What is the domain of G?

Answer:

To approximate the total number of people in the park at 6 p.m. using a midpoint Riemann sum with three equal subintervals, we need to first determine the width of each subinterval.

Since we want to approximate the number of people in the park at 6 p.m., which corresponds to t=6, and t=0 corresponds to 12 p.m., we have a total time interval of 6 hours. Dividing this by three equal subintervals gives us a width of 2 hours per subinterval.

Next, we need to evaluate the function at the midpoint of each subinterval and multiply it by the width of the subinterval. Then we sum up these values to obtain our approximation.

Using the midpoint of the first subinterval, which is at t=1, we have:

R(1.5) = 0.2(1.5^3) - 0.6(1.5^2) + 0.5(1.5) + 0.3

= 0.825

Using the midpoint of the second subinterval, which is at t=3, we have:

R(3.5) = 0.2(3.5^3) - 0.6(3.5^2) + 0.5(3.5) + 0.3

= 1.975

Using the midpoint of the third subinterval, which is at t=5, we have:

R(5.5) = 0.2(5.5^3) - 0.6(5.5^2) + 0.5(5.5) + 0.3

= 3.375

Finally, we add up these values, multiplied by the width of each subinterval, to obtain our approximation:

(2 hours/subinterval)[R(1.5) + R(3.5) + R(5.5)]

= (2/3)[0.825 + 1.975 + 3.375]

= 4.725

Therefore, the total number of people in the park at 6 p.m., in hundreds, is approximately 4.725.

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The sample size needed to obtain a 99% confidence interval with a margin of error of 0.05 for the true proportion of homes in the city that are heated by oil is 666.

To calculate the required sample size, we need to use the formula n = [tex](z^2 * p * q) / e^2[/tex], where z is the z-score for the desired confidence level (2.58 for 99% confidence), p is the estimated proportion of homes heated by oil, q is 1-p, and e is the desired margin of error (0.05).

Using the information given in the question, we can estimate p as 0.5 (assuming equal probability of homes being heated by oil or other means) and q as 0.5. Plugging these values into the formula, we get n = [tex](2.58^2 * 0.5 * 0.5) / 0.05^2[/tex], which simplifies to n = 665.64. Therefore, we would need a sample size of at least 666 homes to obtain a 99% confidence interval with a margin of error of 0.05 for the true proportion of homes in the city that are heated by oil.

Thus, the answer is 666.

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The value of x in this triangle is approximately 5.83.

We can use the Pythagorean theorem to find the value of x.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

In this triangle, the hypotenuse is x, and the other two sides have lengths 3 and 5. So we have:

x² = 3² + 5²

x² = 9 + 25

x² = 34

Taking the square root of both sides, we get:

x = √34

So, the value of x in this triangle is approximately 5.83.

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The numerical value of the slope for the least squares regression line

is -2.95.

What is slope?

In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.

To find the slope for the least-squares regression line, we need to use the formula: slope = r * (SDy / SDx)

where r is the correlation coefficient, SDy is the standard deviation of the y-values, and SDx is the standard deviation of the x-values.

To calculate the slope, we first need to calculate the mean and standard deviation of the weight (x) and tail length (y) values.

x-bar = (20.8 + 19.1 + 15.9 + 16.7 + 15.7) / 5 = 17.64

y-bar = (82.5 + 82.5 + 67.0 + 70.5 + 73.5) / 5 = 75

Using these values, we can calculate the standard deviations:

SDx = sqrt(((20.8 - 17.64)² + (19.1 - 17.64)² + (15.9 - 17.64)² + (16.7 - 17.64)² + (15.7 - 17.64)²) / 4) = 2.066

SDy = sqrt(((82.5 - 75)² + (82.5 - 75)² + (67 - 75)² + (70.5 - 75)² + (73.5 - 75)²) / 4) = 6.889

Next, we need to calculate the correlation coefficient (r).

r = [((20.8-17.64) * (82.5-75)) + ((19.1-17.64) * (82.5-75)) + ((15.9-17.64) * (67-75)) + ((16.7-17.64) * (70.5-75)) + ((15.7-17.64) * (73.5-75))] / [sqrt(((20.8-17.64)² + (19.1-17.64)² + (15.9-17.64)² + (16.7-17.64)² + (15.7-17.64)²) * ((82.5-75)² + (82.5-75)² + (67-75)² + (70.5-75)² + (73.5-75)²))]

r = -0.883

Now we can calculate the slope:

slope = r * (SDy / SDx) = -0.883 * (6.889 / 2.066) = -2.95

Therefore, the numerical value of the slope for the least squares regression line is -2.95.

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Answer:

500 × P(blue marble) = 500 × 14/50 = 140

500 × P(red marble) = 500 × 30/50 = 300

Based on the results, the best number of predictions Paola will draw a red marble or a blue marble is 440 times in 500 trials.

The interval of convergence is (6,8). The interval of convergence, we need to test the endpoints x = 6 and x = 8.

To find the radius of convergence, we can use the formula:

R = 1/lim sup |an|^(1/n)

Here, an = (x-7)^n(n^3+1)

Taking the limit superior of |an|^(1/n), we get:

lim sup |an|^(1/n) = lim sup |(x-7)^n(n^3+1)|^(1/n)

= lim sup |x-7|(n^3+1)^(1/n)

= |x-7| lim sup (n^3+1)^(1/n)

Now, we know that lim (n^3+1)^(1/n) = 1, so:

lim sup (n^3+1)^(1/n) = 1

Therefore, we have:

R = 1/lim sup |an|^(1/n) = 1/lim sup |x-7|(n^3+1)^(1/n) = 1/|x-7|

Thus, the radius of convergence is R = 1/|x-7|.

To find the interval of convergence, we need to test the endpoints x = 6 and x = 8.

When x = 6, we have:

∑(x-7)^n(n^3+1) = ∑(-1)^n(n^3+1)

= -1 + 2 - 3 + 4 - 5 + ...

which diverges by the alternating series test. Therefore, the series diverges when x = 6.

When x = 8, we have:

∑(x-7)^n(n^3+1) = ∑1^(n)(n^3+1)

= ∑n^3 + ∑1

= (1/4)(n(n+1))^2 + n

which diverges by the p-series test. Therefore, the series diverges when x = 8. Thus, the interval of convergence is (6,8).

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The correct function for the graph of dotted line is,

⇒ y = -  (x - 2)² + 3

We have to given that;

The function f (x) = x² is shown in image.

Here, The dotted graph is translation of f (x) = x² by 3 units up, 2 units right and jus opposite to f (x) = x²

Hence, The correct function for the graph of dotted line is,

⇒ y = -  (x - 2)² + 3

Thus, After translation, The correct function for the graph of dotted line is,

⇒ y = -  (x - 2)² + 3

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f(x)= x³− 6x²− 15x the maximum value of f on the interval [0,6] is 0

f(x) = x³− 6x²− 15x

F(x) = 3x² - 12x - 15

For maximum value f'(x) = 0

3x² - 12x - 15 = 0

3x² + 3x - 15x -15 = 0

3x(x + 1)-15(x+1)=0

(3x-15)(x+1) = 0

x = -1 and x = 5

f(x) is decreasing (-∞,-1) ∪ (5,∞)

f(x) is increasing (-1,5)

x ∈ [0,6]

f(0) = 0

f(6) = 6³ - 6(6)² -15(6)

f(6) = -90

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Answer:

Answer is as follows

Step-by-step explanation:

a. The probability of choosing a blue marble can be found by dividing the number of blue marbles by the total number of marbles in the jar. So the probability of choosing a blue marble is:

P(blue) = 4/18 = 2/9

b. Similarly, the probability of choosing a green marble is:

P(green) = 4/18 = 2/9

c. There are no black marbles in the jar, so the probability of choosing a black marble is 0.

Answer:

Blue marbles: [tex]\frac{2}{9}[/tex]

Green marble: [tex]\frac{2}{9}[/tex]

Black marble: [tex]0[/tex]

Step-by-step explanation:

It is given that a jar contains 4 blue, 4 green, 7 yellow, and 3 red marbles, for a total of 18 marbles in all. To solve for probability, you will put the part of what you are solving for (in this case, a certain color marble) over the whole (which includes all colors of the marble together).

a. What is the probability of choosing a blue marble?

It is given to us that there are 4 blue marbles total in the given jar. Therefore, the fraction of blue marbles/all marbles will be 4/18.

You may be asked to simplify. Simplify fractions by dividing common factors. The common factor in this case will be 2:

[tex]\frac{(\frac{4}{18})}{\frac{2}{2}} = {\frac{2}{9}[/tex]

[tex]\frac{2}{9}[/tex] is your probability for blue marbles.

b. What is the probability of choosing a green marble?

It is given to us that there are 4 green marbles total in the given jar. Therefore, the process will be the same as blue, meaning that your answer is 2/9 simplified:

[tex]\frac{\frac{4}{18}}{\frac{2}{2}} = \frac{2}{9}[/tex]

[tex]\frac{2}{9}[/tex] is your answer.

c. What is the probability of choosing a black marble?

There are no black marbles in the given set (the colors being blue, green, yellow, and red). Therefore, within the given set, there will be no chance of obtaining a black marble.

[tex]0[/tex] is your answer.

~

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tan theta=1/√3

2×1/√3/1-1/3

=2/√3÷2/3

=√3

Answer:

2

Step-by-step explanation:

tanθ+

tanθ

1

=2

Squaring both sides, we get

⇒(tanθ+

tanθ

1

)

2

=4

⇒tan

2

θ+

tan

2

θ

1

+2.tanθ.

tanθ

1

=4

⇒tan

2

θ+

tan

2

θ

1

+2=4

⇒tan

2

θ+

tan

2

θ

1

=2

Hence, the answer is 2.

The larger hospital to more closely match the population value

The binomial distribution, is a probability distribution that describes the number of successes (in this case, female births) in a fixed number of independent trials (in this case, the number of babies born in a week) when the probability of success is constant (in this case, 0.5).

Use the expected value of the binomial distribution to calculate the number of female births we expect in each hospital in a week, assuming that the probability of a baby being female is 0.5.

Here we have

Akron ohio is served by two hospitals.

In the larger hospital, about 50 babies are born each day, and in the smaller hospital, about 25 babies are born each day in the U.S about 50% of all babies born are girls.

Here can use the binomial distribution to calculate the expected number of female births in each hospital in a week, assuming that the probability of a baby being female is 0.5.

For the larger hospital, we expect 50 x 7 to be born in a week.

Hence, the expected number of female births = 0.5 x 350 = 175.

For the smaller hospital, we expect 25 x 7 to be born in a week.

Hence, the number of female births is therefore 0.5 x 175 = 87.5.

Since the expected number of female births in the larger hospital is closer to the population value of 50%, we expect the larger hospital to more closely match the population value.  

Therefore,

The larger hospital to more closely match the population value

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The calculated value of the commission percentage is 4%

From the question, we have the following parameters that can be used in our computation:

Hourly rate = $15

Commission = x%

So, the function of the earnings is

f(x) = x% * 1400 + Hourly rate * Number of hours

This gives

When the total earning is 176, we have

x% * 1400 + 15 * 8 = 176

This gives

x% * 1400 + 120 = 176

So, we have

x% * 1400= 56

Divide

x = 4

Hence, the commission percentage is 4%

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We divide both sides by 8, which yields -2 = x. This means that x is equal to -2, the correct answer is B) x = -2.

To solve the equation -9x + 1 = -x + 17, we can simplify and isolate the variable x.

First, let's combine like terms by adding 9x to both sides:

-9x + 9x + 1 = -x + 9x + 17

Simplifying further:

1 = 8x + 17

Next, let's isolate the variable x by subtracting 17 from both sides:

1 - 17 = 8x + 17 - 17

Simplifying again:

-16 = 8x

To solve for x, we divide both sides by 8:

-16/8 = 8x/8

-2 = x

Therefore, the solution to the equation -9x + 1 = -x + 17 is x = -2.

To solve the equation, we want to isolate the variable x on one side of the equation. We start by combining like terms. By adding 9x to both sides, we eliminate the variable terms on the left side, resulting in 1 = 8x + 17.

Next, we isolate the variable x by subtracting 17 from both sides. This simplifies the equation to -16 = 8x.

To solve for x, we divide both sides by 8, which yields -2 = x. This means that x is equal to -2. Therefore, the correct answer is B) x = -2.

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The slope and intercept values of the data obtained from the graph given are 11.11 and 80 respectively.

Slope = change in y-axis / change in x - axis

Slope = (400 - 200) / (30 - 12)

Slope = 200 / 18

Slope = 11.11

The intercept of the line is the point where the line of best fit intersects the x-axis of the graph. From the plot, the intercept is 80.

Therefore, the slope and intercept values of the data are 11.11 and 80 respectively.

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The ideal graphical depiction for the state's 13-year-old population's heights would be a histogram.

A histogram is a sort of bar graph that shows how continuous or discrete data are distributed. It is made up of bars that stand in for various data ranges or intervals, with the height of each bar indicating the frequency or relative frequency of the data included inside that range.

It is possible that the data acquired contains a variety of different heights because the nutritionist received information from a random sample of 400 pediatricians. The dietitian can see the height distribution and spot any trends, clusters, or gaps in the data by utilizing a histogram. This graphical representation makes it possible to see how all the state's 13-year-old population is distributed.

Therefore, the best graphical representation would be a histogram.

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Answer:

Step-by-step explanation:

The depth underground would be represented by 260. This integer is the opposite of 60, the

above ground height.

The option with the correct factor of 12ax² - 3a is option C) 3a.

Given the expression in the question:

12ax² - 3a

To factor the expression 12ax² - 3a, we can begin by factoring out the greatest common factor, which is 3a:

12ax² - 3a = 3a(4x² - 1)

Next, we can recognize that the expression 4x² - 1 is a difference of squares, which can be factored as follows:

a² - b² = ( a + b )( a - b )

Hence:

4x² - 1 = (2x)² - 1² = ( 2x + 1 )( 2x - 1 )

Therefore, the factors of 12ax² - 3a are 3a(2x + 1)(2x - 1).

Option C) 3a is the correct answer.

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The number of gallons needed to fill 3/4 of the bathtub is 123 gallons. Option C.

To calculate the number of gallons of water needed to fill 3/4 of the bathtub, we need to find the volume of 3/4 of the rectangular prism-shaped bathtub and then convert that volume into gallons.

Given dimensions of the bathtub:

Width = 30 inches

Length = 60 inches

Depth = 21 inches

Volume of the bathtub = Width × Length × Depth

Volume = 30 inches × 60 inches × 21 inches

Volume in cubic feet = (30 inches × 60 inches × 21 inches) / ([tex]12^3[/tex])

Volume of 3/4 of the bathtub = (3/4) × [(30 inches × 60 inches × 21 inches) / ([tex]12^3[/tex])]

Now, to convert the volume from cubic feet to gallons, we multiply by the conversion factor of 7.48 gallons per cubic foot:

Volume in gallons = (3/4) × [(30 inches × 60 inches × 21 inches) / ([tex]12^3[/tex])] × 7.48

Volume in gallons ≈ 123 gallons

Therefore, the approximate number of gallons of water needed to fill 3/4 of the bathtub is 123 gallons.

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Based on the information, the correct answer is: reflect over the x-axis, vertically stretch by a factor of 3, and then shift down 1 unit.

The graph of function g is a reflection of the graph of the parent function f(x) = x over the x-axis. This is because the y-values of the points on the graph of g are the negative of the y-values of the corresponding points on the graph of f.

The graph of function g is also vertically stretched by a factor of 3. This is because the distance between any two points on the graph of g is 3 times the distance between the corresponding points on the graph of f.

The graph of function g is also shifted down 1 unit. This is because the y-values of the points on the graph of g are 1 less than the y-values of the corresponding points on the graph of f.

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Consider the graph of function g below. A diagonal curve declines from (negative 3, 8), (negative 2, 5), (negative 1, 2), (0, negative 1), (1, negative 4), (2, negative 7), and (3, negative 10) on an x y coordinate plane. Determine which sequences of transformations could be applied to the parent function f(x) = x to obtain the graph of g.

reflect over the y-axis, vertically stretch by a factor of 3, and then shift down 1 unit

reflect over the x-axis, vertically stretch by a factor of 3, and then shift down 1 unit shift right 1 unit,

reflect over the x-axis, and then vertically stretch by a factor of 3 shift right 1 unit, reflect over the y-axis, and then vertically stretch by a factor of 3 shift down 1 unit,

reflect over the x-axis, and then vertically stretch by a factor of 3 shift left 2 units, reflect over the x-axis, and then vertically stretch by a factor of 3

The  equation of the tangent line to the curve x(t) = 2/t, y(t) = t^2 + 1 at the point (2, 2) is y = -x + 4.

To find the equation of the tangent line to the curve x(t) = 2/t, y(t) = t^2 + 1 at the point (2, 2), we need to find the slope of the curve at that point and then use the point-slope form of a linear equation.

First, we need to find the derivative of y with respect to x:

dy/dx = (dy/dt) / (dx/dt)

To find dy/dt and dx/dt, we differentiate y(t) and x(t) with respect to t:

dy/dt = 2t
dx/dt = -2/t^2

So, we have:

dy/dx = (dy/dt) / (dx/dt) = (2t) / (-2/t^2) = -t^3

Now, we can find the slope of the tangent line at the point (2, 2) by plugging in t = 1:

dy/dx = -1

Therefore, the slope of the tangent line is -1.

Next, we use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where (x1, y1) is the point on the curve where the tangent line intersects it, and m is the slope of the tangent line.

Since the point (2, 2) lies on the curve, we have x1 = 2 and y1 = 2. Plugging in the slope and the point, we get:

y - 2 = -1(x - 2)

Simplifying, we get:

y = -x + 4

Therefore, the equation of the tangent line to the curve x(t) = 2/t, y(t) = t^2 + 1 at the point (2, 2) is y = -x + 4.

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The container can fit 1600 cube-shaped boxes.

To find out how many cube-shaped boxes can fit into the larger container, we need to calculate the volume of the larger container and divide it by the volume of each cube-shaped box.

The volume of the larger container can be calculated by multiplying its length, width, and height:

Volume of the larger container = 4 ft · 1 1/4 ft · 2 ft

We need to convert the mixed fraction 1 1/4 to an improper fraction:

1 1/4 = (4 · 1 + 1) / 4 = 5/4

Volume of the larger container = 4 ft · (5/4) ft · 2 ft

= (20/4) ft · (5/4) ft · 2 ft

= 50/4 · 2 ft

= 100/4

= 25 ft³

Now let's calculate the volume of each cube-shaped box.

Since all edges are equal to 1/4 ft, the volume can be calculated as the cube of the edge length:

Volume of each cube-shaped box = (1/4 ft)³

= 1/4 ft · 1/4 ft · 1/4 ft

= 1/64 ft³

Finally, we can divide the volume of the larger container by the volume of each cube-shaped box to find out how many boxes can fit:

Number of cube-shaped boxes = (Volume of the larger container) / (Volume of each cube-shaped box)

= 25 / 1/64

= 25 × 64/1

= 1600

Therefore, the container can fit 1600 cube-shaped boxes.

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For the 2-parameters, m and n, both the functions [tex]m^{ln(n)}[/tex] and [tex]n^{ln(m) }[/tex] have the same θ-complexity.

In order to find the θ-complexity of the function,

We let, f(m,n) = [tex]m^{ln(n)}[/tex]  , and g(m,n) = [tex]n^{ln(m) }[/tex] ;

To simplify, we take "ln" for both sides,

we get,

ln(f(m,n)) = ln([tex]m^{ln(n)}[/tex]),

ln(f(m,n)) = ln(n)×ln(m),    ...equation(1)

and for g(m,n),

We have,

ln(g(m,n)) = ln([tex]n^{ln(m) }[/tex] ),

ln(g(m,n)) = ln(m)×ln(n),     ...equation(2)

On comparing both equation(1) and equation(2), we observe that both f(m,n) and g(m,n) are reducible to exactly same forms, thus, f(m,n) = g(m,n);

Therefore, both functions have same θ-complexity.

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The given question is incomplete, the complete question is

Suppose we have two parameters, m and n, with m → ∞ and n → ∞, perhaps at different rates independent of one another. Which has larger θ-complexity: [tex]m^{ln(n)}[/tex] or [tex]n^{ln(m) }[/tex] ?

Answer: B.) 32

Step-by-step explanation:

Because the triangles are similar, you can use proportions to find GH. 10/15 is 2/33, so triangle GEH is 2/3 the size of triangle DEF.
2/3 of 21 is 14, so GH = 14. 8 + 10 + 14 = 32

ANSWER

A 153/225 = 17/25 =0.68=68%

B 225/153 = 25/17 =1.47=147%

C 153/225 = 51/75 =0.51=51%

D 225/153 = 75/51 =0.75=75%

Transcription is the process of creating mRNA from a gene. RNA polymerase binds to the gene and synthesizes mRNA by adding complementary nucleotides according to base-pairing rules: A with U, G with C. This forms a single-stranded mRNA molecule with a sequence complementary to the gene.

In transcription, the gene's DNA double helix unwinds, and RNA polymerase attaches to the promoter region of the gene. The RNA polymerase moves along the DNA strand, reading the nucleotides, and adds complementary RNA nucleotides. Adenine (A) pairs with uracil (U) instead of thymine (T) in RNA, while guanine (G) pairs with cytosine (C). This process continues until the RNA polymerase reaches the terminator sequence, signaling the end of transcription. The result is a single-stranded mRNA molecule with a sequence complementary to the gene, ready for translation into proteins.

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Yes, given explanation is correct.if the calculated test statistic is less than -1.645 then the null hypothesis can be rejected.

For test the claim that the proportion of people who smoke is less than 22.5%.

A one-tailed test of hypothesis can be used. Specifically, a one-sample z-test for a proportion can be used where:

Null hypothesis: p ≥ 0.225 (the proportion of people who smoke is equal to or greater than 22.5%)

Alternative hypothesis: p < 0.225 (the proportion of people who smoke is less than 22.5%)

The test statistic for the one-sample z-test for a proportion is calculated as:

z = (p - P0) / √[(P0 × (1 - P0)) / n]

where p is the sample proportion, P0 = the hypothesized proportion under the null hypothesis and n = The sample size.

If the calculated test statistic falls in the rejection region which is determined by the chosen significance level (e.g., alpha = 0.05) then the null hypothesis can be rejected and it can be concluded that there is evidence to support the claim that the proportion of people who smoke is less than 22.5%.

For a one-tailed test with alpha = 0.05, the critical value is -1.645.

Hence, if the calculated test statistic is less than -1.645 then the null hypothesis can be rejected.

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The potential function for the given vector field f is φ = (3/2)xyz. To find it, we integrated the given equations with respect to their variables and found a constant of integration that makes them consistent.

To find a potential function f for the given vector field f, we need to find a scalar function φ such that the gradient of φ is equal to f. That is,

∇φ = f

So, we need to find a scalar function φ such that

∂φ/∂x = yz

∂φ/∂y = x²z

∂φ/∂z =x²y

Integrating the first equation with respect to x, we get

φ = xyz + g(y,z)

where g(y,z) is the constant of integration with respect to x. Now, we differentiate φ with respect to y and z and compare with the given equations to find g(y,z). We get

∂φ/∂y = xz + ∂g/∂y = x²z

∂φ/∂z = xy + ∂g/∂z = x²y

Integrating these two equations with respect to y and z, respectively, we get

g(y,z) = x²yz/2 + h(z)

g(y,z) = x²yz/2 + h(y)

where h(z) and h(y) are constants of integration. To make the two equations consistent, we set h(z) = h(y) = 0. Therefore, the potential function f for the given vector field f is

φ = xyz + x²yz/2

or

φ = (3/2)xyz

To know more about potential function:

https://brainly.com/question/28156550

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