The equation of the quadratic function is x² + x - 6
How to determine the quadratic functionNote that functions are equations, laws or expressions showing the relationship between two variables.
These variables are;
the dependent variableIndependent variableFrom the information given, we have that;
x = 2 and = -3 are the roots
Then,
(x -2)(x + 3)
expand the bracket, we get;
x² + 3x - 2x - 6
collect the like terms, we have;
x² + x - 6
Hence, the equation is x² + x - 6 = 0
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a two-way anova experiment has: factor a with 3 levels factor b with 7 levels 100 replications if we fit the interaction model, how many degrees of freedom for error are there?
The degrees of freedom for error in a two-way ANOVA experiment with 3 levels for factor a, 7 levels for factor b, and 100 replications is 2071.
The degrees of freedom (df) for error in a two-way ANOVA experiment depend on the sample size (n) and the number of parameters estimated in the model.
In a two-way ANOVA experiment, we are interested in modeling the response variable as a function of two factors, a and b, and their interaction. The model can be written as follows:
Yij = μ + αi + βj + (αβ)ij + εij
In general, the df for error can be calculated as follows:
df error = n - k
where k is the number of parameters estimated in the model.
In our case, we have 3 levels for factor a, 7 levels for factor b, and 100 replications. Therefore, the total sample size is n = 3 x 7 x 100 = 2100.
To estimate the parameters in the model, we need to calculate the following:
The overall mean μ
The effect of factor a, αi, for i = 1, 2, 3
The effect of factor b, βj, for j = 1, 2, ..., 7
The interaction effect between factors a and b, (αβ)ij, for i = 1, 2, 3 and j = 1, 2, ..., 7
Therefore, the total number of parameters estimated in the model is
=> k = 1 + 3 + 7 + 3 x 7 = 29.
Finally, we can calculate the df for error as:
df error = n - k = 2100 - 29 = 2071.
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Find the missing variable and indicated
angle measure.
D
X =
7x°
62°
F
E
m
K
Answer:
x = 4
The missing angle is 28°
Step-by-step explanation:
7x + 62 = 90 These angles are complementary which means that they add to 90°
7x + 62 = 90 Subtract 62 from both sides of the equation
7x = 28 Divide both sides by 7
x = 4
The graph of the sales of a new product at a candy store, where x is time in months and y is number sold in hundreds, goes through the points (4, 2) and (6, 8). What is the rate of change.
in candies sold per month?
A 200
B 300
C 400
D 600
The rate of change in candies sold per month can be found by finding the slope of the line that goes through the two points (4, 2) and (6, 8). The slope of a line can be found by using the formula:
slope = (y2 - y1) / (x2 - x1)
Plugging in the values from the two points, we have:
slope = (8 - 2) / (6 - 4) = 6 / 2 = 3
So the rate of change in candies sold per month is 3. This means that the number of candies sold is increasing by 300 (3 * 100) per month. Therefore, the answer is B) 300.
simplify 3 to the -2 power
Answer: 0.1 decimal 1/9 fraction
Step-by-step explanation:
Answer:
0.1 or 1/9 i think so but I am sure
There are 5 slices of pepperoni pizza, 1 slice of sausage pizza, and 3 slices of cheese pizza left. Without looking, Douglas took a slice of pizza, ate it, and then took another slice.
What's the probability of Douglas eating two of the same kinds of pizza?
Answer:
Step-by-step explanation:
well if there are 5 pepperoni pizzas that means that he eats 2 meaning he has 3 pepperoni slices of pizza.
Write a quadratic equation with -1 and 5 as its roots
A quadratic equation with -1 and 5 as its roots is x^2 - 4x - 5 = 0 by multiplying the terms.
The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.
Derive factor from the roots
x = -1 and x = 5
x + 1 = 0 and x - 5 = 0
Now, (x+1)(x-5) = 0
x(x - 5) + 1(x - 5) = 0
x^2 - 5x + x - 5 = 0
x^2 - 4x - 5 = 0
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2) Jane wants to buy some compost. Both Suttons Shop and Greens Garden Shop sell compost. Suttons Shop Bags of compost 20 litres £2.25 each bag £3.25 for 2 bags Jane needs 140 litres of compost. She wants to buy all the compost from the same shop. She wants to buy the compost as cheaply as possible. Which shop should Jane buy the compost from? You must show all your working. Greens Garden Shop Bags of compost 70 litres £4.99 each bag
The cheapest option for Jane is to buy from Suttons Shop, as the total cost is £12, whereas, at Greens Garden Shop, the total cost is £9.98.
To determine the cheapest option, we need to calculate the cost of purchasing 140 liters of compost from each shop.
First, we'll calculate the cost at Suttons Shop:
Jane needs 140 liters of compost, so she needs 140 / 20 = 7 bags of compost.
If she buys 1 bag of compost, it will cost her £2.25.
If she buys 2 bags of compost, it will cost her £3.25.
Since she needs 7 bags of compost, she can buy 3 sets of 2 bags (6 bags) and 1 bag.
So the cost of 6 bags will be 3.25 x 3 = £9.75, and the cost of 1 bag will be 2.25.
The total cost of 7 bags at Suttons Shop will be 9.75 + 2.25 = £12.
Next, we'll calculate the cost at Greens Garden Shop:
Jane needs 140 liters of compost, so she needs 140 / 70 = 2 bags of compost.
Each bag at Greens Garden Shop costs £4.99.
So the total cost of 2 bags at Greens Garden Shop will be 4.99 x 2 = £9.98.
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In the figure, ACCB. D is a point on AB such that CD AB.
Prove that x = y.
Answer: x = y
Step-by-step explanation:
x and y are angles with vertical sides, and angles with vertical sides are always equal
Help please!
I don’t understand how to do any of this.
The answers to the geometry questions are given as follows:
2)
a)
A = 8
b = 10
x = 118°
y = 62°
b)
a = 8
b = 15
y = 50
x = 100°
3)
(a)
∠2 = 25°
3 = 65°
∠4 = 65°
∠5 = 90°
(b)
since SL = 10,
i) LT 10
ii) TM = 10
iii) SM = 10
4)
a) Since m∠118
∠2 = 18°
∠3 = 72°
∠4 = 72°
If FA = 27, then LO = 13.5
5)
a) All the angles in the diagram are equal to ∠45°
b) Line BC = 6√2
c) Line BE = 6
The above are solved using the principles behind the properties of Parallelograms; Rhombus, Rectangle, and Square.
What is the Justification for the above responses?Since the above answers are justified by the qualities or properties of :
Parallelograms; Rhombus, and Rectangle, let's look at them one by one.
2
a)
A = 8 - opposite sides of a parallelogram are equal in length
b = 10 -opposite sides of a parallelogram are equal in length
y = 62° - opposite angles of a parallelogram are of equal measure.
x = 118° - Sum of angles of a parallelogram - 360°. x = (360 - (62*2))/2
= 118°
3)
(a) Here we have a Rhombus.
∠2 = 25° - Opposite angles of a rhombus are equal; Diagonals bisect the angles of a rhombus. Thus ∠1≅∠2
∠3 = 65° - Since diagonals bisect each other at right angles, ∠3 = 180 - (25+90) = 65°
∠4 = 65° - Diagonals bisect the angles of a rhombus. Thus, ∠3≅∠3
∠5 = 90° - [properties of a Rhombus]
(b)
since SL = 10,
i) LT 10 - All sides of a Rhombus are equal
ii) TM = 10 - All sides of a Rhombus are equal
iii) SM = 10 - All sides of a Rhombus are equal
4) Here we have a Rectangle.
a) Since m∠18
∠2 = 18° because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠2≅∠1 (AAS)
∠3 = 72° - Each interior angle is equal to 90 degrees. Thus, m∠ = 90-18 = ∠72°
∠4 = 72° - because The diagonals bisect each other; and both the diagonals have the same length. Thus, m∠4≅∠3(AAS)
If FA = 27, then LO = 13.5 - The diagonals bisect each other.Thus,
LO = FA/2
LO = 27/2
LO = 13.5
5) Here we have a square.
a) All the angles in the diagram are equal to ∠45°. This is because, the diagonals bisect all interior angles. Since each interior angle is 90°, thus, each of the resulting angle bisected 45°
b) Line BC = 6√2 - This is be
c) Line BE = 6
The length of one-half of the diagonal of a square can be found using the Pythagorean theorem, which relates the lengths of the sides of a right triangle.
Let s be the side length of the square. Then, the length of the diagonal of the square (d) can be found using the equation d = s√2.
In this case, s = 6√2. So, the length of the diagonal (d) is:
d = s√2 = (6√2)√2 = 6(√2)(√2) = 6(2) = 12
Therefore, one-half of the diagonal of the square is:
(1/2)d = (1/2)(12) = 6
So, the length of one-half of the diagonal of the square ABCD is 6.
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Keiko was working with a new function, g(x). He wrote down the following steps for g(x):
• Add 5.
• Divide by 2.
• Cube it. (Find the third power.)
Multiply by 6.
a. What is the equation for g(x)? What is the output when 3 is put in?
b. Help Keiko write down the steps (in words) of the inverse machine, g¹(a), and then write its equation.
c. Verify that your equation in part (b) correctly "undoes" the output of g(x) in part (a).
a.) The equation for g(x) is g(x) = 6((x+5)/2)³and output is 384.
b.) The inverse machine, g¹(a), we need to undo each of the four steps in reverse order is g¹(a) = [tex]((a/6)^{(1/3)})*[/tex]2 - 5
c.) To verify that g¹(a) correctly "undoes" the output of g(x), we can plug in the output of g(3) (384) into g¹(a) and see if we get 3 as the result is 3.
What is Function?
A function is a mathematical rule that takes one or more inputs (also called independent variables or arguments) and produces a single output (also called a dependent variable or function value). In other words, a function is a relationship between the inputs and the output, where each input produces a unique output.
Functions can take many different forms and can be used to describe a wide variety of mathematical and real-world phenomena.
a. The equation for g(x) is:
g(x) = 6((x+5)/2)³
When 3 is put in for x, the output is:
g(3) = 6((3+5)/2)³= 6(4)³ = 384
b. To find the inverse machine, g¹(a), we need to undo each of the four steps in reverse order:
Undo step 4: Divide a by 6.Undo step 3: Take the cube root of the result from step 1.Undo step 2: Multiply the result from step 2 by 2.Undo step 1: Subtract 5 from the result from step 3.Putting this in equation form, we get:
g¹(a) = [tex]((a/6)^{(1/3)})[/tex]*2 - 5
c. To verify that g¹(a) correctly "undoes" the output of g(x), we can plug in the output of g(3) (384) into g¹(a) and see if we get 3 as the result:
g¹(384) =[tex]((384/6)^{(1/3)})[/tex]*2 - 5 =[tex](64^{(1/3)})[/tex]2 - 5 = 42 - 5 = 3
Since the output of g¹(a) is 3 when we input the output of g(x), we can conclude that g¹(a) correctly undoes the output of g(x).
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Point W is located at (-5, -3). Select all of the following that are 5 units away from point W
These are the four points that are exactly 5 units away from point W. To find points that are 5 units from point W, which is located at (-5, -3).
To find points that are 5 units from point W, which is located at (-5, -3), we need to find all points that are a distance of 5 units away from (-5, -3) using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the distance between two points) is equal to the sum of the squares of the lengths of the other two sides
Given a point (x, y), the distance between that point and point W can be found using the formula:
distance = sqrt((x + 5)^2 + (y + 3)^2)
Setting this distance equal to 5 and solving for x and y, we get the following points:
(0, -8), (-10, -8), (0, 2), and (-10, 2).
These are the four points that are exactly 5 units away from point W.
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Given two points of a line, slope=
change in___
Over
change in___
Determine if the two are equivalent.choose 3 different values for x and complete the table.Explain your reasoning.X
2(x + 5) + 3x
5x + 10
Answer:
The expressions are identical, as shown by two methods: 1) equation rearrangement and 2) mathematical calculations.
Step-by-step explanation:
2(x + 5) + 3x
Let's simplify this expression.
2(x + 5) + 3x
2x + 10 + 3x [remove parentheses]
5x + 10 [combine like terms]
This matches the other expression.
5x + 10
Several values of x are calculated for both expressions and are shown on the attached table. Each expression results in the same value for a given value of x. This comparison also holds for negative numbers.
a square with area is inscribed in a square with area with one vertex of the smaller square on each side of the larger square. a vertex of the smaller square divides a side of the larger square into two segments, one of length , and the other of length . what is the value of ?
The value of is equal to the length of the side of the larger square minus the sum of the lengths of the two segments.
The value of is equal to the length of the side of the larger square minus the sum of the lengths of the two segments. This is because the area of the smaller square inscribed in the larger square is equal to the product of the side lengths of the smaller square. If a vertex of the smaller square is located on the side of the larger square, the side of the larger square is divided into two segments with one segment having length and the other having length . The side length of the larger square is then equal to the sum of the lengths of the two segments plus the side length of the smaller square, which is . Therefore, the side length of the larger square minus the sum of the lengths of the two segments is equal to the side length of the smaller square, or the value of is equal to two segments.
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Scatter plot, 8 grades help please!!!
Answer: 4 people
Step-by-step explanation:
As you can see the money spent is on one side of the graph and the people attending on the other. Try to go along the line of where 60 is and find where the line meets the line on 60. Look down and you can see 4.
please help if answered correctly ill give the brainiest and all stars and ill cavxsh avxpp u 15 if it's correct.
Hi there, here's your answer:
Before answering this question, we need to know the concept of 'End Behavior'.
What's "end behavior"?
The end behavior of a function [tex]f[/tex] describes the behavior of the graph of the function at the "ends" of the x-axis.
In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞) and to the left end of the x-axis (as x approaches -∞).
Thus, as V approaches negative infinity, V(x) approaches negative infinity.
And
As V approaches infinity, V(x) approaches infinity.
Hope it helps! Please mark as brainliest!
Answer:
Not enought information
Step-by-step explanation:
We need the function in question 1
However, If I had to guess I'd say
1. infinity
2. negative infinity
[tex]-11+6x+25-3x[/tex]
Answer:
If you want it simplified, it is 3x + 14!
Hope it helps!
Graph the inequality below on the number line. a<3
The number line for a < 3 is as shown in the figure below and we use an open circle on 3 and all the numbers to the left of 3 in the number line will be the values of a.
What is a number line?
A number line is a representation of a graduated straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point. The endpoints of this line go on forever.
We can see the values that inequality represents by placing them on a number line. On a number line, inequalities are represented by drawing a straight line and designating the endpoints with either an open or closed circle. An empty circle indicates that the value is not included. A closed circle indicates that the value is included.
Given the inequality a < 3.
This means that the value of a is less than three and does not include three.
Therefore we use an open circle on 3 and all the numbers to the left of 3 in the number line will be the values of a.
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A line has a slope of -2/3 and passes through the point (6, -10). What is the equation of the line?
Answer:
= 3y-2x+18=0
Step-by-step explanation:
Gradient (m) = -2/3
The equation of the line is given by the formula
[tex] = \frac{y - y1}{x - x1} = m[/tex]
Point = (6,-10)
y1 = -10
x= 6.
note// y and x were not given .
=
[tex] = \frac{y - ( - 10)}{x -6} = \frac{ - 2}{3} \\ = \frac{y + 10}{x - 6} = \frac{ - 2}{3} \\ = 3(y + 10) = - 2(x - 6) \\ = 3y + 30 = - 2x + 12 \\ = 3y = - 2x + 12 - 30 \\ = 3y = 2x - 18 \\ = 3y - 2x + 18 = 0[/tex]
therefore the equation of the line = 3y-2x+18=0
The height of a hill, h(x), in a painting can be written as a
function of x, the distance from the left side of the
painting. Both h(x) and x are measured in inches.
h(x) = -(x)(x-13)
Mark this and return
4
What is the height of the hill in the painting 3 inches from
the left side of the picture?
O 6 inches
O
13 inches
O 30 inches
O 150 inches
Save and Exit
Next
Submit
The height of the hill in the painting 3 inches from the left side of the picture is 30 Inches. Option C
How to determine the height
From the information given, we have that;
h(x) represents the height of a hill, h(x), in a paintingx represents the distance from the left side of the paintingBoth the height and the distance are measured in inchesWe also have that the function is;
h(x) =-(x)(x-13)
Given that the distance is 3 inches
Substitute the values, we have;
h(3)= -(3)(3-13)
substract the values
h(3) = (-3)(-10)
multiply the values
h(3) = 30 inches
Hence, the value is 30 inches
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Help me please!!!!!!!
Answer: 1/m^2n^2
Step-by-step explanation: when dividing powers, we subtract.
so, the top would all cancel out
and we would be left with only m^-2n^-2.
to get rid of the negative we put the number into the denominator.
so m^-2n^-2 would become 1/m^2n^2.
Solve the equation -5(y +0.2) = 25.
y =
Answer:
y = -5 [tex]\frac{1}{5}[/tex] o r -5.02 as a decimal
Step-by-step explanation:
-5(y + 0.2) = 25 Distribute the -5
-5(y) + -5(0.2) = 25 Adding a negative is the same as subtracting a positive
-5y - 1 = 25 add 1 to both sides
-5y - 1 + 1 = 25 + 1
-5y = 26 Divide both sides by -5
[tex]\frac{-5y}{-5}[/tex] = [tex]\frac{26}{-5}[/tex]
y = -5 [tex]\frac{1}{5}[/tex] o r -5.02 as a decimal
Answer: To solve the equation -5(y + 0.2) = 25, we need to isolate y by performing the following steps:
Distribute the -5 to the expression inside the parenthesis:
-5 * y - 5 * 0.2 = 25
-5y - 1 = 25
Add 1 to both sides of the equation to isolate -5y on one side:
-5y - 1 + 1 = 25 + 1
-5y = 26
Divide both sides of the equation by -5 to find y:
(-5y) / -5 = 26 / -5
y = -5.2
So, the solution to the equation -5(y + 0.2) = 25 is y = -5.2.
Step-by-step explanation:
Factor 26r³s
O 13(2r³s + 475-37²54)
037²s(27+ 47³-38³)
O 13r²(2rs + 4r3 – 384)
O 13r²(26r³s + 527-5-39²4)
+5275-39724. What is the resulting expression?
The resulting expression of the algebraic expression is 13r²(2rs + 4r³ - 3s⁴).
option C.
What is the resulting expression of the algebraic expression?The resulting expression of the algebraic expression given as
26r³s + 52r^(5) - 39r²s⁴
can be determined by finding the highest common factor here and factorize out.
The highest common factor of the letters is r²
Factors of 26 = 1, 2, 13, 26
Factors of 39 = 1, 3, 13, 39
Factors of 52 = 1, 2, 4, 13, 26, 52
The highest common factor for the 3 numbers is 13.
Thus, in total, the highest common factor for the algebraic expression is 13r².
Finally, we have;
13r²(2rs + 4r³ - 3s⁴)
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The complete question is below:
Factor 26r³s + 52r^(5) - 39r²s⁴
A right triangle has an area of 36 square units if you draw scaled copies of this triangle using the scale factor in the table, what will the areas of these scaled copies be? Explain or show your reasoning
The areas of the scale factors 2, 3, 5, 1/2 and 2/3 are 144, 324, 900, 9 and 16 square units respectively.
The area of the right triangle = 36 square units
Scale factor of each scaled copies of the right triangles are given
Scale factor = 2
Then the area will be = Area at scale factor 1 × square of scale factor
Substitute the values in the equation
Area = 36 × 2^2
= 36 × 4
= 144 square units
Scale factor = 3
Area = 36 × 3^2
= 36 × 9
= 324 square units
Scale factor = 5
Area = 36 × 5^2
= 36 × 25
= 900 square units
Scale factor = 1/2
Area = 36 × (1/2)^2
= 36 × 1/4
= 9 square units
Scale factor = 2/3
Area = 36 × (2/3)^2
= 36 × 4/9
= 16 square units
Therefore, area of the each scale factor has been found
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The given question is incomplete, the complete question is :
A right triangle has an area of 36 square units if you draw scaled copies of this triangle using the scale factor in the table, what will the areas of these scaled copies be?
answer the question below please
The total surface area is π[(4/3)x]² + π(4/3)x². The base area is greater than the lateral area.
What is an equation?An equation is an expression that shows how numbers and variables are related using mathematical operations. Equations can be linear, quadratic, cubic and so on.
Given the cone. The surface area (SA) is given by the equation:
SA = πr² + πrs
where r is the radius of the cone and s is the slant height.
Given that the slant height is x and the radius of the cone is 4/3 the slant height = (4/3)x
Hence:
SA = πr² + πrs
substituting:
SA = π[(4/3)x]² + π(4/3)x(x)
SA = π[(4/3)x]² + π(4/3)x²
The base area = π[(4/3)x]², the lateral area = π(4/3)x²
The base area is greater than the lateral area.
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To raise money for a charity, a Year 10 class has decided to organise a school
luncheon. Tickets will cost $6 each. The students have negotiated a special deal for
delivery of drinks and pizzas, and they have budgeted $200 for drinks and $250 for
pizzas. If they raise $1000 or more, they qualify for a special award.
a) write an equation to represent this situation.
b) solve the equation to find the number of tickets they must sell to qualify for the award. explain your answer.
The equation that represents this situation is $6t - $450 ≥ $1000.
The number of tickets that should be sold is 242.
How many tickets should be sold?The form of the equation is:
total revenue - total cost ≥ $1000
(cost of one ticket x number of tickets sold) - cost of pizza and drinks ≥ $1000
($6 x t) - ($200 + $250) ≥ $1000
$6t - $450 ≥ $1000
$6t ≥ $1000 + $450
$6t ≥ $1450
t ≥ $1450 / 6t
t ≥ 242
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A water well is composed of 28 cements rings with 1.4 m of diameter and 0.2 m height if labour of cost for digging out the well is RS.500 per cubic meter and cost of cement ring is 2500
The total cost of the cement rings for the water well is RS. 70,000. This cost is only for the cement rings and does not include the cost of labour for digging the well.
What is the total cost of the cement rings for the water well?The cost of each cement ring is given as RS. 2500. Since there are 28 cement rings used in the water well, the total cost of the cement rings can be calculated as follows:
Total cost of cement rings = Cost of each cement ring x Number of cement rings used
Total cost of cement rings = 28 x 2500 = RS. 70,000
Volume of the well = [tex]\mathrm{ \pi r^2h = \pi (0.7)^2(5.6) = 9.768m^3 }[/tex]
Cost of digging out the well = 500 x 9.798 = RS. 4,899
Total cost of the well = RS. 74,899
Total cost of cement rings = 2500 x 28 = RS. 70,000
Therefore, the total cost of the cement rings for the water well is RS. 70,000. This cost is only for the cement rings and does not include the cost of labour for digging the well.
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πrl,
curved surface area of a cone =
where r is the radius and is the slant height.
Work out the total surface area of the cone
shown below.
Give your answer to 1 d.p.
33 m
6 m
The total surface area of this cone is equal to 735.1 square meters.
How to calculate total surface area of a cone?Mathematically, the total surface area (TSA) of a cone can be calculated by using this mathematical expression:
Total surface area (TSA) of a cone = πr(l + r)
Where:
l represents the slant height of the cone.r represents the radius of the cone.Substituting the given parameters into the total surface area (TSA) (SA) of a cone formula, we have the following;
Total surface area (TSA) of a cone = πr(l + r)
Total surface area (TSA) of a cone = 3.142 × 6 × (33 + 6)
Total surface area (TSA) of a cone = 3.142 × 6 × (39)
Total surface area (TSA) of a cone = 735.1 square meters.
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A ladder which is 6.9 m long is placed on the ground 2.9 m from a vertical wall and then leaned over to the wall. How high up the wall can the ladder reach? Give your answer rounded to 1 DP.
Not sure but i think it's 6.3.
Pythagoras theorem
a²+b²=c²
6.9 is the hypotenuse (c)
2.9 is the base (b)
a is the altitude of the wall or the height of the wall (a)
a²+2.9²=6.9²
a= 6.3
is (, ) = 3 − 32 an harmonic function? if yes, then find a corresponding analytic function ()
No, f(x, y) = 3x - 3y^2 is not a harmonic function.
A harmonic function is a twice continuously differentiable function f(x, y) that satisfies the Laplace equation:
∂²f/∂x² + ∂²f/∂y² = 0.
Let's check if f(x, y) = 3x - 3y^2 satisfies the Laplace equation:
∂²f/∂x² = ∂/∂x(3) = 0
∂²f/∂y² = ∂/∂y(-6y) = -6
∂²f/∂x² + ∂²f/∂y² = 0 + (-6) = -6 ≠ 0
Since the Laplace equation is not satisfied, f(x, y) = 3x - 3y^2 is not a harmonic function.
As for finding a corresponding analytic function, an analytic function is a function that is locally given by a convergent power series. Since f(x, y) is not a harmonic function, there is no corresponding analytic function.
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