Step-by-step explanation:
the coordinates of a midpoint are
x = (x1 + x2)/2
y = (y1 + y2)/2
with (x1, y1) and (x2, y2) being the endpoints.
so, our midpoint here is
((-7 + 3)/2, (3 + -7)/2) = (-4/2, -4/2) = (-2, -2)
f(x) = x² + 3x, g(x) = 5x + 2, (f - g)(3) = ?
Answer:
1
Step-by-step explanation:
f(x) = x² + 3x
g(x) = 5x + 2
f(3) = 3² + 3 x 3
f(3) = 9 + 9
f(3) = 18
g(3) = 5(3) + 2
g(3) = 15 + 2
g(3) = 17
(f - g)(3) = 18 - 17
(f - g)(3) = 1.
A solid right pyramid has a regular hexagonal base with an area of 5.2 cm2 and a height of h cm. a solid right pyramid has a regular hexagonal base with an area of 5.2 centimeters squared and a height of h centimeters. which expression represents the volume of the pyramid?
The calculations show that this pyramid's volume is equivalent to:
5.2h/3 cm3.
What is a pyramid?A polyhedron constructed by joining a polygonal base and a point, is called a pyramid. A lateral face is a triangle formed by the base edge and vertex of each base. Conic solid with a polygonal basis describes it. The number of vertices, faces, and edges on a pyramid with an n-sided base is n + 1.
Given information:Base area = 5.2 [tex]cm^2[/tex].
Height in centimeters is equal to h.
How can the volume of a pyramid be calculated?The following formula is used to determine a pyramid's volume mathematically:
Base area divided by height equals one-third of the volume.
When we enter the parameters into the formula, we get;
Volume = 1/3 *5.2* h
Volume = 5.2h/3 [tex]cm^3.[/tex]
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I understand that the question you are looking for is :
A solid right pyramid has a regular hexagonal base with an area of 5. 2 cm2 and a height of h cm. a solid right pyramid has a regular hexagonal base with an area of 5. 2 centimeters squared and a height of h centimeters. which expression represents the volume of the pyramid? one-fifth(5. 2)h cm3 start fraction 1 over 5 h infraction(5. 2)h cm3 one-third(5. 2)h cm3 start fraction 1 over 3 h infraction(5. 2)h cm3
rounding to 1 significant figure, estimate the
answers to these questions:
a)
78 × 92
b)
615 × 38
C)
423 × 764
Answer:
a) 7000
b) 20000
c) 300000
Rounding is the act of replacing a number with values that are an approximation.
can be used to create simpler, or more explicit answersBasic rounding rules:
1. If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 68 rounded to 1 significant figure would be 70.
2. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down. Example: 13 rounded to 1 significant fugue is 10.
3. Zero digits that come after a non zero digit are non significant. Example: 10000 only has 1 significant figure
Calculations:
A) 78 x 92 = 7176
to round to 1 sig fig we must make all digits after 7 insignificantwe must also take note of whether the 7 will remain the same or be rounded upthe digit that comes after is a 1, following the rules of rounding it will remain a 7The answer for A is 7000
B) 615 x 38 = 23370
all digits after 2 must be insignificant the digit that comes after is a 3, following the rules of rounding the 2 will remain a 2Answer for B is 20000
C) 423 x 764 = 323172
all digits after 3 must be insignificantthe digit that comes after is a 2, following the rules of rounding the 3 will remain a 3Answer for C is 300000
7/3=7:
what will seven over three equals seven divide be
Answer:
3(7/3=7:3)Step-by-step explanation:
7/3=7:
what will seven over three equals seven divide be
7/3 is a division (7:3)
so
your answer is :
3
(7/3=7:3)
Given a polynomial function f(x)=2x²+ 7x+6 and an exponential function g(x)=2+ 5, what key features do f(x) and g(x) have in common?
Both f(x) and g(x) increase over the interval of [-4,∞)
Both f(x) and g(x) have the same x-intercepts of (-2, 0) and (-1.5, 0).
Both fox) and gox) have the same y-intercept of (0,6)
Both f(x) and g(x) have the same range of (-00.01]
Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:
Both f(x) and g(x) have the same y-intercept of (0,6)What is the polynomial function about?Polynomial functions are known to be a kind of an expressions that is made up of a set of variables of different extent or degrees, non-zero coefficients, positive exponents (of variables), and also it is made up of constants.
Note that the equation of the functions are stated as:
f(x) = 2x² + 7x + 6
g(x) = 2^x + 5
The right and next thing to do is to plot a graph of both functions (see image attached)
From the graph, we have the fact that Both f(x) and g(x) have the same y-intercept of (0,6)
Therefore, Since the common features of the polynomial function is f(x) = 2x² + 7x + 6 and exponential function g(x) = 2^x + 5 then:
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Tina wrote a check for $35 on Monday. On Tuesday she made of withdrawal of $60 and on
Wednesday she deposited $75. What is the change in Tina's account after the three days?
The change in Tina's account after the three days; Monday, Tuesday and Wednesday is $-25
Deposit and withdrawalDeposit is a sum of money or other asset given as an initial payment, to show good faith, or to reserve something for purchase.
Withdrawal on the other hand, is to extract money from an account.
Check = $35Withdrawal = $60Deposit = $75Change in Tina's account after the three days = - 35 - 60 + 75
= -95 + 75
= $-20
Therefore, the change in Tina's account after the three days; Monday, Tuesday and Wednesday is $-25.
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A rubber gasket has a circumference of 3.2 cm. when placed in service, it expands by a scale factor of 2. what is the circumference of the gasket when in service?
6.4 cm is the needed circumference of the gasket following dilatation with a scale factor of 2.
What does circumference mean?The boundary length of any circular shape is known as the circumference.
What is scale factor?A scale factor is a quantity multiplier (also known as a scale). The scaling factor for x, for instance, is represented by the letter "C" in the equation y = Cx. The factor would be 5 if y = 5x were the equation.
According to the given data:After scale factor 2 is applied, 6.4 cm must be the gasket's needed circumference.
It includes a rubber gasket with a 3.2 cm circumference. The circumference of the gasket has must be calculated after scaling up by factor 2.
Here,
3.2 cm is the gasket's circumference.
The circumference changed upon scale factor 2 dilatation.
Dilated gasket circumference: 2 * 3.2 = 6.4 cm
As a result, 6.4 cm is the needed circumference of the gasket following dilatation with a scale factor of 2.
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Answer:
6.4cm
Step-by-step explanation:
I Just Took the Test.
4|a| + 8 -a, if a = -2
PLEASE HELP!!!!!!!!!!!!!! I'm stuck on this!!
4|a| + 8 - a, if a = -2
What we're doing here is plugging in the given value of a for every instance of a in the expression.
4|-2| + 8 - (-2)
---The absolute value of a number is its distance from 0. -2 is 2 units away from 0, so the absolute value of -2 is 2. And, remember two negatives make a positive!
4(2) + 8 + 2
8 + 8 + 2
16 + 2
18
Hope this helps!
A basketball player averages 12.5 points per game. There are 24 games in a season. At this rate, how many points would the player score in an entire season?
In the entire season, the basketball player would score
point
Answer:
300 points
Step-by-step explanation:
Since we have a constant rate (12.5 points/game), we can find the number of points by setting up a proportion:
[tex]\frac{12.5}{1}=\frac{x}{24}\\\\x=(12.5*24)=300[/tex]
From the top of a 6m house, the angle of elvation to the top of a flappole is across the street is 9 degrees. the angle of depression is 22 degrees to the base of the flapole. Redraw the diagram below and label all the angles. How tall is the flagpole? Round naswer to one decimal place.
The height of the flag pole which is described as in the task content is; 8.2m.
What is the height of the flagpole as described from the top of the 6m house?The horizontal distance between the 6m house and the flagpole in discuss can be evaluated by means of the angle of depression and trigonometric identity, tan as follows;
tan 22° = 6/x
x = 6/tan 22 = 14.9m.
Consequently, the horizontal distance from the top of the house to the top of the flagpole is therefore;
tan 9° = y/14.9
y = 14.9 tan 9° = 2.2m
Ultimately, the height of the flagpole is; 6+2.2 = 8.2m.
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with a linear, exponential, or quadratic function.
You have to decide which of two prizes you will accept!
Prize A: $5,000 for the first month with a $100 increase every month thereafter.
Prize B: $2,000 for the first month with a 10% increase every month thereafter.
9. Create an equation for each situation (Prize A and Prize B).
The equation s for each scenario in which case, the former, Prize A is represented as a linear equation while the latter, Prize B is represented as an exponential function are;
Prize A = $5,000 + $100m (where m = no. of months).Prize B = $2,000(1.1)^m.What equations represents the given situation?It follows from the task content that in scenario which pertains to Prize A, the initial price which represents the y-intercept is; $5,000 while the slope which represents the increase per month is; $100.
Consequently, we have; Prize A = $5,000 + $100m
While, for Prize B, in which case the function via exponential, we have;
Prize B = $2,000(1.1)^m.
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Simplify 10 times the square root of quantity 3 x end quantity plus 4 times the square root of quantity 3 x end quantity plus 5 times the square root of quantity 3 x end quantity. 9 times the square root of quantity 3 x end quantity 9 times the square root of quantity 6 x end quantity 19 times the square root of quantity 3 x end quantity 19 times the square root of quantity 9 x cubed
The square root of the quantity x plus 7 end quantity minus 1 equals x=2.
What is square root?A number's square root is the factor that can be multiplied by itself to yield that number. Square root of, end square root is the symbol for square root. Finding an integer's square root is the inverse of squaring a number.To find the square root:
√(x + 7) − 1 = x√(x + 7) = x + 1x + 7 = (x + 1)²x + 7 = x² + 2x + 10 = x² + x − 60 = (x + 3) (x − 2)x = -3 or 2Check for extraneous solutions:
√(-3 + 7) − 1 = -3√4 − 1 = -32 − 1 = -31 = -3x ≠ -3√(2 + 7) − 1 = 2√9 − 1 = 23 − 1 = 22 = 2x = 2Therefore, the square root of the quantity x plus 7 end quantity minus 1 equals x = 2.
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The correct question is given below:
The square root of the quantity x plus 7 end quantity minus 1 equals x
What is the five-number summary for this data set?
17, 21, 22, 26, 28, 31, 33, 41, 46, 52
Assume the numbers in each answer choice are listed in this order: min, Q1,
median, Q3, max.
Step-by-step explanation:
17, 21, 22, 26, 28, 31, 33, 41, 46, 52
min: 17
Q1: 26
median: 28
Q3: 31
max: 52
Today, Stephen is three times as old as Gautham. Ten years ago Stephen turned 2. How old will Gautham be
in 8 years?
[tex]2x+5\ \textless \ \frac{x+1}{4}[/tex]
Answer:
x < -19/7
Step-by-step explanation:
Solve for x
2x+5 < (x+1)/4
Multiply each side by 4
4( 2x+5) < (x+1)/4 *4
8x + 20 < x+1
Subtract x from each side
8x+20-x < x+1-x
7x + 20 < 1
Subtract 20 from each side
7x+20-20 < 1-20
7x< -19
Divide by 7
7x/7 < -19/7
x < -19/7
Answer:
[tex] \red{x < \frac{ - 19}{7} }[/tex]
Step-by-step explanation:
[tex]2x + 5 < \frac{x + 1}{4} \\ \text{use \: cross \: muliplication} \\ 4(2x + 5) < x + 1 \\ 8x + 20 < x + 1 \\ 8x - x < - 20 + 1 \\ 7x < - 19 \\ \frac{7x}{7} < \frac{ - 19}{7} \\ x < \frac{ - 19}{7} [/tex]
4|a|+8-a if a=-2
ASAP GIVING BRAINLIEST PLEASE HELP!!
Answer: 18
Step-by-step explanation:
4 I-2I + (8+2)=
4(2) + 8+2=
8+8+2=
18
Diego wants to paint his room purple. He bought one gallon of purple paint that is 30% red paint and 70% blue paint. Diego wants to add more blue to the mix so that the paint mixture is 20% red, 80% blue.
1. How much blue paint should Diego add? Test the following possibilities: 0.2 gallons, 0.3 gallons, 0.4 gallons, 0.5 gallons.
0.2 gallons
0.2 gallons,
0.3 gallons
0.3 gallons,
0.4 gallons
0.4 gallons,
0.5 gallons
0.5 gallons,
BoldItalicUnderlineImage (12 image limit)Increase indentDecrease indentFormula keypadUndoRedoBullet listNumbered list
Edit imageView imageDelete image
2. Write an equation in which x
represents the amount of paint Diego should add.
3. Check that the amount of paint Diego should add is a solution to your equation.
idrk but I hope you have a good day and good luck with ur answer
help on this math problem!! if there is any work that can be shown it would be great thanks!!!
Answer:
4230.44
Step-by-step explanation:
Sandy used a virtual coin toss app to show the results of flipping a coin 80 times, 800 times, and 3,000 times. Explain what most likely happened in Sandy's experiment.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 80 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 800 flips.
Sandy's experimental probability was closest to the theoretical probability in the experiment with 3,000 flips.
Question 2(Multiple Choice Worth 2 points)
(Experimental Probability MC)
A spinner with 4 equal sections is spun 20 times. The frequency of spinning each color is recorded in the table below.
Outcome Frequency
Pink 6
White 3
Blue 7
Orange 4
What statement best compares the theoretical and experimental probability of landing on orange?
The theoretical probability of landing on orange is one fifth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The theoretical probability of landing on orange is one fifth, and the experimental probability is 30%.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 50%.
Question 3(Multiple Choice Worth 2 points)
(Experimental Probability MC)
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
Question 4(Multiple Choice Worth 2 points)
(Experimental Probability LC)
A number cube is tossed 60 times.
Outcome Frequency
1 12
2 13
3 11
4 6
5 10
6 8
Determine the experimental probability of landing on a number less than 2.
35 over 60
25 over 60
13 over 60
12 over 60
Question 5(Multiple Choice Worth 2 points)
(Experimental Probability MC)
A coin is flipped 200 times. The table shows the frequency of each event.
Outcome Frequency
Heads 98
Tails 102
Determine the experimental probability of landing on heads.
102%
98%
50%
49%
Question 6 (Essay Worth 4 points)
(Experimental Probability HC)
A coin is flipped at the start of every game to determine if Team A (heads) or Team B (tails) will get the ball first.
Part A: Find the theoretical probability of a fair coin landing on heads. (1 point)
Part B: Flip a coin 14 times and record the frequency of each outcome. Be sure to include the frequency of each outcome in your answer. Then, determine the experimental probability of landing on heads and compare it to the theoretical probability. (3 points)
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The experimental probability of selecting an orange marble is 0.33.
The experimental probability of landing on a number less than 2 is 12 over 60.
The experimental probability of landing on heads is 49%.
The theoretical probability of a fair coin landing on heads is 0.5.
How to calculate the probability?It should be noted that a coin has a head and tail. Therefore, the probability of getting either will be:
= 1/2 = 0.5
Therefore, Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
The statement that compares the theoretical and experimental probability of landing on orange is that the theoretical probability of landing on orange is one fourth, and the experimental probability is 20%.
The experimental probability will be:
= 4/(6+3+7+4)
= 4/20 = 1/5
Based on the given frequency, the experimental probability of selecting an orange marble will be:
= 5/(4+6+5)
= 5/15
= 0.33
The experimental probability of landing on a number less than 2 is 12 over 60.
The experimental probability of landing on heads will be:
= 98/(98 + 102)
= 98/200
= 49%
The theoretical probability of a fair coin landing on heads will be:
= 1/2 = 0.5
Flip a coin 14 times and record the frequency of each outcome gives:
Head, Tail, Head, Head, Head, Tail, Tail, Head, Tail, Tail, Tail, Tail, Head, Head. The theoretical and experimental probability are 0.5.
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NEED URGENT HELP: A random sample is taken of people who have bought tickets for a concert. In the sample, 21 out of 150 people say they will contribute $5.00 each towards a music scholarship for a local high school students. If 3,500 people bought concert tickets, predict how much will be raised for the scholarship.
Answer:
$2,450
Step-by-step explanation:
21:150 is the ratio of people who will donate $5.
21:150 / 3 = 7:50
7:50 x 2 = 14:100
14:100 = 21:50
14:100 x 35 = 490:3500
490 out of 3500 people will contribute $5.
490 x 5 = $2,450
is it true or false! I need help fast thanks!
The answer is True.
On differentiating using product rule,
[tex]\mathsf {\frac{d}{dx}[xe^{x}] = x(e^{x})+e^{x}(1)}[/tex]
[tex]\mathsf {\frac{d}{dx}[xe^{x}] = e^{x}(x + 1)}[/tex]
The general form of product rule :
[tex]\boxed {\frac{d}{dx}(ab) = a(b')+b(a')}[/tex]
Brass is an alloy made by melting and mixing copper and zinc. A metallurgist has two brass
alloys, one that is 65% copper and one that is 90% copper. He would like to combine a
portion of each alloy to produce 500 g of a new alloy that is 75% copper.
Write a system of equations for this problem
Answer:
x +y = 5000.65x +0.95y = 0.75(500)solution: (x, y) = (300, 200)Step-by-step explanation:
A system of equations for the problem can be written using the two given relationships between quantities of brass alloys.
SetupLet x and y represent the quantities in grams of the 65% and 90% alloys used, respectively. There are two relations given in the problem statement.
x + y = 500 . . . . . . quantity of new alloy needed
0.65x +0.90y = 0.75(500) . . . . . quantity of copper in the new alloy
These are the desired system of equations.
SolutionThis problem does not ask for the solution, but it is easily found using substitution for x.
x = 500 -y
0.65(500 -y) +0.90y = 0.75(500)
(0.90 -0.65)y = 500(0.75 -0.65) . . . . . . subtract 0.65(500)
y = 500(0.10/0.25) = 200
x = 500 -200 = 300
300 grams of 65% copper and 200 grams of 90% copper are needed.
a 3 gallon jug of water cost $11.04. what’s the price per cup?
Anderson uses the discriminant to correctly find the number of real solutions of the quadratic equation one-halfx2 4x 8 = 0. which explanation could anderson provide?
Anderson could provide 0.5x2 + 4x + 8 = 0 has exactly one real root if the discriminant is 0,
What is quadratic equation?Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.
What is discriminant?A polynomial's discriminant is a quantity that depends on the coefficients and enables for some root attributes to be inferred without actually computing them. It is actually a polynomial function of the original polynomial's coefficients.
According to the given information:0.5x^2 + 4x + 8 = 0
The discriminant is computed utilizing:
d = b^2 - 4ac
Thus, we have:
d = 4^2 - 4 * 0.5 * 8
Evaluate
d = 0
The equation has only one real root since the discriminant is 0,
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for each reasons it gives you the options to choose: commutative property of addition, associative property of addition, distributive property, and combining like terms
Answer:
associative
combining
commutative
Step-by-step explanation:
1. associative property of addition since the grouping is changed
2. combining like terms since it's the addition of 4 and 6
3. commutative property of addition since it's a change of order
Hazel is measuring two prisms whose bases are squares.
Given the volume V and the base's side length a of the first prism, Hazel uses the formula
h=V/a^2
to compute its height h to be 10 centimeters.
The base of the second prism has the same side length, but has 5 times the volume. What is its height?
The height of the second square base prism is 50 cm.
How to find volume of a square base prism?The volume of the first square base prism is represented as follows:
v = ha²
where
h = heighta = side length of the baseTherefore, the height of the prism is 10 cm.
v = 10a²
Hence, the volume of the initial prism is 5 times the volume. Therefore,
v = 5(10a²)
v = 50a²
Therefore,
50a² = ha²
divide both sides by a²
50a² / a² = ha² / a²
50 = h
h = 50 cm
Therefore, the height of the second square base prism is 50 cm.
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Natalie charges $1,490 per month to rent each of her three rental houses. natalie must pay $5,850 in maintenance costs per house per year. if all three houses are occupied, how much money will natalie earn over seven years? a. $334,250 b. $252,630 c. $84,210 d. $375,480
The correct option is B.
Natalie charges $1490 in rent for each home Per month.
According to given information:Natalie charges $1490 in rent for each home.
Given that Natalie owns three homes, her monthly rent will be:
= $4470 (3 * 1490) dollars.
The annual income Natalie receives from her three homes is
=($12 * $4470)
= $53680.
Natalie spends $5850 a year on maintenance for each home.
The total amount Natalie spends annually to maintain her three homes is therefore:
=(3 * 5850) dollars, which comes to 17550 dollars.
Then Natalie's annual income would be
= [(53640 - 17550) dollars]
= 36090 dollars.
The total amount Natalie made over the course of seven years was
= ($7 * 36090)
=$252630
The correct option is B.
Natalie charges $1490 in rent for each home Per month.
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Answer:B) $252630
Step-by-step explanation:edge
Which of the following equations is an example of inverse variation?
Since this is the result of the second function, hence equations I and II are inverse of each other.
Inverse of a function
Inverse of a function is s a function that serves to undo another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.
Given the function f(x) = 3x
Find its inverse
Replace with y with x
y = 3x
x =3y
Make y the subject of the formula
3y = x
y = x/3
Since this is the result of the second function, hence equations I and II are inverse of each other.
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Airport administrators take a sample of airline baggage and record the number of bags that weigh more than 75 pounds. What are the cases?
In this situation, the cases are the bags or each piece of baggage.
What is a case?In statistics, the word case is used to refer to the individual from which data is collected. For example, in a study about students' performance, the cases are each of the students.
What is the case in this situation?Considering the administrators will need to weight and record each bag, the cases are each piece of baggage.
Note: This question is incomplete; here are the missing options:
A. Number of bags weighing more than 75 pounds.
B. Average weight of the bags.
C. Each piece of baggage.
D. The airport administrators.
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Write the first five terms of the recursively defined sequence. a1 = 6, ak 1 = 1 3 ak2
The first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
For given question,
We have been given the recursive formula of a sequence.
[tex]a_{k+1}=\frac{1}{3}{a_k}^2[/tex]
Also, the first term of the sequence is,
a1 = 6
Substitute k = 1 in given recursive formula.
⇒ [tex]a_{1+1}=\frac{1}{3}{a_1}^2[/tex]
⇒ a2 = 1/3 (6)²
⇒ a2 = (1/3) × 36
⇒ a2 = 12
Substitute k = 2 in given recursive formula.
⇒ [tex]a_{2+1}=\frac{1}{3}{a_2}^2[/tex]
⇒ a3 = (1/3) × (12)²
⇒ a3 = (1/3) × 144
⇒ a3 = 48
Substitute k = 3 in given recursive formula.
⇒ [tex]a_{3+1}=\frac{1}{3}{a_3}^2[/tex]
⇒ a4 = (1/3) × (48)²
⇒ a4 = (1/3) × 2304
⇒ a4 = 768
Substitute k = 4 in given recursive formula.
⇒ [tex]a_{4+1}=\frac{1}{3}{a_4}^2[/tex]
⇒ a5 = (1/3) × (768)²
⇒ a5 = (1/3) × 589824
⇒ a5 = 196608
Therefore, the first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
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