The energy for a rigid rotator constrained to rotate in the x-y plane is given by 21 where the moment of inertia I is a constant. (a) What is the Hamiltonian? Show that the Hamiltonian and L commute. What are the allowed energies and normalized energy eigenfunctions of the rigid rotator?

The total area of the given figure is 85.2m² respectively.

The quantity of unit squares that cover a closed figure's surface is its area.

Square units like cm² and m² are used to measure area.

A shape's area is a two-dimensional measurement.

The space inside the perimeter or limit of a closed shape is referred to as the "area".

Area of rectangle one:

= l*b

= 4*11.4

= 45.6m²

Area of rectangle second:

= l*b

= 4*8.4

= 33.6m²

Area of the triangle:
= 1/2*b*h

= 1/2*4*(11.4-8.4)

= 1/2*4*3

= 2*3

= 6m²

Total area of the figure: 45.6 + 33.6 + 6 = 85.2m²

Therefore, the total area of the given figure is 85.2m² respectively.

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At x=0 only, the function f with first derivative f'(x) = x(x-5)²(x+1) has a relative minimum.

Hence the correct option is (A) 0 only.

The first derivative of the function is,

f'(x) = x(x-5)²(x+1)

Differentiating the function with respect to x we get, The second derivative of the function is,

f''(x) = x(x-5)².(1) + x(x+1).2(x-5) + (x-5)²(x+1).1 = (x-5)² (x+x+1) + 2x(x+1)(x-5) = (x-5)²(2x+1) + 2x(x+1)(x-5)

Now, f'(x) = 0 gives,

x(x-5)²(x+1) = 0

We know that if product of more than one terms is zero then either of them is zero.

Either, x=0

Or, (x-5)² = 0

x-5 = 0

x = 5

Or, x+1 = 0

x = -1

So the extremum points of the function are, x = -1, 0, 5.

At x=-1, f''(-1) = (-6)²(-2+1) + 2(-1)(-1+1)(-6) = -36

At x=0, f''(0) = (-5)²*1 + 0 = 25

At x=5, f''(5) = 0 + 0 = 0

Since the value of second derivative is positive at only x = 0.

Thus, at x = 0 only the function has a relative minimum.

Hence the correct option is (A).

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Answer:

There are a total of 4 + 6 + 10 = 20 CDs in the case. Eric has a 10/20 = 1/2 chance of picking a pop CD since there are 10 pop CDs in the case.

Therefore, the answer is D) 1/2.

Answer:

Step-by-step explanation:

Eric has a total of 4 + 6 + 10 = 20 CDs in the case.

The probability of picking a pop CD is the number of pop CDs divided by the total number of CDs:

P(pick a pop CD) = 10/20 = 1/2 = 0.5

Therefore, the probability of Eric picking a pop CD is 0.5 or 50%.

The final expression that gives us the cost of x skirts and y hats in pounds is 24x + 15y.

In this case, our variables are x and y, which represent the number of skirts and hats, respectively. Our constants are 24 and 15, which represent the cost of one skirt and one hat, respectively. And our operations are multiplication and addition.

The cost of x skirts is simply the cost of one skirt (which is 24) multiplied by the number of skirts (which is x). So, the expression for the cost of x skirts would be:

24x

Similarly, the cost of y hats is the cost of one hat (which is 15) multiplied by the number of hats (which is y). So, the expression for the cost of y hats would be:

15y

To find the total cost of x skirts and y hats, we simply add the two expressions together. Thus, the expression for the cost in pounds of x skirts and y hats is:

24x + 15y

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The approximate shortest distance, to the art hundredth of a foot, between first and third base is 127.28 feet.

Distance refers to the amount of space between two objects or points. It can be measured in units such as meters, kilometers, miles, or feet, and is commonly used to describe the length or extent of a journey, path, or separation.

According to the given information:

The distance between first and third base in a baseball diamond is the diagonal of the square with side lengths of 90 feet. Using the Pythagorean theorem, we can calculate this distance as follows:

d² = 90² + 90²

d²= 8,100 + 8,100

d²  = 16,200

d = √(16,200)

d ≈ 127.28 feet

Therefore, the approximate shortest distance, to the nearest hundredth of a foot, between first and third base is 127.28 feet. The correct answer is option (b).

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The period for the following graph is 90 degrees. So correct option is C.

In mathematics, a period is a specific type of repetition in a function or a sequence. A period is the smallest positive value of a constant T for which a function or a sequence f(x + T) = f(x) for all x.

Periods are used to describe the behavior of functions and sequences that exhibit a repeating pattern. The length of the period determines the frequency of the pattern, and it is often used to describe the periodicity of functions in various applications, such as signal processing, harmonic analysis, and Fourier series.

For example, the sine function sin(x) is periodic with a period of 2π. This means that sin(x + 2π) = sin(x) for all x. Similarly, the cosine function cos(x) is also periodic with a period of 2π. Other common examples of periodic functions include the tangent function, cotangent function, and exponential function.

In addition to their applications in mathematics, periods also have practical applications in fields such as physics, engineering, and computer science, where they are used to model periodic phenomena such as waves and oscillations.

Overall, periods are an important concept in mathematics and are used to describe the repeating patterns that are found in many mathematical functions and sequences.

The period for the following graph is 90 degrees.

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The results from the probability (rounded to 4 decimal places) are:

2. Exactly two of the marbles are red = 0.4460.

3. None of the marbles are red =  0.5380.

Probability is a measure of the likelihood of an event occurring, expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty.

Therefore:

The total number of marbles = 6 + 5 + 8 = 19.

2. The Probability that exactly two marbles are red:

The number of ways to choose 2 red marbles out of 6 red marbles = C(6,2), using the combination formula, without replacement.

To choose 1 marble out of 13 non-red marbles (5 white + 8 blue) = C(13,1)

To choose 3 marbles out of 19 marbles = C(19,3),

using the combination formula for choosing 3 items out of 19 without replacement.

The probability of choosing exactly 2 red marbles =

P(exactly 2 red) = (C(6,2) * C(13,1)) / C(19,3)

Plugging in the values, we get:

P(exactly 2 red) = (C(6,2) * C(13,1)) / C(19,3)

≈ 0.4460 (to 4 decimal places)

3. The probability that none are red:

To choose 3 marbles out of 13 non-red marbles (5 white + 8 blue) = C(13,3), using the combination formula.  without replacement.

The probability of choosing none of the marbles as red =

P(none red) = C(13,3) / C(19,3).

Plugging in the values, we get:

P(none red) = C(13,3) / C(19,3)

≈ 0.5380 (to 4 decimal places)

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Answer:

156

Step-by-step explanation:

Use the system of PEMDAS.
6*3 = 18
6*4 = 24
6*5 = 30
6*8 = 48
2[3*4+1/2(3*4)] = 36
Add all.
18+24+30+48+36 = 156

Answer:48

Step-by-step explanation:

Answer:

The electrons in the battery will flow from the negative electrode (anode) to the positive electrode (cathode) through an external circuit, driven by the potential difference created by the ionic paste.

Step-by-step explanation:

In a battery, the ionic paste, which is usually an electrolyte solution, allows the flow of ions between the electrodes of the battery. This flow of ions creates a potential difference between the two electrodes, which in turn creates an electric field.

The electrons in the battery will flow from the negative electrode (anode) to the positive electrode (cathode) through an external circuit, driven by the potential difference created by the ionic paste. As the electrons move through the external circuit, they can be used to power a device or do useful work.

It is important to note that the flow of electrons occurs only in the external circuit, while the flow of ions occurs only within the battery itself, through the ionic paste. The flow of electrons and ions is connected but separate processes that work together to generate electrical energy in a battery.

The y-intercept of the tangent line is b. -1

The y-intercept of a line is the value of y at which the line crosses the y axis

To determine the value of y-intercept of a line with the given slope -3 that is a tangent line to the curve y = -x² - 5x -5.

We proceed as follows

First we differentiate the equation of the curve.

So,  y = -x² - 5x -5.

dy/dx = d(-x² - 5x -5)/dx

=  d-x²/dx - d5x/dx - d5/dx

= -2x - 5 - 0

= -2x - 5

Since the derivative of the curve equals the value of the tangent at the point, we have that

dy/dx = -3

-3 = -2x - 5

-3 + 5 = -2x

2 = -2x

x = 2/-2

x = -1

So, substituting x = -1 into the equation for y to find the y intercept, we have that

y = -x² - 5x -5.

y = -(-1)² - 5(-1) -5

= -1 + 5 - 5

= -1 + 0

= -1

So, the y-intercept is b. -1

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Given the survey, the completed table is as follows:

                   Print             Electronic             Total

Youth             23               40                          63

Adults               23             36                           59

Total                46               76                           122

To fill in the missing values, we can use the fact that the total number of youths is 63 and the total number of adults is 59. Thus, we can subtract the number of known values from the total to find the missing values.

For the number of youths who prefer printed books, we have:

Print + Electronic = Total

Print + ? = 63

23 + ? = 63

? = 63 - 23

? = 40

For the number of adults who prefer electronic books, we have:

Print + Electronic = Total

? + Electronic = 59

23 + Electronic = 59

Electronic = 59 - 23

Electronic = 36

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Answer:

y=1.6x+3

Step-by-step explanation:

Answer: y=1/2x+3 i don’t know if I’m right, be warned!

Step-by-step explanation:

first find the slope (the m) by doing rise over run or you can find 2 points and find slope by using subtraction. Then get the +b by finding out where the line crosses the y intercept and put that all together leaving the y and x variables the same.

The measure of variability that the charity should use to accurately represent the data is B. The IQR of 13 is the most accurate to use, since the data is skewed.

The charity should use the Interquartile Range (IQR) as the measure of variability since the data is skewed. The IQR measures the range of the middle 50% of the data, which is less affected by outliers or skewed data.

Q1 is the median of the first half of the data: 5, 5, 6, 8, 10, 15 (Q1 = 7)

Q3 is the median of the second half of the data: 15, 18, 20, 20, 20, 20, 20 (Q3 = 20)

Now, we can calculate the IQR:

IQR = Q3 - Q1

IQR = 20 - 7

IQR = 13

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According to the function, the rate of change with respect to the number of minutes purchased is $1.05 per minute.

The function given in the problem is y = 5.45 + 1.05(x + 7), where y represents the cost in dollars for a prepaid cell phone plan of x minutes. This means that if you want to know how much it will cost to purchase a certain number of minutes, you can simply plug in that number for x and the equation will give you the corresponding cost in dollars.

Now, the rate of change with respect to the number of minutes purchased is also known as the slope of the function. This tells us how much the cost will change for each additional minute purchased. To find the slope, we need to take the derivative of the function with respect to x.

The derivative of y with respect to x is given by:

dy/dx = 1.05

This means that for each additional minute purchased, the cost will increase by $1.05.

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The loose sweets are better value, as they cost only £0.0089 per gram, compared to £0.01242 per gram for the pre-packed sweets.

We need to calculate their price per gram.

Price per gram of pre-packed sweets:

120 g of pre-packed sweets cost £1.49

1 g of pre-packed sweets costs £1.49 / 120 = £0.01242 (rounded to 5 decimal places)

Price per gram of loose sweets:

100 g of loose sweets cost £0.89

1 g of loose sweets costs £0.89 / 100 = £0.0089

So, the loose sweets are better value, as they cost only £0.0089 per gram, compared to £0.01242 per gram for the pre-packed sweets.

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The first month in which HBM Corporation's cumulative donation total exceeds the Gades Foundation's cumulative total is the sixth month. This is calculated by finding an equation for each organization's cumulative donation total and solving an inequality.

Let's start by finding an equation for the cumulative donation total for each organization after n months. Let GF(n) and HBM(n) represent the cumulative donation totals for the Gades Foundation and HBM Corporation, respectively.

The Gades Foundation's cumulative donation total can be represented by the arithmetic sequence

GF(n) = 250 + 100(n-1)

The HBM Corporation's cumulative donation total can be represented by the geometric sequence

HBM(n) = 64(1.75)ⁿ⁻¹

To find the month in which HBM Corporation's cumulative donation total exceeds the Gades Foundation's cumulative total, we need to solve the inequality

HBM(n) > GF(n)

Substituting the expressions for GF(n) and HBM(n), we get

64(1.75)ⁿ⁻¹ > 250 + 100(n-1)

Simplifying and solving for n, we get

1.75ⁿ⁻¹ > (250/64) + (100/64)(n-1)

Taking the logarithm of both sides, we get

(n-1)log(1.75) > log(250/64) + log(1+(100/250)(n-1))

Using a calculator to evaluate the logarithms, we can solve for n

n > 5.74

Since n must be an integer, the smallest integer greater than 5.74 is 6. Therefore, the first month in the Gades Foundation's cumulative total is the sixth month.

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The circumference of the circle actually is  25.12 inches

So the diameter is 8 inches, and the circumference is pi times the diameter, so you must have:

c = 3.14*8in = 25.12 inches

That is the circumference of the circle, im not sure of what did you did to ger 43.96 inches.

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Grand mean of the response variable. In a two-way ANOVA (Analysis of Variance) test, the sum of squares for factor A (also called the "between-groups" sum of squares for factor A) measures the variation in the response variable that can be attributed to the levels of factor A.

Specifically, it measures the sum of the squared differences between the mean of each level of factor A and the grand mean of the response variable (which is the mean of all the observations across all levels of factor A and factor B).

Mathematically, the sum of squares for factor A can be expressed as:

SSA = ∑ni(ȳi.-ȳ..)²

where ni is the sample size of the i-th level of factor A, ȳi. is the mean of the i-th level of factor A, and ȳ.. is the grand mean of the response variable.

In other words, the sum of squares for factor A represents the variation in the response variable that is due to the differences between the means of the levels of factor A, after taking into account the overall mean of the response variable.

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In a two-way ANOVA test, the sum of squares for factor A is based on the sum of the squared differences between the mean for each level of factor A and the overall mean of the data.

This represents the variation in the data that can be attributed to the different levels of factor A.

The sum of squares for factor B is calculated in the same way, but for the levels of factor B instead.

The interaction term in the ANOVA represents the variation that cannot be explained by either factor A or factor B

alone, but is instead due to the combination of the two factors.

Overall, the ANOVA test allows us to determine if there are significant differences between the means of different

groups, and if these differences are due to the factors being tested or random chance.

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The technique being described is random sampling without replacement, which is option a.

This technique is called "sampling without replacement."

However, you've also mentioned convenience sampling, which is a different method.

Let me briefly explain both concepts.

Sampling without replacement is a method in which each item, score, event, or participant is chosen from the population and is not returned to the pool for further selections.

This ensures that each element can only be selected once, eliminating the chance of duplication in the sample.

This method is often used in surveys, experiments, and research to maintain the independence of observations and provide a more accurate representation of the population.
Select an item, score, event, or participant from the population.
Record the selected item and remove it from the population.

Repeat steps 1-2 until the desired sample size is obtained.
Convenience sampling, on the other hand, is a non-probability sampling method where researchers select participants based on their accessibility and ease of recruitment.

This approach may introduce bias and limit the generalizability of the study results, as it does not ensure that the sample is representative of the population.
Identify the target population.
Recruit participants who are easily accessible and willing to participate.
Collect data from the selected participants.
In summary, sampling without replacement is a technique that prevents the same item from being selected more than once, while convenience sampling is an approach that focuses on selecting participants based on their accessibility. Both methods serve different purposes in research and should be chosen based on the study's objectives and available resources.

Option a is correct.

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The graph of the function q(x) = -9/2x^2 is a downward-facing parabola with vertex at the origin (0, 0).

The graph of the quadratic function q(x) = -9/2x^2 is a downward facing parabola because the coefficient of x^2 is negative. The vertex of the parabola can be found by using the formula x = -b/2a, where a is the coefficient of x^2 and b is the coefficient of x. In this case, a = -9/2 and b = 0, so the vertex is at x = 0.

To find the y-coordinate of the vertex, we substitute x = 0 into the equation q(x) = -9/2x^2. This gives us q(0) = 0, so the vertex is at the point (0, 0).

Since the coefficient of x^2 is negative, the graph of the function opens downwards. The value of the function decreases as we move away from the vertex in either direction.

Therefore, the graph of the function q(x) = -9/2x^2 is a downward-facing parabola with vertex at the origin (0, 0).

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The inequality to represent the possible number of hours Kat can afford to book the DJ is 80x + 225 ≤ 970 and one possible length Kat can afford to book the DJ is 9 hours.

(a) Let x be the number of hours that Kat can book the DJ. Then, the total cost of the DJ is 80x, and the total cost of the party is 80x + 225.

Since Kat has $410 saved and will earn another $560, the total amount she can spend on the party is $410 + $560 = $970.

Therefore, we can write the following inequality to represent the possible number of hours Kat can afford to book the DJ:

80x + 225 ≤ 970

b) To solve for x, we can start by subtracting 225 from both sides of the inequality:

80x ≤ 745

Then, we can divide both sides by 80:

x ≤ 9.3125

Since Kat can only book the DJ in whole hours, the largest integer less than or equal to 9.3125 is 9. Therefore, one possible length Kat can afford to book the DJ is 9 hours.

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If the figure "WXYZ" is a kite and m∠WXY=13x+24, then the measure of the angle-ZYX is 101.6 degrees.

A "Kite" is defined as quadri-lateral which has two pairs of "adjacent-sides" which are congruent and "one-pair" of "opposite-angles" which are congruent .

We know that the sum of all the vertices of the kite is 360 degree,

So, we add all the vertices of the kite,

We get,

⇒ m∠WXY + m∠WZY + m∠ZWX + m∠ZYX = 360°,

Substituting the values,

We get,

⇒ 13x + 24 + 35 + 13x + 4 + m∠ZYX = 360°,

⇒ 26x + 63 + m∠ZYX = 360°,

⇒ m∠ZYX = 360 - 63 - 26x,

⇒ m∠ZYX = 297 - 26x,      ...equation(1)

We also know that, "two-angles of kite are equal where "unequal-sides" meet".

So, m∠ZWX = m∠ZYX,

Substituting the values,

We get,

⇒ 13x + 4 = m∠ZYX,       ....equation(2),

Equating equation(1) and equation(2),

we get,

⇒ 13x + 4 = 297 - 26x,

⇒ x = 293/39,

Substituting this in equation(2),

We get,

⇒ 13(293/39) + 4 = m∠ZYX,

⇒ 293/3 + 4 = m∠ZYX,

⇒ m∠ZYX ≈ 101.6 degree.

Therefore, the measure of the angle ZYX is 101.6 degrees.

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The given question is incomplete, the complete question is

The figure WXYZ is a kite. If m∠WXY=13x+24, m∠WZY=35, and m∠ZWX=13x+4, find m∠ZYX?

The requried surface area of the regular pyramid is 147.6 cubic meters.

The surface area of the regular pyramid is given as:

Surface area = base area + 1/2 [perimeter×slant height]
Surface area = 1/2 × base × height + 1/2 [perimeter×slant height]
Surface area =1/2 × 8 × 6.9 + 1/2 [3×8 × 10]
Surface area =147.6 cubic meters

Thus, the requried surface area of the regular pyramid is 147.6 cubic meters.

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Answer:

on what

Step-by-step explanation:

The unit rate of water dropped per day is [tex]$\frac{12}{5}$[/tex] gallons per day.

We can start by finding the unit rate of water dropped per hour.

If the sink drips [tex]$\frac{2}{5}$[/tex] gallon of water in 4 hours, then it drips [tex]\frac{1}{5}$[/tex] gallon of water in 2 hours (since [tex](\frac{2}{4} = \frac{1}{2}$).[/tex]

The unit rate of water dropped per hour is:

[tex]$\frac{1/5}{2} = \frac{1}{10}$[/tex] gallon per hour.

To find the unit rate of water dropped per day, we can multiply the unit rate per hour by the number of hours in a day:

[tex]$\frac{1}{10} \text{ gallon per hour} \cdot 24 \text{ hours per day} = \frac{12}{5} \text{ gallons per day}$[/tex]

Therefore, the unit rate of water dropped per day is [tex]$\frac{12}{5}$[/tex] gallons per day.

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The unit rate of water dropped per day is 12/5 gallons.

To find the unit rate of water dropped per day for a sink that drips 2/5 gallons of water in 4 hours, we'll follow these

steps:

Determine how many gallons of water are dripped in one hour.

Calculate the gallons of water dripped in 24 hours (one day).

Calculate gallons per hour.

Since the sink drips 2/5 gallons in 4 hours, we'll divide the gallons by the number of hours:

(2/5) / 4 = (2/5) × (1/4) = 2/20 = 1/10

So, the sink drips 1/10 gallons per hour.

Calculate gallons per day.

Now, we'll multiply the gallons per hour by 24 hours to find the gallons per day:

(1/10) × 24 = 24/10 = 12/5

The unit rate of water dropped per day is 12/5 gallons.

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Answer:

b. 8/17

Step-by-step explanation:

hope this helps ;)

The angle x subtended by the arc of the circle between the two tangents is 130 degrees.

In trigonometry, the tangent (often abbreviated as tan) is a mathematical function that describes the ratio of the length of the side opposite to an angle in a right-angled triangle to the length of the adjacent side.

The formula 50=180-x represents the fact that the angle between two tangents drawn to a circle from an external point is equal to the difference of the angles subtended by the tangents in the opposite segment of the circle.

Using this formula, we can solve for x as follows:

50 = 180 - x (given)

x = 180 - 50 (subtracting 50 from both sides)

x = 130 (simplifying)

Therefore, the angle x subtended by the arc of the circle between the two tangents is 130 degrees.

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The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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The requried equation of the circle with center (-3,0) passing through (-3,3/2) is 4(x + 3)² + 4y² = 9

We are given that the center of the circle is (-3,0) and it passes through (-3, 3/2). Since the x-coordinate of both points is the same, we know that the center lies on a vertical line passing through (-3, 3/2). Therefore, the distance between the center and the point (-3, 3/2) is the radius of the circle.

The radius is found using the distance formula:

r = √[(x₂ - x₁)² + (y₂ - ₁)²]

r = √[(-3 - (-3))² + (0 - 3/2)²] = √[9/4] = 3/2

So, the equation of the circle in standard form is:

(x - (-3))² + (y - 0)² = (3/2)²

(x + 3)² + y² = 9/4

4(x + 3)² + 4y² = 9

Therefore, the standard form of the equation for the circle is: 4(x + 3)² + 4y² = 9

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