If the function is [tex](x-3)^{-2}[/tex] and f(4) − f(1) = f '(c)(4 − 1) then there is not any answer.
Given function is [tex](x-3)^{-2}[/tex] and f(4) − f(1) = f '(c)(4 − 1).
In this question we have to apply the mean value theorem, which says that given a secant line between points A and B, there is at least a point C that belongs to the curve and the derivative of that curve exists.
We begin by calculating f(2) and f(5):
f(2)=[tex](2-3)^{-2}[/tex]
f(2)=1
f(5)=[tex](5-3)^{-2}[/tex]
f(5)=1
And the slope of the function:
[tex]f^{1}[/tex](x)=[tex]f(5)-f(2)/(5-2)[/tex]
[tex]f^{1}[/tex](c)=0
Now,
[tex]f^{1} (x)=-2*(x-3)^{-3}[/tex]
=-2[tex](x-3)^{-3}[/tex]
=0
-2 is not equal to 0. So there is not any answer.
Hence if the function is [tex](x-3)^{-2}[/tex] and f(4) − f(1) = f '(c)(4 − 1) then there is not any answer.
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If the expression below has a negative value, which inequality represents all possible values of n in the expression?
Answer: B
Step-by-step explanation:
We know N cannot be 0 as the value would not be negative.
We know N cannot be negative as that would make the expression positive.
B is the only answer that works.
A plot of land in the shape of a horizontal ellipse has a pole at each focus. the foci are 16 feet from the center. if the plot of land is 40 feet across one axis, how long is it across the other axis?
If a plot of land in the shape of a horizontal ellipse has a pole at each focus. the foci are 16 feet from the center. if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.
Length across the other axisUsing Pythagoreans theorem formula
a²=b²+c²
Where:
c=16 feet
a=40/2=20 feet
Hence:
20²=b²+16²
b²=20²-16²
b²=400-256
b²=√144
b=12
2b=12×2
2b=24 feet
Therefore if the plot of land is 40 feet across one axis, how long is it across the other axis is: c. 24 feet.
The complete question is are:
A plot of land in the shape of a horizontal ellipse has a pole at each focus. The foci are 16 feet from the center. If the plot of land is 40 feet across one axis, how long is it across the other axis?
a. 34 feet
b. 46 feet
c. 24 feet
d. 30 feet
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Which of the following equations represents the area of a sector?
1.) A360nxr², where n is the central angle of the sector
2.)A = n², where n is the central angle of the sector
n
3.) A= TT, where n is the central angle of the sector
360°
4.) A =
360
T², where n is the central angle of the sector
From the given options we can say that the only one that represents the area of the sector is; A = n/360 * πr²
What is the Area of the Sector?
In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.
The formula for Area of a sector is given as;
θ/360 * πr²
where;
θ is the central angle of the sector
r is radius
Now, looking at the given options we can say that the only one that represents the area of the sector is;
A = n/360 * πr²
where n is the central angle of the sector
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Answer:
A!
Step-by-step explanation:
question down below about linear equations and grapghing.
The system of equations is -x + y = 4 and -2x + y = 0
How to create the system of linear equations?To do this, we make use of the following ordered pairs
(4, 8)
The above point represents April 2008.
Let the system of equations be
mx + ny = 4
2mx + ny = 0
Substitute (4, 8) for x and y in the above equations.
4m + 8n = 4
8m + 8n = 0
Subtract both equations
4m - 8m = 4
This gives
-4m = 4
Divide by 4
m = -1
Substitute m = -1 in 8m + 8n = 0
-8 + 8n = 0
This gives
8n = 8
Divide by 8
n = 1
So, the system of equations is -x + y = 4 and -2x + y = 0
The graph of the system of equationsThe system of equations is -x + y = 4 and -2x + y = 0
See attachment for the graph of the system of equation
Prove that the solution is (4, 8)The above is represented in the (a) part of this solution
Verify that the solution is (4, 8)
We have:
-x + y = 4 and -2x + y = 0
Substitute (4, 8) for x and y in the above equations.
-4 + 8 = 4 --- true
-2*4 + 8 = 0 --- true
Both equations are true
Hence, the system of equations have been verified
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PLEASE HELP!!! This table shows the profit for a company (in millions of dollars) in different years. The quadratic regression equation that models these data is y=-0.34x^2+4.43x +3.46. Using the quadratic regression equation, what was the predicted profit in year 4?
Answer:
15740000 million dollars in profit in year 4
Step-by-step explanation:
Now since you didn't provide the table, im going to have to assume the years are going to be the X while the Y is going to be profit.
Using the equation you provided y=-0.34x^2+4.43x +3.46, we can simply put 4 as our x value (since x represents years) and we would get 15.74. Now you have to remember to convert it into millions to show the profit so 15.74 times 1,000,000 would be 15740000 million dollars
25. A chocolate bar which weighs of a pound is 9/16 cut into seven equal parts. How much do three parts weigh? (A) pound 21/112 (B) pound/27/112 (C) pound 16/63 (D) pound 47/63
The three parts weigh 27/112 pound ( letter B).
Rules for Multiplication and Division of FractionsFor Multiplication - First, you should multiply both numerators after that you should multiply both denominators. Finally, you can simplify if it is necessary.For Division- First, you should repeat the numerator and after that you should multiply the numerator by the reciprocal of denominators. Finally, you can simplify if it is necessary.The question gives:
A chocolate bar that weighs = 9/16A chocolate bar cut into seven equal parts.Therefore, each part will be [tex]\frac{\frac{9}{16} }{7} =\frac{9}{16} *\frac{1}{7} =\frac{9}{112}[/tex].
For knowing the three parts weigh, you should mulitiply the previous value for 3. Thus,
[tex]\frac{9}{112}*3=\frac{27}{112}[/tex].
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The weight of three parts is 27/112 pounds
How to determine the weight of three parts?The weight of the chocolate bar is given as:
Weight = 9/16
When it is cut into 7 equal parts, the weight of each part is
Each = Weight/7
This gives
Each = 9/16 * 1/7
Evaluate the product
Each = 9/112
The weight of three parts is then calculated as:
Three parts = Each * 3
This gives
Three parts = 9/112 * 3
Evaluate the product
Three parts = 27/112
Hence, the weight of three parts is 27/112 pounds
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In a grade 11 class there are 30 learners. 16 of them are girls. there are 7 girls and 6 boys with blue eyes. a student is selected at random tone the class monitor what is the probability that the class monitor is a girl
Answer:
8/15
Step-by-step explanation:
possibilities/ sample size=16 girls/30 "learners"=8/15
A tape diagram. There are 65 students out of 100 students who ride the bus. There are question mark students out of 800 students who ride the bus.
65% of the 800 students at North High School ride the bus. How many students ride the bus?
Answer:
800÷100 = 8
65×8=520
[tex]\frac{520}{800}[/tex]
another way:
100%-65%=35%
35% = 0.35
800×0.35= 280
800-280=520
another way:
65% = 0.65
0.65×800=520
Hope it helped! :)
Explain the steps for moving three disks from one peg to another. start with moving the small disk to the right peg.
There are some ways by which move the steps from sequence and series method like
Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.
According to the statement
we have to explain the moving steps to change the position of the given three disk from one peg to another.
So, for the solution of this problem
Firstly we know that the sequence and series
An itemized collection of elements in which repetitions of any sort are allowed is known as a sequence, whereas series is the sum of all elements.
we have to use the sequence and series method.
So, according to this method
Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.
So, there are some ways by which move the steps from sequence and series method like
Move the medium desk to the left peg. Move the small desk to the left peg. Move the large desk to the right peg. With the small disc to the middle peg. Move the middle desk to the right peg. With the small desk to the right peg.
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Peanuts cost 6.40 per kg what is the cost of 400 g peanuts
Answer:
$25.60
Step-by-step explanation:
1 kg = 1000 grams
peanuts = 6.40 per kg = 0.064 per grams
0.064*400 = 25.6
Please help me with these problems, if you give an answer without work or isn’t correct I will report your comment and you won’t get points
The angles and side lengths for both triangles are;
3) A = 36°; B = 54°; C = 90°; a = 7; b = 9.63; c = 4.11
4) A = 64°; B = 26°; C = 90°; a = 1.798; b = 0.88; c = 2
How to solve Pythagoras theorem?
3) From the diagram, we are already given;
B = 54°
C = 90°
a = 7
We know that sum of angles in a triangle is 180° and so;
A = 180 - (90 + 54)
A = 36°
By trigonometric ratios;
b/7 = tan 54
b = 7 * tan 54
b = 7 * 1.376
b = 9.63
7/c = cos 54
c = 7 * cos 54
c = 4.11
4) From the diagram, we are already given;
B = 26°
C = 90°
c = 2
We know that sum of angles in a triangle is 180° and so;
A = 180 - (90 + 26)
A = 64°
By trigonometric ratios;
b/2 = sin 26
b = 2 * sin 26
b = 2 * 0.4384
b = 0.88
a/2 = cos 26
a = 2 * cos 26
a = 1.798
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Find the length of one edge of a cube if its lateral surface area is 144 square centimeters. a. 4 cm b. 8 cm c. 6 cm d. 3 cm
The length of one edge of the cube exists 6 centimeters.
What is the lateral surface area of a cube?The lateral surface area of a cube exists
[tex]$A=4 a^{5}$[/tex]
where a stands the length of one edge of a cube.
It exists given that the lateral surface area of the square stands at 144 square centimeters.
Substitute A = 144 in the above formula.
[tex]$144=4 a^{2}[/tex]
Divide both sides by 4.
[tex]$36=a^{2}[/tex]
Taking square root on both sides.
[tex]$\sqrt{36}=\sqrt{a^{2}}[/tex]
6 = a
The length of one edge of the cube exists 6 centimeters.
Therefore, the correct answer is option c. 6 cm.
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How do I solve “1+2+3+4+5+…100=“
A. 1010
B. 5050
C. 5000
D. 1000
Answer:
5050
Step-by-step explanation:
we know that 100/2 is 50 and 50 x 100 is 5000
so now another 50 is remaining but we can't multiply but add so
1+2+3+4+5...100 = in simple form= 50x100+50=5050//
Nuber 17 pls (question on quadratics)
Considering the equation of the parabola, the coefficients are given as follows: p = 5, q = -20, r = 19.
The graph is the one given at the side of the question.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the turning point is (2,-1), hence h = 2, k = -1, and the equation has the following format:
y = a(x - 2)² - 1
The curve passes through (3,4), that is, when x = 3, y = 4, and we use it to find a.
y = a(x - 2)² - 1
4 = a(3 - 2)² - 1
a = 5.
Hence the equation is:
y = 5(x - 2)² - 1
Placing it into standard form, we have that:
y = 5(x² - 4x + 4) - 1
y = 5x² - 20x + 19
Hence the coefficients are:
p = 5, q = -20, r = 19.
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20 points please help
The data set below has 7 values. Find the mean absolute deviation for the data set. If necessary, round your answer to the nearest hundredth. 14, 13, 16, 12, 17, 21, 26
Answer:
3.71
Step-by-step explanation:
The mean absolute deviation(MAD) of a data set is given by the formula
[tex]$ MAD =\frac{1}{n} \sum_{i=1}^n |x_i-\bar{x}|$[/tex]
[tex]n[/tex] = number of data set values. Here [tex]n = 7[/tex]
[tex]\bar{x}=[/tex] mean of the data set values; [tex]\bar{x}=[/tex] [tex](14+13+16+12+17+21+26)/7[/tex] = [tex]119/7=17[/tex]
[tex]x_{i}[/tex] are the n individual values
[tex]\frac{1}{7} |14-17| + |13-17| + |16-17| + |12-17| + |17-17| + |21-17| + |26-17|\\= (3 + 4 + 5 + 1+ 0 + 4 + 9)/7\\= 26/7 = 3.71428 \\[/tex]
= [tex]3.71 \textrm{ rounded to the nearest hundredth}[/tex] Answer
Can someone pls help me get the anwser for this question
Answer: [tex]\Large\boxed{x=6.5}[/tex]
Step-by-step explanation:
Given equation
-9 - (x + 1) = -2 - (3x - 5)
Expand the parenthesis
-9 - x - 1 = -2 - 3x + 5
Combine like terms
-9 - 1 - x = -2 + 5 - 3x
-10 - x = 3 - 3x
Add 3x on both sides
-10 - x + 3x = 3 - 3x + 3x
-10 + 2x = 3
Add 10 on both sides
-10 + 2x + 10 = 3 + 10
2x = 13
Divide 2 on both sides
2x / 2 = 13 / 2
[tex]\Large\boxed{x=6.5}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
(08.01 mc) sue wants to know how many families in her small neighborhood of 50 homes would volunteer to help at a neighborhood animal shelter. she put all the addresses in a bag and drew a random sample of 25 addresses. she then asked those families if they would volunteer to help at the shelter. she found that 18% of the families would volunteer to help at the shelter. she claims that 18% of the neighborhood families would be expected to help at the animal shelter. is this a valid inference?
Answer:
Yes, this is a valid inference because she took a random sample of the neighborhood.
Step-by-step explanation:
As we can see, Sue's survey was perfectly random and without any prejudice.
18% of the families, according to her research, would volunteer at the shelter. According to her, 18% of the local households should be required to volunteer at the animal shelter.
Therefore, given that she chose a representative sample of the area, her conclusion is valid.
Urgent Help please: My neighbor just got two new cats and now she has more than 5 cats. How many cats did she have before?
Answer:
Wouldn't she have had 5 cats before? Adding 2 other cats would make it 7, which fits the "more than 5 cats" requirement.
Frank went to the playground at 5:20 P.M. He played on the slide for 45 minutes and the swings for 5 minutes, then went home. What time was it when Frank left the playground?
The time it was when Frank left the playground is; 6:10 PM.
How to calculate time difference?We are given;
Time at which Frank went to the playground; 5:20 p.m
Amount of time that frank played on the slide = 45 minutes
Amount of time that frank swings on the play ground = 5 minutes
Now, we are told that after he played on the slide and swung on the playground, that he went home.
Thus, he spent a total time of 45 + 5 = 50 minutes on the playground before going home.
Thus, time he went home = 5:20 p.m + 50 minutes = 6:10 p.m
Thus, we can conclude that the time it was when Frank left the playground is; 6:10 PM.
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Find the taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0. ] f(x) = ln x, a = 9
Taylor series is [tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]
To find the Taylor series for f(x) = ln(x) centering at 9, we need to observe the pattern for the first four derivatives of f(x). From there, we can create a general equation for f(n). Starting with f(x), we have
f(x) = ln(x)
[tex]f^{1}(x)= \frac{1}{x} \\f^{2}(x)= -\frac{1}{x^{2} }\\f^{3}(x)= -\frac{2}{x^{3} }\\f^{4}(x)= \frac{-6}{x^{4} }[/tex]
.
.
.
Since we need to have it centered at 9, we must take the value of f(9), and so on.
f(9) = ln(9)
[tex]f^{1}(9)= \frac{1}{9} \\f^{2}(9)= -\frac{1}{9^{2} }\\f^{3}(x)= -\frac{1(2)}{9^{3} }\\f^{4}(x)= \frac{-1(2)(3)}{9^{4} }[/tex]
.
.
.
Following the pattern, we can see that for [tex]f^{n}(x)[/tex],
[tex]f^{n}(x)=(-1)^{n-1}\frac{1.2.3.4.5...........(n-1)}{9^{n} } \\f^{n}(x)=(-1)^{n-1}\frac{(n-1)!}{9^{n}}[/tex]
This applies for n ≥ 1, Expressing f(x) in summation, we have
[tex]\sum_{n=0}^{\infinite} \frac{f^{n}(9) }{n!} (x-9)^{2}[/tex]
Combining ln2 with the rest of series, we have
[tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]
Taylor series is [tex]f(x) = ln2 + \sum_{n=1)^{\infty}(-1)^{n-1} \frac{(n-1)!}{n!(9)^{n}(x9)^{2} }[/tex]
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system of equations 9x+8y=-19 ; 7x+9y=-12
Answer:
(-3,1)
Step-by-step explanation:
9x+8y=-19
7x+9y=-12
I'll assume the question is to find the solution to these equations. The solution will be the point (x,y) where the two lines intersect. The intersection is the one point that satisfies both equations (the smae value of (x,y) works in both.
We can either solve matematically of graph to find the intersection. I'll do both, and hope the answers are identical.
Matematically
Rearrange either equation to isolate one of the variables (either x or y). I'll take the second and isolate x:
7x+9y=-12
7x = -9y - 12
x = (-9y - 12)/7
Now use this definition of x in the other equation:
9x+8y=-19
9((-9y - 12)/7) + 8y = -19
(-81y - 108)/7 + 8y = -19
-81y - 108 + 56y = - 133
-25y = -25
y = 1
If y = 1, then:
9x+8y=-19
9x+8(1)=-19
9x = -27
x = -3
The solution is (-3,1)
Graphing
Graph both lines and look for the intersection. The attached graph shows the lines cross at (-3,1).
The solution, bu both approachjes, is (-3,1)
A system of linear equations is shown below, where A and B are real numbers.
3x + 4y = A
Bx – 6y = 15
What values could A and B be for this system to have no solutions?
Answer:
A = 0; B = -9/2
Step-by-step explanation:
To have no solutions, you need parallel lines with equal slopes and different y-intercepts.
3x + 4y = A Eq. 1
Bx - 6y = 15 Eq. 2
In Eq. 1, notice that the coefficient of x is 3/4 of the coefficient of y.
We must have the same ratio for the coefficients in Eq. 2.
B/(-6) = 3/4
4B = -6(3)
4B = -18
B = -9/2
Now we have
3x + 4y = A Eq. 1
-9/2 x - 6y = 15 Eq. 2
How do we change the left side of the second equation into the left side of the first equation? -6/4 = -3/2 and also -9/2 ÷ 3 = -3/2
To change the left side of the second equation into the left side of the first equation, divide the left side by -3/2.
If we divide 15 by -3/2 we get -10.
The equation -9/2 x - 6y = -10 is the same as Eq. 1, so that would create a system of equations with only one equation and an infinite number of answers.
To have no equations, the y-intercepts must be different, so A can be any number other that -10.
Answer: A = 0; B = -9/2
3(x - 5) = 2(x - 5) + x
Solve for x please helppp
Answer: No solution
Distribute the parenthesis
3x-15=2x-10+x
Combine like terms
3x-15=3x-10
This answer has no solution for x.
Exponential Growth
Find f(4), where f(x) = 3x.
f(x) = 3^x
f(4) = 3^4
f(4) = 3 * 3 * 3 * 3
f(4) = 9 * 9
f(4) = 81
Hope this helps!
What is the euclidean distance between x(3,2,5) and y(2,3,3) in three dimensional space?
a) 4
b) 2. 45
c) 3
d) 1. 5
Answer:
b) 2.45
Step-by-step explanation:
The Euclidean distance in 3-space is the root of the sum of the squares of the x-, y-, and z-differences between the points.
ApplicationFor the given points ...
[tex]x(3,2,5)=(x_1,y_1,z_1)\quad\textsf{and}\quad y(2,3,3)=(x_2,y_2,z_2)[/tex]
The distance between x and y is ...
[tex]d=\sqrt{(x_2-x_1)^2+(y_2=y_1)^2+(z_2-z_1)^2}\\\\d=\sqrt{(2-3)^2+(3-2)^2+(3-5)^2}=\sqrt{1+1+4}\\\\d=\sqrt{6}\approx2.45[/tex]
5a<2a is a negative or positive
Answer:
Positive
Step-by-step explanation:
5a < 2a
Divide 2 on both sides
5/2a < a
2x-1, x < 2 12. Show that f(x) = { 3x 2 x ≥ 2 is continuous.
Using the continuity concept, since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
The definition of the piecewise function is given by:
f(x) = 2x - 1, x < 2.f(x) = 3x/2, x >= 2.Since the definition of the function changes at x = 2, and the domain of the function has no restrictions, this is the only point in which there may be a discontinuity.
The lateral limits are:
[tex]\lim_{x \rightarrow 2^-} f(x) = \lim_{x \rightarrow 2} 2x - 1 = 2(2) - 1 = 3[/tex].[tex]\lim_{x \rightarrow 2^+} f(x) = \lim_{x \rightarrow 2} 1.5x = 1.5(2) = 3[/tex].The numeric value is:
f(2) = 1.5 x 2 = 3.
Since the lateral limits and the numeric value of the function are equal at the point in which the definition changes, the function is continuous.
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Instructions: Find the surface area of
each figure. Round your answers to the
nearest tenth, if necessary.
Surface Area:
5.2 cm.
cm²
Answer:
Given is radius of circle that is 5.2, you just need to find the area of the circle.
To find the are of circle is A=πr2
π value is 3.14 and radius value is 5.2 you just need to square the 5.2, answer will come 27.04
now multiply the πr and 27.04.
the answer will come 84.9 and question says to round to the nearest tenth, that will be 85.
Rounding to the nearest tenth, the surface area of the circle with a 5.2 cm radius is approximately 84.8 cm².
The surface area of a circle can be calculated using the formula:
Surface Area = π * radius²
where π (pi) is a mathematical constant approximately equal to 3.14159, and the radius is the distance from the center of the circle to any point on its edge.
Given the radius is 5.2 cm, we can now calculate the surface area:
Surface Area = 3.14159 * (5.2 cm)²
Surface Area = 3.14159 * 27.04 cm²
Surface Area ≈ 84.823 cm²
The surface area represents the total area of the circle's two-dimensional space. In this case, it gives us the total area of the circular region with a 5.2 cm radius.
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In two or more complete sentences, identify the parent function, and describe the transformations that were applied to
obtain the graph, f(x) = √2x+6 -1
The nth term of a sequence is given by 3n² + 11 Calculate the difference between the 6th term and the 9th term of the sequence.
The difference between the 6th term and the 9th term of the sequence is 135
How to determine the difference
Given that the nth term is;
3n² + 11
For the 6th term, the value of n is 6
Let's solve for the 6th term
= 3( 6)^2 + 11
= 3 × 36 + 11
= 108 + 11
= 119
For the 9th term, n = 9
= 3 (9)^2 + 11
= 3( 81) + 11
= 243 + 11
= 254
The difference between the 6th and 9th term
= 254 - 119
= 135
Thus, the difference between the 6th term and the 9th term of the sequence is 135
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