions
3
[tex]3 \sqrt{81} [/tex]
what's the answer
Answers
Answer will be 27.
Given,
3√81
Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.
For example, squares of
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
Square roots,
√100 = 10
√81 = 9
√64 = 8
√49 = 7
√36 = 6
√25 = 5
√16 = 4
√9 = 3
√4 = 2
√1 = 1
Now ,
3√81 = 3× 9
= 27.
Thus the value is 27.
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Write the equation for a parabola that opens down, translated to the right 3, and translated down 2
Answers
Answer:
The equation for a parabola that opens down, translated to the right 3, and translated down 2 can be written in the standard form as:
y = a(x - h)^2 + k
where (h,k) represents the vertex of the parabola. Since the parabola opens down, the value of 'a' must be negative. The vertex is translated to the right 3 and down 2, so we have:
h = -3 and k = -2
Substituting these values in the standard form equation, we get:
y = a(x + 3)^2 - 2
This is the equation for a parabola that opens down, translated to the right 3, and translated down 2.
There is a math oriented pizza restaurant that advertises their slices based on arc measurement and pie radius . Recently they had a lunch special for a Personal Pie with a radius of 4 inches . What would the area of a 135 slice of pizza be? Round your answer to the nearest hundredth.
Answers
The area of a 135 slice of pizza be,
⇒ 6,782.41 inches²
We have to given that;
Recently they had a lunch special for a Personal Pie with a radius of 4 inches .
Since, WE know that;
Area of circle is,
A = πr²
Where, r is radius of circle
Here, Radius of circle = 4 inches
Hence, Area of pizza is,
⇒ A = 3.14 x 4²
⇒ A = 50.24 inches²
Hence, the area of a 135 slice of pizza be,
⇒ 50.24 × 135
⇒ 6,782.41 inches²
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help solve and explain
Answers
Answer:
6
Step-by-step explanation:
(3√3)^2/3 = (∛3)² X ∛(√3)²
= 3
27^2/3 = (∛27)²
= 3² = 9
9^-1/2 = 1/√9
= 1/3
so the answer is 3 + (9 X 1/3)
= 3 + 3
= 6
The profit a company earns is the revenue the company makes minus the expenses. The
revenue the company makes in a month is represented by the equation R(x) = 5,000 - 2x²,
while the expenses of the company for the month are represented by the equation
E(x) = 15x + 1,000.
Answers
The expression to calculate the profit be,
⇒ P(x) = -2x² - 15x + 4,000
To calculate the profit of the company in a month,
we need to subtract the expenses from the revenue.
The profit equation (P) for the company in a month can be represented as,
⇒ P(x) = R(x) - E(x)
Substituting the given revenue and expense equations, we get,
⇒ P(x) = (5,000 - 2x²) - (15x + 1,000)
Simplifying the equation, we get,
⇒ P(x) = -2x² - 15x + 4,000
Therefore,
The profit of the company in a month can be calculated using the above equation,
where x represents the number of units sold or any other relevant variable.
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Justin's garden is shown below.
6 yards
8 yards
100
Part A
How can you convert the dimensions
of Justin's garden from yards to
inches?
Answers
Answer:
Multiply the number of yards by 3. Then multiply the number of feet by 12.
6 yards= 216 inches
8 yards= 288 inches
Step-by-step explanation:
Based on the supply graph and the demand graph shown above, what is the price at the point of equilibrium?
Hint: Think about the point where they both meet. For example, if you were to place the graphs on top of each other, what would be the point of intersection?
Type the correct number below without the dollar sign.
Answers
Based on the supply graph and demand graph shown above, the price at the point of equilibrium is $ 30.
Demand refers to quantity of a commodity that the consumers are willing to, able to purchase at a given price during a given period of time. Supply refers to quantity of a commodity that the producers are willing to, able to offer for sale at a given price during a given period of time.
Demand curve slopes downward due to inverse relationship between price and quantity demanded whereas supply curve slopes upward due to direct relationship between quantity supplied and price. When both demand and supply curve intersect with each other balance is achieved. Intersection point between demand and supply curve is known as equilibrium.
At this point when prices are equal is known as equilibrium price and when quantiy demanded or supplied are equal it is known as equilibrium quantity. When we combine the given graph. Equilibrium is achieved at a point when price is equal to $ 30 and quantity is equal to 20 units.
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Company X tried selling widgets at various prices to see how much profit they would make. The following table shows the widget selling price, x, and the total profit earned at that price, y. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the profit, to the nearest dollar, for a selling price of 18.75 dollars.
Answers
Using calculator, the quadratic regression function that models the data is
f(x) = -290.6x² + 7127.4x - 43447.5.
the profit ≈ 582.43
How did we arrive at this?To find the profit for a selling price of $18.75, we substitute x = 18.75 into the equation.
f(18.75) = -147.30(18.75)² + 3231.00(18.75) - 8213.66
= -147.30 x 351.5625 + 60581.25 - 8213.66
=582.43375
f(18.75) ≈ 582.43
Therefore, the profit for a selling price of $18.75 is approximately $ 582.43
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Janine built a raised garden bed that is 10 feet long, 5 feet wide, and 1.5 feet tall. She plans to fill the garden bed with premium soil that costs $16.31 per cubic yard. Recall that 1 yard = 3 feet. how much will it cost Janine to fill her garden bed with premium soil?
Answers
Answer: $45.31
Step-by-step explanation:
10*5*1.5=75
75/27 (formula)=2.77778
2.77778*16.31=45.31
Valerie took a job that paid $14 per hour after a pay raise she earned $15.05 per hour find the percent of increase
Answers
Answer:
Valerie's pay increased by 7.5%.
Step-by-step explanation:
The percent increase in Valerie's pay can be calculated as follows:
Percent increase = ((New pay - Old pay) / Old pay) x 100%
Substituting the given values, we get:
Percent increase = ((15.05 - 14) / 14) x 100%
Percent increase = (1.05 / 14) x 100%
Percent increase = 0.075 x 100%
Percent increase = 7.5%
Step-by-step explanation:
She now gets $1.05 per hour more .....1.05 is what percent of 14.00 ?
$ 1.05/ $ 14 x 100% = 7.5% increase
15, 16, 19, 20 how do i label it pls help
Answers
The quadrant of the terminal side for 15) is fourth quadrant.
How to change radians in degree?To change from radians to degrees, you need to the multiple the number of radians by 180/π.
Multiple the number of radians by 180/π.
15) 5 radians = 5 * (180/π)
16) 11π/6 = (11*180)/6 = 330.
19) 3.5 = 3.5*(π/180) degree.
20) 1 = 1*(π/180) degree.
therefore, terminal side for 15) is fourth quadrant.
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What is the sale price of a pillow originally priced at 12 dollars
Answers
The sale price of a pillow originally priced at 12 dollars is given as follows:
$9.
How to obtain the sale price?The sale price of a pillow originally priced at 12 dollars is obtained applying the proportions in the context of the problem.
The original price is given as follows:
$12.
The markdown rate for this problem is given as follows:
25%.
Hence the sale price of a pillow originally priced at 12 dollars is given as follows:
0.75 x 12 = $9.
(markdown of 25% means that 75% of the price is paid).
Missing InformationThe complete problem is:
"A pillow was marked down at 25%. What is the sale price of a pillow originally priced at 12 dollars?"
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Camila has 6 bags of candy. She can pour 1/3 of a bag of candy into a bowl. How many bowls of candy can Camila make in all?
Answers
Answer:
18 Bowls of Candy
Step-by-step explanation:
Camila has 6 bags of candy, and she can pour 1/3 of a bag into a bowl. To determine how many bowls of candy she can make in total, we need to divide the total amount of candy by the amount of candy per bowl.
Since Camila can pour 1/3 of a bag into a bowl, it means she can make 3 bowls of candy with a full bag.
Now, we can calculate the total number of bowls of candy:
Total bowls of candy = (Number of bags) x (Bowls per bag)
Total bowls of candy = 6 bags x 3 bowls per bag
Total bowls of candy = 18 bowls
Therefore, Camila can make a total of 18 bowls of candy with her 6 bags of candy.
MARKING AS BRAINLIST PLEASE HELP!!
Answers
The correct probability that either event will occur is 0.533.
What is probability?A measure of the likelihood of an event to occur.
P(A or B) = P(A) + P(B).
Probability = Number of favorable outcomes/Total number of outcomes
P(A) = 1/5 = 0.3
P(B) = 1/3 = 0.33
P(A) + P(B) = 1/5 +1/3
= 0.533
Probability = 0.533.
Therefore, the probability that either event will occur is 0.533.
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Find the area of a circle with radius,
r
= 46cm.
Give your answer rounded to 3 SF.
Answers
Answer:
6650 cm³
Step-by-step explanation:
area of a circle = π r², where r is the radius
area = π (46)²
= 2116 π
= 6650 cm³ to 3 significant figures
Enter the number that belongs in the green box
Answers
The angles of the triangle with sides 11, 12 and 20 are approximately 117.6 degrees.
We are given that;
The angles of triangle sides are 11, 12 and 20.
Now,
To find the angles of a triangle when its sides are given, we can use the law of cosines. The law of cosines states that c^2 = a^2 + b^2 - 2ab cos©, where a, b, and c are the sides of the triangle and C is the angle opposite to side c.
Using this formula, we can find the angle opposite to side 20 as follows: [tex]cos© = (a^2 + b^2 - c^2) / 2ab cos© = (11^2 + 12^2 - 20^2) / (2 * 11 * 12) cos© = -0.45 C = arccos(-0.45) C[/tex] = 117.6 degrees
Similarly, we can find the other two angles:[tex]cos(A) = (b^2 + c^2 - a^2) / 2bc cos(A) = (12^2 + 20^2 - 11^2) / (2 * 12 * 20) cos(A) = 0.25 A = arccos(0.25) A[/tex] = 75.5 degrees
[tex]cos(B) = (a^2 + c^2 - b^2) / 2ac cos(B) = (11^2 + 20^2 - 12^2) / (2 * 11 * 20) cos(B) = -0.55 B = arccos(-0.55) B[/tex]= 87 degrees
The triangle with sides 11, 12 and 20 are approximately 117.6 degrees, 75.5 degrees, and 87 degrees
Therefore, by the angle the answer will be 117.6 degrees.
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1.2 If Erin had 150m/ of buttermilk and recipe require 0.25 cups of buttermilk, would Erin have enough buttermilk for the recipe (2) 1.3 A cake recipe calls for 0.8 kg of flower, 650g of sugar and 900 000mg of butter.
Answers
If Erin had 150m/ of buttermilk and recipe require 0.25 cups of buttermilk. Erin would have enough buttermilk for the recipe (2).
What is the recipe?1.2. Convert the units of measurement to a common unit.
Erin has:
150 ml of buttermilk
Recipe requires 0.25 cups of buttermilk.
1 cup= 236.59 ml
So,
0.25 cups = 0.25 * 236.59 = 59.15 ml
Therefore Erin has enough buttermilk for the recipe.
1.3. The cake recipe calls for the following ingredients:
0.8 kg of flour
650 g of sugar
900,000 mg of butter
Simplify the units by converting them to a common unit
0.8 kg = 0.8 * 1000 g = 800 g
650 g = 650 g (no conversion needed)
900,000 mg = 900,000 mg / 1000 = 900 g
Therefore the required amounts of the ingredients are: 800 g of flour, 650 g of sugar, 900 g of butter.
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Plot the image of Figure ABCDEFGH after a dilation with scale factor 3. One of
the sides has been plotted for you.
Click twice to plot a segment.
Click a segment to delete it.
Answers
I can guide you on how to perform the dilation with a scale factor of 3 for the figure.
To perform a dilation with a scale factor of 3, you would multiply the coordinates of each point of the original figure by 3. This will result in the figure being enlarged by a factor of 3.
Let's assume the coordinates of the original figure ABCDEFGH are as follows:
A: (1, 1)
B: (4, 1)
C: (4, 4)
D: (1, 4)
E: (2, 2)
F: (3, 2)
G: (3, 3)
H: (2, 3)
To obtain the image of the figure after dilation with a scale factor of 3, multiply each coordinate by 3:
A': (3, 3)
B': (12, 3)
C': (12, 12)
D': (3, 12)
E': (6, 6)
F': (9, 6)
G': (9, 9)
H': (6, 9)
These new coordinates (A', B', C', D', E', F', G', H') represent the image of figure ABCDEFGH after the dilation with a scale factor of 3. You can plot these new coordinates on a graph or use a drawing tool to visualize the enlarged figure.
8.8.PS-13
Find the surface area of the
regular hexagonal prism.
3.5 cm
The surface area is cm Superscript 2
4 cm
11 cm
...
Answers
Answer:
348 cm²
Step-by-step explanation:
In this problem, we are asked to find the surface area of the regular hexagonal prism. We can use the formula:
[tex]SA = 2A + (P \cdot h)[/tex]
where [tex]A[/tex] is the area of the prism's hexagonal faces, [tex]P[/tex] is the perimeter of the hexagonal faces, and [tex]h[/tex] is the prism's height.
We can solve for the area of the hexagonal faces by splitting it into 6 triangles and multiplying the area of each triangle by 6.
[tex]A = 6\left(\dfrac{1}{2} bh\right)[/tex]
where [tex]b[/tex] is the triangle's base and [tex]h[/tex] is the triangle's height.
[tex]A = 6\left(\dfrac{1}{2}\cdot 4 \cdot 3.5\right)[/tex]
[tex]A = 6\left(2 \cdot 3.5\right)[/tex]
[tex]A = 12 \cdot 3.5[/tex]
[tex]A = 42\text{ cm}^2[/tex]
We can solve for the perimeter by multiplying one side length by 6.
[tex]P = 6(4) = 24\text{ cm}[/tex]
We are given that the height of the prism is 11 cm.
[tex]h = 11\text{ cm}[/tex]
Finally, we can solve for the surface area of the prism by plugging these values into the above formula.
[tex]SA = 2A + (P \cdot h)[/tex]
[tex]SA = 2(42) + (24 \cdot 11)[/tex]
[tex]SA = 84 + 264[/tex]
[tex]\boxed{SA = 348 \text{ cm}^2}[/tex]
help it’s past due and i have a test on it tomorrow
Answers
Reflect on what led to this situation and identify strategies to prevent it from happening again. This way, you can develop better time management skills and study habits for future assignments and tests.
Stay calm: It's important to remain calm and composed to think clearly and make the best use of your time.
Prioritize: Assess the situation and determine the importance of each task. Focus on completing the task that is past due first.
Communicate: If possible, reach out to your teacher or professor and explain the situation. Apologize for the delay and request an extension or an opportunity to make up the assignment or test.
Allocate time: Allocate dedicated time to work on the overdue task. Break it down into smaller, manageable parts to make it less overwhelming.
Seek help: If you're struggling with the task or need clarification, reach out to classmates, friends, or online resources for assistance. Don't hesitate to ask for help when you need it.
Plan your study time: Make a study schedule for the test that you have tomorrow. Allocate sufficient time for each subject or topic, focusing on areas that require more attention.
Review efficiently: Prioritize the key concepts, formulas, or theories that are likely to be covered in the test. Use active studying techniques such as summarizing, creating flashcards, or teaching the material to someone else.
Take breaks: While it's important to work efficiently, don't forget to take short breaks to rest and recharge. Breaks can help improve focus and prevent burnout.
positive: Maintain a positive mindset and believe in your ability to overcome challenges. Negative thoughts can hinder your productivity and performance.
Learn from the experience: Reflect on what led to this situation and identify strategies to prevent it from happening again. This way, you can develop better time management skills and study habits for future assignments and tests.
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Which of the following correctly defines a population parameter?
A. a characteristic of the population
B. the difference between the maximum and minimum value of a sample
C. the difference between the maximum and minimum value of the population
D. a characteristic of a sample
Answers
The correct answer is A. a characteristic of the population.
A population parameter refers to a specific characteristic
A population parameter refers to a specific characteristic or numerical value that describes the entire population being studied. It is a fixed value that is typically unknown and estimated using sample data. Examples of population parameters include the population mean, population standard deviation, population proportion, etc.
A square garden has a length of (x+3) ft and a width of (x+2) ft. what is the perimeter and area of the garden?
Answers
Answer:
Perimeter:[tex]4x+10[/tex] feet
Area:[tex]x^{2}+5x+6[/tex] feet
Step-by-step explanation:
The perimeter is equal to 2*width +2*length. The width is x+2 and the length is x+3, therefore the perimeter is equal to 2x+4+2x+6 which equals 4x+10.
The area is equal to width*length
(x+3)(x+2)=[tex]x^{2}+2x+3x+6=x^{2}+5x+6[/tex]
Calculate the area of the composite figure
Answers
Answer:
Step-by-step explanation:
See image below
Use the remainder theorem to find P(2) for P(x)=-x^3+3x^2+6.
Specifically, give the quotient and the remainder for the associated division and the value of P(2).
Answers
Answer: The value of P(2) is equal to 26
Step-by-step explanation:
To find P(2) for the given polynomial P(x) = -x^3 + 3x^2 + 6, we can use the remainder theorem by dividing the polynomial by (x - 2).
-x^2 + 5x - 4
__________________________
x - 2 | -x^3 + 3x^2 + 0x + 6
(x^3 - 2x^2)
___________
5x^2 + 0x
(5x^2 - 10x)
____________
10x + 6
(10x - 20)
__________
26
The quotient is -x^2 + 5x - 4, and the remainder is 26.
Therefore, the value of P(2) is equal to the remainder, which is 26.
What's the circumference
of a
circle with a diameter of 20
inches? Use 3.14 for .
C = [?] inches
Round to the nearest hundredth, if necessary.
Hint: C = πd
Enter
Answers
Answer:
C=62.8
Step-by-step explanation:
1) In the formula C=πd, d represents the diameter, which is 20 inches. All you need to do is apply 20 into the equation and you get C=π20.
2) They said to use 3.14 instead of pi, so we are going to multiply 20*3.14, which is 62.8.
A bank offers a CD that pays a simple interest rate of 7.0%. How much must you put in this CD now in order to have $4500 for a home-entertainment center in 5 years.
The present value that must be invested to get $4500 after 5 years at an interest rate of 7.0% is $__ (Round up to the nearest cent.)
Answers
Rounding up to the nearest cent, the present value that must be invested in the CD now is approximately $3333.34.
To calculate the present value required to have $4500 after 5 years with a simple interest rate of 7.0%, you can use the formula for simple interest:
Present Value = Future Value / (1 + (Interest Rate × Time))
In this case:
Future Value = $4500
Interest Rate = 7.0%
= 0.07
Time = 5 years
Substituting these values into the formula:
Present Value = $4500 / (1 + (0.07 × 5))
Present Value = $4500 / (1 + 0.35)
Present Value = $4500 / 1.35
Present Value ≈ $3333.33
You may use the simple interest calculation to get the present value necessary to have $4500 after five years with a simple interest rate of 7.0%:
Future Value / (1 + (Interest Rate Time)) = Present Value
In this instance
$4500 is the future value.
Rate of Interest = 7.0% = 0.07
t = 5 years
Substituting these values into the formula:
$4500 / (1 + (0.07 5)) = Present Value
$4500 / (1 + 0.35) equals the present value.
Present Value = $4500 / 1.35
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The present value that must be invested now in order to have $4500 for a home-entertainment center in 5 years at an interest rate of 7.0% is approximately $3333.33
How to find the present value that must be invested to get $4500 after 5 yearsUsing the formula for calculating the future value of a single sum:
Future Value (FV) = Present Value (PV) + (PV * Interest Rate * Time)
We rearrange the formula to solve for the present value (PV):
PV = FV / (1 + Interest Rate * Time)
Plugging in the given values:
FV = $4500
Interest Rate = 7.0% = 0.07
Time = 5 years
PV = $4500 / (1 + 0.07 * 5)
PV = $4500 / (1 + 0.35)
PV = $4500 / 1.35
PV ≈ $3333.33
Therefore, the present value that must be invested now in order to have $4500 for a home-entertainment center in 5 years at an interest rate of 7.0% is approximately $3333.33 (rounded up to the nearest cent).
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point H is between G and I and GI=50. Use postulate to slove for x.
GH= 4x - 6
HI= 2x + 2
Answers
The value of x is equal to 4 units.
How to determine the midpoint of a line segment?In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).
Since H is the midpoint of line segment GI, we can logically deduce the following relationship:
Line segment GI = Line segment GH + Line segment HI
Line segment GH = Line segment HI
By substituting the given line segments into the equation above, we have the following:
4x - 6 = 2x + 2
4x - 2x = 6 + 2
2x = 8
x = 8/2
x = 4 units.
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application of divisibility rules in real life?
Answers
While these examples demonstrate some practical applications, divisibility rules are primarily mathematical tools that assist in simplifying calculations, verifying results, and understanding number properties.
Divisibility rules can be applied in various real-life scenarios, particularly in mathematics, finance, and everyday calculations. Here are a few examples:
Checking for even or odd numbers: The divisibility rule for 2 states that a number is divisible by 2 if its last digit is even (0, 2, 4, 6, or 8). This rule can be helpful when determining if a given quantity or count is even or odd. For example, in inventory management, you can quickly estimate the number of items in a collection by checking the parity of the count.
Divisibility by 3: The divisibility rule for 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3. This rule can be useful when dealing with numbers or quantities that need to be evenly distributed or divided.
Divisibility by 9: The divisibility rule for 9 states that a number is divisible by 9 if the sum of its digits is divisible by 9. This rule can be applied in various financial calculations, such as checking if a large number is divisible by 9 to verify the accuracy of calculations involving money, invoices, or balances.
Divisibility by 10: The divisibility rule for 10 states that a number is divisible by 10 if its last digit is 0. This rule is often used in practical situations like determining if a given quantity can be divided evenly into groups of 10 or used in financial transactions involving rounding to the nearest multiple of 10.
Checking prime numbers: Divisibility rules can also help in determining whether a number is prime. For example, the rule that states a number is not divisible by any number greater than its square root can be used to quickly eliminate potential factors when checking for primality.
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Solve for the exact solutions in the interval [0,2]
List your answers separated by a comma, if it has no real solutions, enter DNE.
Answers
The solutions to the trigonometric equation in this problem are given as follows:
θ = π/6.θ = 5π/6.θ = 7π/6.θ = 11π/6.What are complementary angles?Two angles are said to be complementary angles when the sum of their measures is of 90º.
For complementary angles, we have that the sine of one of the angles is the cosine of the other angle, hence in this problem we have that 2θ and θ are complementary angles.
Then the value of θ is obtained as follows:
2θ + θ = 90
3θ = 90
θ = 30º.
θ = π/6.
The equivalent angles, which are also solutions to the equation, are given as follows:
θ = 5π/6. -> second quadrant.θ = 7π/6. -> third quadrant.θ = 11π/6. -> fourth quadrant.More can be learned about complementary angles at brainly.com/question/98924
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the three consecutive term of geometric series be increased by their middle term, then prove that the resulting term will be in Harmonic series.
Answers
Let x, xr , xr² be the terms of GP.
After the increase, the terms are : x+xr , xr+xr , xr²+xr
or in simplified manner : x(1+r), 2xr, xr (r+1) .
For these terms to be in Harmonic Progression, their reciprocals should be in Arithmetic Progression .
Thus,
Arithmetic mean of first and last terms should be equal to the middle term.
First term = 1/[x(1+r)] ; Middle term= 1/(2xr) ; Last term = 1/[xr(r+1)]
Assume,
A = Arithmetic mean of first and last term
A= [1/[x(1+r)]+[1/[xr(r+1)] /2
A= (1/2)[(r+1)/(xr(1+r))]
A= (1/2)(1/xr)
A= 1/(2xr)
A = Middle term
Thus, the reciprocals are in AP.
Hence x(1+r), 2xr, xr(r+1) in HP.
Learn more about Harmonic series ,
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