Find the center and radius of the circle
represented by the equation below.
x² + y² - 6x + 4y+4= 0
Center:

(a) (i) Average velocity = change in displacement / change in time = 20 feet / 1 second = 20 feet per second.

(ii) Average velocity = change in displacement / change in time = 14 feet / 0.5 seconds = 28 feet per second.

(iii) Average velocity = change in displacement / change in time = 1.76 feet / 0.1 seconds = 17.6 feet per second.

(b) To find the instantaneous velocity at t = 2 seconds, we substitute t = 2 into the velocity function: v(2) = 100 - 32(2) = 100 - 64 = 36 feet per second

(a) To find the average velocity of the projectile over the given time intervals, we need to calculate the change in displacement divided by the change in time for each interval. The average velocity is a vector quantity, so we need to consider both magnitude and direction.

(i) [2,3]:

To find the average velocity over the interval [2,3], we can calculate the displacement at t = 3 and t = 2, and then divide it by the time difference.

At t = 3:

s(3) = 100 * 3 - 16 * 3^2 = 300 - 144 = 156 feet.

At t = 2:

s(2) = 100 * 2 - 16 * 2^2 = 200 - 64 = 136 feet.

Change in displacement = s(3) - s(2) = 156 - 136 = 20 feet.

Change in time = 3 - 2 = 1 second.

Average velocity = change in displacement / change in time = 20 feet / 1 second = 20 feet per second.

(ii) [2,2.5]:

Similarly, for the interval [2,2.5], we can calculate the displacement at t = 2.5 and t = 2, and then divide it by the time difference.

At t = 2.5:

s(2.5) = 100 * 2.5 - 16 * 2.5^2 = 250 - 100 = 150 feet.

At t = 2:

s(2) = 100 * 2 - 16 * 2^2 = 200 - 64 = 136 feet.

Change in displacement = s(2.5) - s(2) = 150 - 136 = 14 feet.

Change in time = 2.5 - 2 = 0.5 seconds.

Average velocity = change in displacement / change in time = 14 feet / 0.5 seconds = 28 feet per second.

(iii) [2,2.1]:

For the interval [2,2.1], we can follow the same process.

At t = 2.1:

s(2.1) = 100 * 2.1 - 16 * 2.1^2 = 210 - 72.24 = 137.76 feet.

At t = 2:

s(2) = 100 * 2 - 16 * 2^2 = 200 - 64 = 136 feet.

Change in displacement = s(2.1) - s(2) = 137.76 - 136 = 1.76 feet.

Change in time = 2.1 - 2 = 0.1 seconds.

Average velocity = change in displacement / change in time = 1.76 feet / 0.1 seconds = 17.6 feet per second.

(b) To find the instantaneous velocity at t = 2 seconds, we can use the concept of limits and algebra.

The instantaneous velocity is the limit of the average velocity as the time interval approaches zero. We can find it by taking the derivative of the position function with respect to time, which gives us the velocity function.

s(t) = 100t - 16t^2

Taking the derivative with respect to t:

v(t) = d(s(t))/dt = 100 - 32t

To find the instantaneous velocity at t = 2 seconds, we substitute t = 2 into the velocity function: v(2) = 100 - 32(2) = 100 - 64 = 36 feet per second

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Answer:

10pq^3 + 2q^3 - 17qp^2 - 7pq^2

Step-by-step explanation:

(5p-q) (2p^2-3pq-2q^2)

= 10p^3 - 15qp^2 - 10pq^2 - 2qp^2 + 3pq^2 + 2q^3

= 10pq^3 + 2q^3 - 17qp^2 - 7pq^2

The length of side BD which is the altitude of the triangle is 2√(70)

The length of BD is solved using similar triangles. This is defined by triangles formed from triangle ABC and they include

Let the altitude be h, hence we have the formula of the proportions as

AD / h = h / DC

plugging the values gives

20 / h = h / 14

h^2 = 20 * 14

h = √(20 * 14 )

h = √(280)

h = 2√(70)

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The distance from Marcel and Katya is 34 metres

From the given diagram, we have the following

Acute angle given = 42 degrees

According to SOH CAH TOA identity

sin theta = opp/hyp

sin 42 = x/50

x = 50sin42

x = 50(0.6691)

x = 33.46

Hene the distance from Marcel and Katya is 34 metres

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To find the distance Add the distance between each point and the y-axis, the correct option is D.

We are given that;

Two points  A(-8,-4) and B(2,-4)

Now,

To find the distance between two points on a coordinate plane, you can use the distance formula: d = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the points. In this case, the points are A(-8, -4) and B(2, -4). Plugging in the values, we get:

d = √((2 - (-8))² + (-4 - (-4))²) d = √(10² + 0²) d = √(100) d = 10

The distance between the points is 10 units.

Therefore, by the distance answer will be Add the distance between each point and the y-axis.

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A. The maximum height of the rock is 2624 feet, and it takes 8 seconds to reach this height.

B. The rock is in the air for 8 + 2√46 seconds before hitting the ground.

In this case, a = -16 and b = 256, so the time it takes for the rock to reach its maximum height is t = -256/(2*(-16)) = 8 seconds.

y = -16(8)² + 256(8) + 1680 = 2624 feet.

b. 0 = -16t² + 256t + 1680

Simplifying, we get:

t² - 16t - 105 = 0

Using the quadratic formula, we get:

t = (16 ± √(16² + 4(105)))/2 = (16 ± √736)/2 = (16 ± 4√46)/2 = 8 ± 2√46

Therefore, the rock is in the air for 8 + 2√46 seconds before hitting the ground.

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Answer:

Step-by-step explanation:

\(\frac{3x^3}{12x^{-2}} = \frac{x^5}{4}\)

Tyna's mistake was that , she miswrote x^-2 as x^2

Answer:

8+k2-6>8(k+2)-4k

Step-by-step explanation:

8+7×2-6 and 8(7+2)-4×7

8+14-16 and (56+16)-28

6 and 44

Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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The integer value of the mathematical statement  is -2

The mathematical statement is given as:

- 2 Feet taller

- 2 Feet taller implies that we have a negative integer -2

i.e.

Value = -2

Hence, the integer value of the mathematical statement  is -2

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To find inflection points from the second derivative, follow these steps  Calculate the second derivative of the function.  Set the second derivative equal to zero and solve for the critical points.Determine the sign changes of the second derivative around each critical point. Identify the intervals where the sign changes occur.

Analyze the behavior of the function within each interval to determine the presence of inflection points. To understand the process more thoroughly, start by calculating the second derivative of the function. This can be done by differentiating the function twice with respect to the independent variable. Next, find the critical points by setting the second derivative equal to zero and solving the resulting equation. Once you have the critical points, examine the sign changes of the second derivative around each point.

A change from positive to negative or vice versa indicates a potential inflection point. Finally, analyze the behavior of the function within each interval to confirm the presence of inflection points. Keep in mind that not all critical points will correspond to inflection points, so it is essential to consider the behavior of the function in each interval.

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Answer:276

Step-by-step explanation:

Answer:

124.6

Step-by-step explanation:

Answer:

Use long division to get the answer of 78.75

Step-by-step explanation:

long division ends with this answer, ➗

Answer:

i think j

if i am wrong sory i am

Step-by-step explanation:

The correct answer to the following question will be 0.000000009 so answer (F) will be correct.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given,

Diameter of structure =  9 × 10⁻⁹ meter

Multiply and divide by 10⁹

Diameter of structure =  9 × 10⁻⁹ ×  10⁹/ 10⁹

By the law of indices

Diameter of structure = 9/10⁹

Diameter of structure = 0.000000009

Hence "The correct answer to the following question will be 0.000000009".

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To solve the given initial-value problem, first find the complementary solution, then the particular solution, and finally apply the initial conditions.

The complementary solution is obtained by solving the homogeneous equation y'' + 4y' + 4y = 0. The characteristic equation is r^2 + 4r + 4 = 0, which can be factored as (r + 2)^2 = 0. The root is r = -2, which is a repeated root, so the complementary solution is y_c(x) = C_1e^(-2x) + C_2xe^(-2x).

Next, find the particular solution y_p(x) for the non-homogeneous equation y'' + 4y' + 4y = (5 + x)e^(-2x). Using the method of undetermined coefficients, let y_p(x) = A(x)e^(-2x) + B(x)e^(-2x). Differentiate y_p(x) and substitute it into the non-homogeneous equation. Then, solve for A(x) and B(x) to obtain y_p(x).

Finally, combine y_c(x) and y_p(x) to form the general solution y(x) = y_c(x) + y_p(x). Apply the initial conditions y(0) = 3 and y'(0) = 9 to find the constants C_1 and C_2. Substitute the values of C_1 and C_2 back into the general solution to get the final answer.

The initial-value problem is given byy'' + 4y' + 4y = (5 + x)e−2x, y(0) = 3, y'(0) = 9.To solve the given initial-value problem, we need to determine the roots of the characteristic equation of the equation y'' + 4y' + 4y = 0.The characteristic equation of the equation is given byr² + 4r + 4 = 0Solving for r,r = -2 (twice)Since the roots of the characteristic equation are equal, the solution to the homogeneous equation is given byy = (c₁ + c₂x)e^(-2x)We need to find the particular solution to the non-homogeneous equation.The right-hand side of the non-homogeneous equation is of the form (5 + x)e^(-2x). This suggests that the particular solution has the formy_p = (Ax + B)e^(-2x)Differentiating the above equation twice, we gety'_p = (-2Ax - 2B + A)e^(-2x)y''_p = (4Ax + 4B - 3A)e^(-2x)Substituting the above equations into the non-homogeneous equation, we get(4Ax + 4B - 3A)e^(-2x) + 4(-2Ax - 2B + A)e^(-2x) + 4(Ax + B)e^(-2x) = (5 + x)e^(-2x)Simplifying, we getA = -1, B = 2Thus, the particular solution is given byy_p = -(x + 2)e^(-2x)The general solution to the non-homogeneous equation is given byy = (c₁ + c₂x)e^(-2x) - (x + 2)e^(-2x)The solution to the given initial-value problem is obtained by substituting the initial values y(0) = 3 and y'(0) = 9 into the above equation.y(0) = (c₁ + c₂ × 0)e^(-2 × 0) - (0 + 2)e^(-2 × 0) = 3Hence,c₁ - 2 = 3c₁ = 5Similarly, y'(0) = -2c₁ + 4c₂ + 2 = 9c₁ - 2c₂ = 7Solving for c₁ and c₂, we getc₁ = 5, c₂ = -1Thus, the solution to the given initial-value problem is given byy = (5 - x)e^(-2x) - (x + 2)e^(-2x)y(x) = (5 - x - x - 2)e^(-2x)y(x) = (3 - 2x)e^(-2x)Hence, y(x) = (3 - 2x)e^(-2x) is the required solution.

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In the given equation r = 2/5 t "r" is the dependent variable.

In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.

An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.

A dependent variable is a variable whose value depends on the value of one or more other variables in the equation

Here we have

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups.

She writes the equation r = 2/5 t to describe the relationship.

In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.

Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.

The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.

Therefore,

In the given equation r = 2/5 t "r" is the dependent variable.

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Complete Question:

Lin notices that the number of cups of red paint is always  2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.

The graph that matches sine function y = 2 sin (x – π) + 2 is:

On a coordinate plane, a function has a maximum of 4 and minimum of 0. It completes one period at 2 pi. It decreases through the y-axis at (0, 2).

A graph is a pictorial representation of data. Graphs are usually plotted in a cartesian plane having x and y directions

The graph in the given problem is a graph showing sin function representing sinusoidal waves.

The given equation: y = 2 sin (x – π) + 2

substituting x = 0

y = 2 sin (0 – π) + 2

y = 2 sin (-π ) + 2  (in radians)

y = 2 * 0 + 2

y = 0 + 2

y = 2

Therefore the ordered pair is correct for the graph (0, 2)

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Answer: The answer is D (the last option)

Step-by-step explanation:

The probability that the random sample of 16 people in the elevator will exceed the weight limit is essentially 1. Rounded to 4 decimal places, the answer is 1.0000.

To answer this question, we need to use the central limit theorem, which states that for a large enough sample size, the sample mean will be approximately normally distributed regardless of the underlying population distribution.

In this case, we are given that the weight of students, faculty, and staff is approximately normally distributed with a mean weight of 150 pounds and a standard deviation of 27 pounds. We are also given that the elevator has a weight limit of 2500 pounds and a 16-person limit.

To find the probability that the random sample of 16 people in the elevator will exceed the weight limit, we first need to calculate the mean and standard deviation of the sample.

The mean weight of the sample can be calculated as:

mean = population mean = 150 pounds

The standard deviation of the sample can be calculated using the formula:

standard deviation = population standard deviation / √sample size

standard deviation = 27 / √16 = 6.75 pounds

Next, we need to calculate the z-score for the weight limit:

z = (weight limit - mean) / standard deviation

z = (2500 - 150) / 6.75 = 341.48

This z-score is extremely high, which indicates that the probability of the sample weight exceeding the weight limit is very close to 1 (i.e., almost certain).

To calculate the actual probability, we can look up the z-score in a standard normal distribution table or use a calculator. Using a calculator, we can find that the probability of a z-score of 341.48 or higher is essentially 1.

Therefore, the probability that the random sample of 16 people in the elevator will exceed the weight limit is essentially 1. Rounded to 4 decimal places, the answer is 1.0000.

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The fraction in lowest terms is 2/3. Option C

First, we need to know that a fraction is described as the part of a whole variable, a whole number or a whole element.

The different  fractions in mathematics are listed thus;

From the information given, we have that;

a+1/b

Such that a = 5 and b = 9

Now, substitute the values, we get;

5 + 1/9

Add the values of the numerator

6/9

Divide the values

2/3

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Planets around other stars can be detected by carefully measuring the "brightness" or "light intensity" of stars.

When a planet orbits a star, it causes a slight change in the brightness or light intensity of the star. This is known as the transit method of planet detection. As the planet passes in front of the star from our line of sight, it blocks a small portion of the star's light, causing a temporary decrease in its brightness. By carefully measuring these changes in brightness over time, scientists can infer the presence and characteristics of planets orbiting the star. This method has been instrumental in the discovery of numerous exoplanets in recent years.

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Answer:

Step-by-step explanation:

The four walls have a linear length of (9 m)×4 = 36 m. Of that, the two 1-meter doors are not painted, so the linear length of the painted area is 34 m. The painted area is 2 m high, so the total area being painted is ...

  A = LW

  A = (34 m)(2 m) = 68 m²

The amount of paint needed for this area is ...

  (68 m²) × (1 L/(10 m²) = 6.8 L

If we assume the paint only comes in units of 1 L, then Heather will need 7 L of paint.

The cost of 7 L of paint is ...

  (7 L) × ($3.75/L) = $26.25

Heather will need 7 L of paint, for a total cost of $26.25.

1. 2(8x – 1) + 2(2x + 4)

2. 16x – 2 + 4x + 8

3. (20x + 6)

Step-by-step explanation:

The perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x + 6

The formula for calculating the perimeter of a rectangle is expressed as:

P = 2( l + w)

Given the following parameters

length l = 8x - 1

width w = 2x + 4

Substitute the expressions for the length and width into the formula;

P = 2(8x - 1 + 2x + 4)

P = 2(10x + 3)

Distribute 2 over each term in the parenthesis

P = 2(10x) + 2(3)

P = 20x + 6

Hence the perimeter of the rectangle with length 8x - 1 and width 10x + 3 is 20x + 6

if i help please give brainly

Answer:

below

Step-by-step explanation:

A B C E

all of them but D

The value of the function g(f(x)) when f(x)=x^3+3x^2+4x+5 and g(x)=5 is 225

Functions are defined as expressions, rules or laws that expressed or explains the relationship between two variables.

These variables are termed;

It is important to note that composite functions are determined when the output of a given function is used as the input of another or different variable.

Example of composite functions;

f g ( x )

g(f(x))

Given the functions;

f(x) = x^3+3x^2+4x+5 and

g(x)=5

To determine the value of g(f(x))=, we have to substitute the value of g(x) as 5 for x in (x)

We have;

g(f(x))= (5)³ + 3(5)² + 4(5) + 5

expand the bracket

g(f(x)) = 125 + 75 + 20 + 5

Add the values

g(f(x)) = 225

Thus, the value of the function g(f(x)) when f(x)=x^3+3x^2+4x+5 and g(x)=5 is 225

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The production function Yt =A[αK tv v−1+(1−α)N tv v−1] v−1v does not exhibit constant returns to scale.

The concept of constant returns to scale is a property of production functions. It refers to a situation in which an increase in inputs such as labor, capital, or both results in a proportionate rise in output.

The production function Y = f(K, N) exhibits constant returns to scale if, for all values of K and N, there is a scalar λ such that Y(λK, λN) = λY(K, N)

If this condition holds, then we can say that the production function exhibits constant returns to scale.

Does the production function Yt =A[αK tv v−1+(1−α)N tv v−1] v−1v exhibit constant returns to scale?

Let us determine whether the production function

Yt =A[αK tv v−1+(1−α)N tv v−1] v−1v

exhibits constant returns to scale using the definition above.

Y(λK, λN) = A[α(λK) v (v−1) + (1−α)(λN) v (v−1)] v−1vY(λK, λN)

Y(λK, λN) = A[λvαK v (v−1) + λv(1−α)N v (v−1)] v−1vY(λK, λN)

Y(λK, λN) = A[λvαK v (v−1)v−1v + λv(1−α)N v (v−1)v−1v]Y(λK, λN)

Y(λK, λN) = λvA[αK v−1 + (1−α)N v−1] v

Since λ appears outside the bracket, the production function does not satisfy the condition of constant returns to scale because λ is not eliminated on both sides of the equation.

Therefore, we can conclude that the production function Yt =A[αK tv v−1+(1−α)N tv v−1] v−1v does not exhibit constant returns to scale.

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True when desired information of Census is available for all objects in the population

A census is a study that collects data from every member of a population, making it the most comprehensive form of data collection.

A census can provide highly accurate information on the entire population, without any risk of sampling error.

However, conducting a census can be time-consuming and costly, especially for large populations, and may not always be practical or feasible. In some cases, a sample study may be a more practical approach, as it can provide accurate information with less time and cost.

However, it's important to carefully consider the sampling design to ensure that the sample is representative of the population, in order to minimize sampling bias.

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The formula to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).

The formula presented derived from the formula for the circumference of a circle, which is C = 2πr. By rearranging the equation and isolating the radius (r) on one side, we get r = C/(2π).

So, if the circumference (C) of a circle is 18 centimeters, you can use the formula r = C/(2π) to find the radius (r). Plugging in the given value for the circumference (C), we get:

r = 18/(2π)

Simplifying the equation gives:

r = 9/π

Therefore, the radius (r) of the circle is 9/π centimeters.

In conclusion, the formula you can use to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).

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Vector a = (3, 2), then;

Also, vector b = (-5, 6), then;

Then, -3a + 2b = (-9, -6) + (-10, 12)

The answer is (-19,6)