Prove that the medians of a triangle are concurrent at a point 2/3 of the distance from each vertex to the midpoint of the opposite side.​

Olive will need to buy 8 bags of stone to fill the acquarium.

First, we need to find the volume of the aquarium.

Since the aquarium is rectangular, we can use the formula:

volume = length x width x height

where height is the depth of the stone layer we want to add. In this case, the height is 2 inches.

volume = 24 in x 12 in x 2 in

volume = 576 cubic inches

Now we need to find how many cubic inches of stone we need. We know that we want to add a 2-inch layer of stone, and the aquarium is 24 in x 12 in, so:

stone volume = 24 in x 12 in x 2 in

stone volume = 576 cubic inches

To find the number of bags we need, we can divide the stone volume by the volume of one bag:

bags = stone volume/bag volume

bags = 576 cubic inches / 75 cubic inches per bag

bags ≈ 7.68

Since we can't buy a fraction of a bag, we need to round up to the nearest whole number. Olive will need to buy 8 bags of stone.

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C, that reddish orangish line, it's pointing upwards, so as X increases, Y increases too.

Answer:

Step-by-step explanation:

its c girly

The percent of the days in April that it rains is 66.67%.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 2/3.

A percent is the value of a number out of 100. In order to convert a value to percent, multiply by 100.

Percent of the days that it rains = ( number of days it rains / total number of days) x 100

(2/3) x 100 = 66.67%

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The radius of convergence for the series [tex]\sum_{n=1}^{\infty}[/tex] xⁿ/(n3ⁿ) is 3.

Given the series is,

[tex]\sum_{n=1}^{\infty}[/tex] xⁿ/(n3ⁿ)

So, here the n th term is given by

aₙ = xⁿ/(n3ⁿ)

Then the (n + 1) the term of the series is given by,

aₙ₊₁ = xⁿ⁺¹/((n + 1)3ⁿ⁺¹)

Now, the value is,

aₙ₊₁/aₙ = (xⁿ⁺¹/((n + 1)3ⁿ⁺¹))/(xⁿ/(n3ⁿ)) = (n/(n + 1))*(x/3)

Now the value of the limit is given by,

[tex]\lim_{n \to \infty}[/tex] |aₙ₊₁/aₙ| = [tex]\lim_{n \to \infty}[/tex] |(n/(n + 1))*(x/3)| = [tex]\lim_{n \to \infty}[/tex] |x/3|*|1/(1 + 1/n)| = (|x|/3)*(1/(1 + 0) = |x|/3

So, now [tex]\lim_{n \to \infty}[/tex] |aₙ₊₁/aₙ| < 1 gives

|x|/3 < 1

|x| < 3

-3 < x < 3

Hence, the radius of convergence = 3.

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To find the equation of the tangent plane to the surface z = ln(x - 7y) at the point (8, 1, 0), we need to determine the partial derivatives of z with respect to x and y at that point.

First, let's find the partial derivative ∂z/∂x:

∂z/∂x = 1/(x - 7y)

Next, let's find the partial derivative ∂z/∂y:

∂z/∂y = -7/(x - 7y)

Now, let's evaluate these partial derivatives at the point (8, 1, 0):

∂z/∂x = 1/(8 - 7(1)) = 1/(8 - 7) = 1

∂z/∂y = -7/(8 - 7(1)) = -7/(8 - 7) = -7

At the point (8, 1, 0), the partial derivatives are ∂z/∂x = 1 and ∂z/∂y = -7.

The equation of a plane can be expressed as:

z - z0 = (∂z/∂x)(x - x0) + (∂z/∂y)(y - y0)

Using the values we calculated:

z - 0 = 1(x - 8) + (-7)(y - 1)

Simplifying, we get:

z = x - 8 - 7y + 7

Rearranging terms, the equation of the tangent plane to the surface at the point (8, 1, 0) is:

z = x - 7y - 1

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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 area of the circle is 23. 04 π in²

The formula that is used for calculating the area of a circle is expressed wit the equation;

A = πr²

Such that the parameters are expressed as;

Note that the formula for diameter is expressed as;

Radius = Diameter/2

Substitute the values

Radius = 9.6/2

Divide the values

Radius = 4. 8 in

Substitute the values, we have;

Area = 3.14 × (4.8)²

find the square value, we have;

Area = 3.14 × 23. 04

Multiply the values, we have;

Area = 72. 35 in²

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The 95% confidence interval for b1 is approximately (0.197, 0.703).

The 95% confidence interval for the slope estimate (b1) is given by:

b1 ± t(alpha/2, n-2) * s(e) / (sqrt(SSX) * sqrt(1 - r^2))

where:

t(alpha/2, n-2) is the t-score with alpha/2 probability (alpha = 0.05 for 95% confidence level) and n-2 degrees of freedom

s(e) is the standard error of the estimate for the regression

SSX is the sum of squared deviations of the predictor variable from its mean

r is the correlation coefficient between the predictor and response variables

Substituting the given values, we have:

b1 ± t(0.025, 7) * 2.16 / (sqrt(2.25*8) * sqrt(1 - 0.45^2))

= 0.45 ± 2.365 * 2.16 / (2.121 * 0.676)

= 0.45 ± 1.253

Therefore, the 95% confidence interval for b1 is approximately (0.197, 0.703). So, the answer is (d) (0.11, 0.79).

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Part A:

The arithmetic sequence will be approximately,

42 , 36 , 30 , 24 , ....

Given,

The graph of amount of money a movie earns each week after its release where n is the number of weeks after opening, and a(n) is earnings (in millions).

Now,

After reading the graph carefully it can be judged that the the graph is decreasing linearly. Thus the sequence can be framed as,

42 , 36 , 30 , 24 , ....

here the common difference is 6.

Part B:

The movie will earn $16 million in approximately 3.5 -4 weeks.

As from the graph we can see that the earnings will further decline to $15 million in 3.5 weeks.

So for $16 million the required time will be 3.5 to 4 weeks.

Part C:

The movie will approximately earn

Arithmetic sequence,

41 , 34 , 27 , 20..

Complete the sequence,

42 , 36 , 30 , 24 , 18 , 12 , 6 , 0

For total earning,

Add the earning of the respective weeks.

$(42 + 36 + 30 + 24 + 18 + 12 + 6 + 0) million = $168

Hence the total earning of the movie is approximately $168 million.

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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 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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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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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] ?

The volume of the rectangular prism is 243 cubic centimeters when the length is 6 cm, the width is 4.5 cm and the height is 9cm.

We need to find the volume of a rectangular prism. The volume is determined by using the values length, width, and height. The formula is given as,

V = w × h × l

Where:

w = Width

h = Height

l = Length

We will assume the given data as:

w = 4.5cm

h = 9cm

l = 6 cm

By substuting the values of w,h, and l values in the formula we get:

V = l × h × w

=  6 × 9 × 4.5

= 243

Therefore, the volume of the rectangular prism is 243 cubic centimeters.

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The complete question:

Find the Volume of the Rectangular Prism whose Length is 6cm, width is 4.5 cm and height is 9cm ?

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 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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Let

Now

Charge:-

Pay:-

Now earning:-

Answer:

Y = 1.5x + 5

Step-by-step explanation:

To model the amount of money the florist earns for each delivery, we can break it down into the different components involved.

This can be represented by the term "+10".

This can be represented by the term "+2x", where x represents the number of miles.

This can be represented by the term - ( 0.50x + 5 )

Y = 10 + 2x - (0.50x + 5)

Simplify.

Y = 10 + 2x - 0.50x - 5

Combine like terms.

Y = 1.5x + 5

The missing side length in the triangle is (b) √5

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

The triangle

To find the missing side in a triangle, we can use the pythagoras theorem

So, we have

x² = (2√3)² - (√7)²

Evaluate the difference of exponents

x² = 5

Take the exponent of both sides

x = √5

Hence, the missing side length is (b) √5

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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%

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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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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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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Based on the given diagram 1 to 5, each picture represent a number, diagram 5 is 661.

Based on the diagram;

Diagram 1;

90 = 30 + 30 + 30

Each picture in diagram 1 represents 30

Diagram 2:

1 × 1 × 0 = 0

Diagram 3:

30 ÷ 1 = 30

Diagram 4:

22 × 1 - 1 = 21

Hence,

Diagram 5:

1 + 30 × 22 + 0

Using PEMDAS

P = parenthesis

E = Exponents

M = Multiplication

D = Division

A = Addition

S = Subtraction

1 + 30 × 22 + 0

= 1 + 660 + 0

= 661

Ultimately, diagram 5 equals 661.

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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 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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Answer:

linear - y= x/2 -19, y = x+25/5

non linear- everything else

Step-by-step explanation:

put it into a calc and look for straight lines (linear)

3y=x^2 is NOT linear (it's a parabola)

y=(x/2)-19 is linear - - - it's a straight line

y= x + 25/5 is linear - - - it's straight line

13y = (1/3)x+5 is linear - - - another straight line

y^3 = x is NOT linear.

This scenario where one variable increases, then the other increases, as well describes a positive correlation between two variables. So, correct option is A.

Positive correlation occurs when two variables increase or decrease together, meaning that as the value of one variable increases, the value of the other variable also increases.

For example, if we consider the relationship between the amount of time spent studying and the grade achieved on a test, a positive correlation would exist if students who study more tend to get higher grades.

Positive correlation is often represented by a scatter plot, where the points are clustered around a straight line sloping upwards from left to right.

The correlation coefficient, also known as Pearson's r, can be used to quantify the strength and direction of the relationship between two variables, with a value of +1 indicating a perfect positive correlation and a value of 0 indicating no correlation.

In summary, a positive correlation describes a scenario where two variables increase or decrease together, and is represented by a scatter plot with points clustered around a line sloping upwards from left to right.

So, correct option is A.

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Complete question is:

One variable increases, then the other increases, as well.

Which term would best describe this scenario?

A) positive correlation

B) hypothesis

C) transitional form

D) causation

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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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

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