Y – 84 = -11(x – 6)

What is the point and slope

The equation of the tangent line to the lemniscuses 2(x²+y²) = 25 (z²-y²) at the point (-3, -1) is y = (16/25)x + 23/25.

To find the equation of the tangent line to a curve, we need to take the derivative of the equation of the curve and evaluate it at the given point.

First, let's rewrite the equation of the lemniscate in terms of x and y:

2(x² + y²) = 25(z² - y²)

Dividing both sides by 25, we get:

(x² + y²) / (25/2) = (z² - y²) / 12.5

Now, we can take the partial derivatives with respect to x and y:

∂/∂x [(x² + y²) / (25/2)] = (2x) / (25/2) = (4x) / 25
∂/∂y [(x² + y²) / (25/2)] = (2y) / (25/2) = (4y) / 25

Next, we need to find the value of z at the point (-3, -1). To do this, we can substitute x = -3 and y = -1 into the equation of the lemniscate:

2((-3)² + (-1)²) = 25(z² - (-1)²)
20 = 25(z² + 1)
z^2 = 19/25
z = ±sqrt(19)/5

Since we want the tangent line at the point (-3, -1), we'll use z = -sqrt(19)/5.

Now, we can evaluate the partial derivatives at (-3, -1, -sqrt(19)/5):

(4(-3)) / 25 = -12/25
(4(-1)) / 25 = -4/25

So, the slope of the tangent line is:

m = ∂z/∂x × -12/25 + ∂z/∂y × -4/25
m = (2x / (25/2)) × (-12/25) + (2y / (25/2)) × (-4/25)
m = -24x/125 - 8y/125
m = -24(-3)/125 - 8(-1)/125
m = 72/125 + 8/125
m = 80/125
m = 16/25

Finally, we can use the point-slope form of a line to find the equation of the tangent line:

y - (-1) = (16/25)(x - (-3))
y + 1 = (16/25)(x + 3)
y = (16/25)x + 48/25 - 25/25
y = (16/25)x + 23/25

So the equation of the tangent line to the lemniscuses 2(x²+y²) = 25 (z²-y²) at the point (-3, -1) is y = (16/25)x + 23/25.

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Deion increased the distance he ran by 20%.

To discover the percentage increase within the distance Deion ran, we need to first calculate the amount of increase.

The increase in distance that Deion ran this week compared to final week is:

6.4 miles

To find the proportion increase, we need to divide the increase by means of the original value (the distance he ran last week),

Then multiply by using a hundred to express the result as a percent.

The original price (last week's distance) is:

32 miles

Therefore, the percentage increase within the distance he ran is:

(6.4 miles / 32 miles) x 100% = 20%

So, Deion increased the distance he ran by 20%.

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By evaluating square root and using Pythagorean Theorem the value of a is a= 3.33 (rounded to two decimal places)

The given expression is 5/3, which can be simplified as follows:

a = 5/3

To evaluate the square root of a, we can rewrite it in terms of exponents:

a = (5/3)¹/₂

Using a calculator, we get:

a ≈ 1.83

Next, we can use the Pythagorean Theorem to find the value of c, given that a = 3.33 and b = 4.66:

a² + b² = c²

(3.33)² + (4.66)² = c²

11.0889 + 21.7156 = c²

32.8045 = c²

c ≈ 5.72

Therefore, the final answer is a = 3.33 and c ≈ 5.72.

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The calculated cost of the dryer is $475.

Let's assume that the cost of the dryer is x dollars.

According to the problem, the cost of the washer is $54 more than the dryer.

Therefore, the cost of the washer is (x + $54).

We are given that the combined cost of the washer and the dryer is $1004. So we can set up the equation:

x + (x + $54) = $1004

Simplifying the equation:

2x + $54 = $1004

2x = $950

x = $475

Therefore, the cost of the dryer is $475.

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Answer:

[tex]\left(x\:+\:1\right)^2\:+\:y^2=25[/tex]

Step-by-step explanation:

The equation of a circle with radius r and center at (a, b) is given by
(x - a)² + (y - b)² = r²

Let's first find the radius

The circle intersects the x axis at two points (-6, 0) and (4, 0)

The diameter is therefore the absolute difference between the x values:
|-6 - 4| same as |4 - (-6)| = 10

The radius r = 5  (half of diameter)

Now, let's find the center point of the circle. This will lie midway between (-6, 0) and (4, 0)

Midpoint  (xm, ym) between two points(x1, y) and (x2, y2) :
xm = (x1 + x2)/2 = (-6 + 4)/2 = -1
ym = (y1 + y2)/2 = (0 + 0)/2 = 0

So the center (a, b) = (-1, 0) with a = -1, b = 0

The equation of the circle therefore is
(x - a)² + (y - b)² = r²
( x - (-1) )² + (y - 0)² = 25

(x + 1)² + y² = 25

To find a and b take any point (x, y) and plug these

The solution to the equations obtained using inverse trigonometric function values are;

1. x ≈ 0.65

4. x ≈ 0.95

Trigonometric functions indicates the relationships between the angles in a right triangle and two of the sides of the triangle. Trigonometric functions are periodic functions.

The value of x is obtained from the inverse trigonometric function of the output value of the trigonometric function, as follows;

The inverse function for sine is arcsine

The inverse function for cosine is arccosine

The inverse function for the tangent of an angle is arctangent

1. sin(x) = 0.6051

Therefore; x = arcsine(0.6051) ≈ 0.65 radians

The value of x in the interval [0·π, 2·π] is x ≈ 0.65

4. tan(x) = 1.3972

Therefore, x = arctan(1.3972) ≈ 0.95

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The value of the sides are;

x = 20.4

x = 13.84

There are six different trigonometric identities. They include;

Given that the ratios are;

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

Using the tangent identity, we have;

tan 64 = 42/x

cross multiply the values

x = 42/2. 050

x = 20. 4

Using the sine identity;

sin 70 = 13/x

cross multiply the values

x = 13/0. 939

x = 13. 84

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The volume of water remaining in Abigail’s cup can be found to be 25. 14 cm³ .

First, find the volume of water in the cup when it is full. This would be the volume of the cup which is the formula of the volume of a cone :

Volume = ( 1 / 3 ) × π × r² × h

Volume = ( 1 / 3 ) × π × ( 3 cm )² × ( 8 cm )

Volume = 24π cm³

If Abigail too 2 / 3 to slosh on her face, the amount of water left would be :

= 24π cm³ - ( 1 - 2 / 3 )

= 24π cm³ - 1 / 3

= 8π cm³

= 25. 14 cm³

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Answer:

I believe it is

F = (9/5 x °C) + 32

Answer:

Around 3 years

Step-by-step explanation:

6% of 30000 is 1800. I subtracted 1800 from 30000 until it got down too 24000 so im assuming that's how old

The final value is f'(-1) = 16,777,2160.

We can use the chain rule and the power rule of differentiation to find f'(-1).

Recall that the chain rule states that if f(x) = g(h(x)), then f'(x) = g'(h(x)) h'(x). Applying this rule to f(x) = (h(x))^10, we get:

f'(x) = 10(h(x))^9 h'(x)

Now, we can substitute x = -1 into the above equation, since we are asked to find f'(-1). Thus, we have:

f'(-1) = 10(h(-1))^9 h'(-1)

We are given that h(-1) = 3 and h'(-1) = 6, so we can substitute these values to get:

f'(-1) = 10(3)^9 (6)

Simplifying, we get:

f'(-1) = 16,777,2160

Therefore, f'(-1) = 16,777,2160

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Since the expression is the same, we can conclude that the binary operation ⋆ is associative.

To show that the binary operation ⋆ is commutative, we need to demonstrate that a ⋆ b is equal to b ⋆ a for any integers a and b.

Let's start by evaluating a ⋆ b:

a ⋆ b = 2ab + 5.

Now let's evaluate b ⋆ a:

b ⋆ a = 2ba + 5.

By comparing the expressions for a ⋆ b and b ⋆ a, we can see that they are indeed equal:

2ab + 5 = 2ba + 5.

Since the expression is the same, we can conclude that the binary operation ⋆ is commutative.

To show that the binary operation ⋆ is associative, we need to demonstrate that (a ⋆ b) ⋆ c is equal to a ⋆ (b ⋆ c) for any integers a, b, and c.

Let's evaluate (a ⋆ b) ⋆ c:

(a ⋆ b) ⋆ c = (2ab + 5) ⋆ c = 2(2ab + 5)c + 5 = 4abc + 10c + 5.

Now let's evaluate a ⋆ (b ⋆ c):

a ⋆ (b ⋆ c) = a ⋆ (2bc + 5) = 2a(2bc + 5) + 5 = 4abc + 10a + 5.

By comparing the expressions for (a ⋆ b) ⋆ c and a ⋆ (b ⋆ c), we can see that they are indeed equal:

4abc + 10c + 5 = 4abc + 10a + 5.

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Answer:

Of course, I can assist you with your question. The volume of a sphere with a radius of 2.5 can be calculated using the formula (4/3)*pi*(2.5^3). This results in an answer of approximately 65.45 cubic units in terms of pi.

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EDIT: The volume of a sphere with a radius of 2.5 can be calculated using the formula V = (4/3)πr^3. Plugging in the value of r as 2.5, we get V = (4/3)π(2.5)^3. Simplifying this expression, we get V = 65.45π/3. Thus, the answer in terms of π is 65.45/3π or approximately 21.82π. None of the given options matches the calculated answer.

The equation of the tangent line to the curve at P(2, -12) is y = 2x - 16.

(a) To find the slope of the curve y = x^3 - 10x at the given point P(2, -12), we need to find the derivative of the function y with respect to x, and then evaluate it at x = 2.

Step 1: Find the derivative, dy/dx
y = x^3 - 10x
dy/dx = 3x^2 - 10

Step 2: Evaluate the derivative at x = 2
dy/dx (2) = 3(2)^2 - 10 = 12 - 10 = 2

The slope of the curve at P(2, -12) is 2.

(b) To find an equation of the tangent line to the curve at P(2, -12), we'll use the point-slope form of the equation: y - y1 = m(x - x1).

Step 1: Use the slope found in part (a) and the given point P(2, -12).
m = 2
x1 = 2
y1 = -12

Step 2: Plug the values into the point-slope equation.
y - (-12) = 2(x - 2)
y + 12 = 2x - 4

Step 3: Rearrange the equation to get the final form.
y = 2x - 4 - 12
y = 2x - 16

The equation of the tangent line to the curve at P(2, -12) is y = 2x - 16.

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The integral ∫8(1-tan²(x)/sec² dx Note Use an upper-case "C" for the constant of integration is ∫8(1-tan²(x)/sec²(x)) dx = 8 tan(x) + C where C is the constant of integration.

To evaluate the integral ∫8(1-tan²(x)/sec²(x)) dx, we need to use trigonometric identities to simplify the integrand.

First, we use the identity tan²(x) + 1 = sec²(x) to rewrite the integrand as follows:

8(1 - tan²(x)/sec²(x)) = 8(sec²(x)/sec²(x) - tan²(x)/sec²(x))

Simplifying this expression by canceling out the common factor of sec²(x), we get:

8(sec²(x) - tan²(x))/sec²(x)

Next, we use the identity sec²(x) = 1 + tan²(x) to simplify the expression further:

8(sec²(x) - tan²(x))/sec²(x) = 8((1 + tan²(x)) - tan²(x))/sec²(x)

Simplifying the expression inside the parentheses, we obtain:

8/ sec²(x)

Therefore, the integral simplifies to:

∫8(1-tan²(x)/sec²(x)) dx = ∫8/ sec²(x) dx

We can now use the substitution u = cos(x) and du/dx = -sin(x) dx to transform the integral into a simpler form:

∫8/ sec²(x) dx = ∫8/cos²(x) dx = 8∫cos(x)² dx

Using the power-reducing formula cos²(x) = (1 + cos(2x))/2, we get:

8∫cos(x)² dx = 8/2 ∫(1 + cos(2x))/2 dx = 4(x + 1/2 sin(2x)) + C

Substituting back u = cos(x), we obtain:

∫8(1-tan²(x)/sec²(x)) dx = 8 tan(x) + C

where C is the constant of integration.

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The initial water level is given as follows:

28 units.

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

The function for this problem is defined as follows:

n = 4.5t + 28.

The intercept is of b = 28, representing the initial amount of water.

The graph is given by the image presented at the end of the answer.

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The system of inequalities that models this scenario are:

Part A: Based on the question, we take x be the number of hours that Paula spends watering plants and also we take y be the number of hours she spends sweeping the nursery. Hence system of inequalities equation will be:

x + y ≤ 12 (she is unable to work more than 12 hours each week)

5x + 10y ≥ 60 (she need to make about $60 per week)

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The base of the parallelogram is approximately equal to the circumference of the circle.

The following statements could help Josie justify the area formula for a circle:

Therefore, the area of the circle can be calculated using the formula A = C × r, or in terms of the radius, A = πr².

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The system of equations is.

x + y = 80

12x + 10y = 900

And the solutions are y = 30 and x = 50

Let's define the two variables:

x = number of calculators.

y = number of calendars.

With the given information we can write two equations, then the system will be:

x + y = 80

12x + 10y = 900

Now let's solve it.

We can isolate x on the first equation to get:

x = 80 - y

Replace that in the other equation to get:

12*(80 - y) + 10y = 900

-2y = 900 - 960

-2y = -60

y = -60/-2 = 30

Then x = 50

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the backup goalie saved 42 shots. Answer: 42 shots. We can start by setting up an equation using the information given

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. It is typically written with an equal sign (=) between the two expressions. For example, the equation 2x + 3 = 7 is a statement that asserts that the expression 2x + 3 is equal to 7.

In the given question,

We can start by setting up an equation using the information given:

save percentage = (number of shots saved / total number of shots attempted)

For the backup goalie, we know that their save percentage is 0.560, and we also know the total number of shots attempted on the goal is 75. Let's let the number of shots saved by the backup goalie be represented by the variable "t". Then we can write:

0.560 = t / 75

To solve for t, we can cross-multiply:

0.560 * 75 = t

t = 42

Therefore, the backup goalie saved 42 shots. Answer: 42 shots.

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Answer:

  3.5 feet

Step-by-step explanation:

You want the difference in height between similar isosceles triangles, one with height of 30 ft and a base of 24 ft, the other with a side length of 28.5 ft.

We can find the side length of the larger triangle using the Pythagorean theorem. It will be ...

  longer side = √(30² +12²) ≈ 32.311 ft

Then the length x is the difference between the altitudes of the triangles. The altitudes are proportional to the side lengths, so we have ...

  (30 -x)/28.5 = 30/32.311

  x = 30-(28.5)(30/32.311) = 30(1 -28.5/32.311) ≈ 3.538 ≈ 3.5 . . . . feet

The hand rail is about 3.5 feet above the bridge deck.

We recognize that the distance from the hand rail to the top of the triangle is the product of the given side length (28.5 ft) and the cosine of the angle between the side and the altitude.

The tangent of that angle is the ratio of its opposite side (12 ft) to its adjacent side (30 ft), or θ = arctan(12/30).

The value of x is the difference of the altitudes of the triangles, so is ...

  x = 30 -28.5·cos(arctan(12/30)) ≈ 3.5 ft

We find this easier to compute.

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Answer:

unfortunately there's no questions to be answered

La suma de dos números es 15 y la suma de sus cuadrados es 113. Por lo tanto, los dos números son 7 y 8.

Para resolver este problema, podemos utilizar el método de sustitución. Si llamamos a los dos números "x" e "y", podemos plantear dos ecuaciones con la información que nos dan:

x + y = 15 (ecuación 1)
x² + y² = 113 (ecuación 2)

De la primera ecuación, podemos despejar a "y" para obtener:

y = 15 - x

Ahora, podemos sustituir este valor de "y" en la segunda ecuación:

x² + (15 - x)² = 113

Expandiendo y simplificando:

x² + 225 - 30x + x² = 113
2x^2 - 30x + 112 = 0

Esta es una ecuación cuadrática que podemos resolver utilizando la fórmula general:

x = (-b ± sqrt(b² - 4ac)) / 2a

Donde:

a = 2
b = -30
c = 112

Sustituyendo:

x = (-(-30) ± sqrt((-30)² - 4(2)(112))) / 2(2)
x = (30 ± sqrt(900 - 896)) / 4
x = (30 ± 2) / 4

Esto nos da dos posibles valores para "x":

x₁ = 8
x₂ = 7

Para encontrar los valores correspondientes de "y", podemos utilizar la ecuación que obtuvimos antes:

y = 15 - x

Así que:

y₁ = 15 - 8 = 7
y₂ = 15 - 7 = 8

Por lo tanto, los dos números son 7 y 8.

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The answer of the given question based on the graph could be used to determine the variance levels that would result in a package of vegetables is histogram.

To determine the variance levels that would result in a package of vegetables being rejected because of its weight, X, consider the following:

1. The company has a tolerance level of less than or equal to y grams for a 250-gram package. This means that the graph must represent a relationship between the weight of the package (X) and the tolerance level (y).
2. Since the package is rejected if it weighs more than the allowed tolerance, the graph should show that as the weight (X) increases, the acceptance range decreases (y decreases).
3. The graph should ideally have a boundary line that represents the maximum tolerance level (y). Any points above this line would represent rejected packages.

Based on these criteria, you should select the graph that best represents this relationship between the weight of the package (X) and the tolerance level (y), where packages with a weight exceeding the tolerance level are rejected.

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There would be   1.302 x 10¹² cells in koala, and  there are  3.04 x 10^17 cells in the average hippo.

To find the number of cells in the average koala, we first need to find the volume of the koala in cubic centimeters, since we know the density of the cell and can use that to find the mass of the koala in grams.

The average weight of a koala is 6 kilograms, which is equivalent to 6,000 grams. We can use the density of the cell to find the volume of the koala:

Density = Mass / Volume

1.1 g/cm³ = 6,000 g / Volume

Volume = 6,000 g / 1.1 g/cm³

Volume = 5,454.54 cm³

Next, we need to find the volume of one cell:

Volume of cell = 4/3 * π * (0.001 cm)³

Volume of cell = 4.188 x 10⁻⁹ cm³

Finally, we can divide the volume of the koala by the volume of one cell to find the number of cells in the average koala:

Number of cells = 5,454.54 cm³ / (4.188 x 10⁻⁹ cm³)

Number of cells = 1.302 x 10¹²

Therefore, there are approximately 1.302 x 10¹² cells in the average koala.

To find the number of cells in the average hippo, we can follow the same process. The average weight of a hippo is 1,400 kilograms, which is equivalent to 1,400,000 grams. Using the density of the cell, we can find the volume of the hippo:

Density = Mass / Volume

1.1 g/cm^3 = 1,400,000 g / Volume

Volume = 1,400,000 g / 1.1 g/cm³

Volume = 1,272,727.27 cm³

Dividing the volume of the hippo by the volume of one cell, we get:

Number of cells = 1,272,727.27 cm³ / (4.188 x 10⁻⁹ cm³)

Number of cells = 3.04 x 10¹⁷

Therefore, there are approximately 3.04 x 10¹⁷ cells in the average hippo.

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101 is not in the sequence of 3n-2 because it cannot be obtained by multiplying a positive integer n by 3 and subtracting 2 from the product.

The sequence 3n-2 is a set of numbers obtained by taking a positive integer n, multiplying it by 3 and then subtracting 2 from the product. For example, if n = 1, then 3n-2 = 1. If n = 2, then 3n-2 = 4. If n = 3, then 3n-2 = 7, and so on.

Now, you may wonder why the number 101 is not in the sequence of 3n-2. To understand this, we need to determine whether there exists a positive integer n such that 3n-2 is equal to 101.

Let's start by assuming that such an n exists. Then we can write:

3n-2 = 101

Adding 2 to both sides, we get:

3n = 103

Dividing both sides by 3, we get:

n = 103/3

This means that n is not a whole number, which contradicts our assumption that n is a positive integer. Therefore, there cannot exist any positive integer n such that 3n-2 equals 101.

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Consistent practice is key to improving your math skills over time.

If you feel like you're really bad at math, it's important to start with the basics. This might mean reviewing concepts like arithmetic, fractions, decimals, and percentages. You can find resources online or in books that can help you with this. Once you have a solid foundation, try to identify your strengths and weaknesses so you can focus your efforts on the areas where you need the most improvement. Find a learning style that works best for you, whether it's working independently, with a tutor, or in a study group. Finally, remember that consistent practice is key to improving your math skills over time. Don't give up, and don't be afraid to ask for help when you need it.

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To find the perimeter of a square, you simply add up the lengths of all four sides. If we let "s" be the length of one side of the square, then the perimeter P can be found using the formula:

P = 4s

Since all four sides of a square are equal, we can simplify this expression to:

P = s + s + s + s = 4s

Therefore, the perimeter of the square is equal to 4 times the length of one side. If the length of one side is given in simplified radical form (such as √2 or √3), then the perimeter should also be expressed in simplified radical form.

For example, if the length of one side is 2√2 units, then the perimeter would be:

P = 4s = 4(2√2) = 8√2 units

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Answer:

This relation is a function.

Algebraically, this function is written as

y = 5x.

To use the Integral Test, we need to find an integral that is comparable to the series. We can do this by using a basic comparison test and comparing it to the p-series with p=2.

n^2 / (n^3 + 3) < n^2 / n^3 = 1/n
The series 1/n is a divergent p-series with p=1, so we can conclude that the original series is also divergent.
To find the corresponding integral, we can integrate the function 1/n^2:
∫(n=1 to ∞) 1/n^2 dn = [-1/n] (n=1 to ∞) = 1/1 - 0 = 1
Since the improper integral converges to 1, we can conclude that the infinite series is divergent by the Integral Test.
Hi there! To use the Integral Test to determine whether the given infinite series is convergent, first rewrite the series as a function:
f(x) = x^2 / (x^3 + 3)

Next, we need to check that the function is continuous, positive, and decreasing on the interval [1, ∞). This function satisfies these conditions.
Now, we will calculate the improper integral:
∫(from 1 to ∞) (x^2 / (x^3 + 3)) dx
Let's use substitution: u = x^3 + 3, so du = 3x^2 dx, and x^2 dx = (1/3)du.
Now, the integral becomes:
(1/3) ∫(from 1 to ∞) (1/u) du
This integral is the same as the integral of 1/u from 1 to ∞, which is a well-known improper integral that diverges (ln(u) evaluated from 1 to ∞ results in ∞).

Therefore, by the Integral Test, the infinite series ∑(from n=1 to ∞) (n^2 / (n^3 + 3)) diverges. So the correct answer is B. Diverges.

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