Math
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area of circles - item 34972
the diameter of a quarter is about 1 in.
you trace around the edge of the quarter on a sheet of paper.
what is the area of the circle on the paper?
use 3. 14 as an approximation for a round your answer to the nearest tenth,

To find the critical numbers of h(x) = sin^2(x) + cos(x) in 0 < x < 2π steps are first to find the derivative h'(x), set h'(x) equal to zero and solve for x and check if solutions are within the given interval. The critical numbers are x = π, π/3, and 5π/3.

To find the critical numbers of the function h(x) = sin^2(x) + cos(x) in the interval 0 < x < 2π, we will follow these steps:

Find the derivative of the function, Set the derivative equal to zero and solve for x, Set h'(x) equal to zero and solve for x, Check if the solutions are within the given interval.
1: Differentiate h(x) with respect to x.
h'(x) = d(sin^2(x) + cos(x))/dx
Using chain rule, we get:
h'(x) = 2sin(x)cos(x) - sin(x)
2: Set h'(x) equal to zero and solve for x.
0 = 2sin(x)cos(x) - sin(x)
Factor out sin(x):
0 = sin(x)(2cos(x) - 1)
So, either sin(x) = 0 or 2cos(x) - 1 = 0.
3: Solve for x and check if the solutions are within the interval 0 < x < 2π.
For sin(x) = 0, x = π (since 0 < π < 2π).
For 2cos(x) - 1 = 0, cos(x) = 1/2.
x = π/3 and 5π/3 (since 0 < π/3 < 2π and 0 < 5π/3 < 2π).
Therefore, the critical numbers of the function h(x) = sin^2(x) + cos(x) in the interval 0 < x < 2π are x = π, π/3, and 5π/3.

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The correct statement is: "The line whose equation is 3x-5y=4 is dilated by a scale factor of [tex]y= (\frac{5}{3} )x[/tex] centered at the origin, and the equation of the dilated line is y= (\frac{5}{3} )x

When a line is dilated by a scale factor of k centered at the origin, the equation of the dilated line is given by y = kx, if the original line passes through the origin. If the original line does not pass through the origin, then the equation of the dilated line is obtained by finding the intersection point of the original line with the line passing through the origin and the point of intersection of the original line with the x-axis, dilating this intersection point by the scale factor k, and then finding the equation of the line passing through this dilated point and the origin.

In this case, the equation of the original line is 3x - 5y = 4. To find the intersection point of this line with the x-axis, we set y = 0 and solve for x:

3x - 5(0) = 4
3x = 4
[tex]x = \frac{4}{3}[/tex]

Therefore, the intersection point of the original line with the x-axis is (4/3, 0). Dilating this point by a scale factor of 5/3 centered at the origin, we obtain the dilated point:

[tex](\frac{5}{3} ) (\frac{4}{3},0) = (\frac{20}{9},0)[/tex]

The equation of the dilated line passing through this point and the origin is given by [tex]y= (\frac{5}{3} )x[/tex]. Therefore, the correct statement is: "The line whose equation is 3x-5y=4 is dilated by a scale factor of [tex]\frac{5}{3}[/tex] centered at the origin, and the equation of the dilated line is [tex]y= (\frac{5}{3} )x[/tex]."

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The slope of the line that represents the proportional relationship between x and y in the given table is 1/6. To graph the line, we can plot the points from the table and connect them with a straight line passing through the origin (0,0).

The relationship between x and y is proportional, which means that there is a constant ratio between the two variables. We can find the slope of the line that represents this relationship by calculating the ratio of the change in y over the change in x between any two points on the line. Let's use the first and last points

slope = (y2 - y1) / (x2 - x1) = (2.0 - 0) / (12 - 0) = 2/12 = 1/6

So, the slope of the line that represents this proportional relationship is 1/6.

To graph the line, we can plot the points from the table and connect them with a straight line. The line will pass through the origin (0,0) and have a slope of 1/6. The graph will look like.

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Answer:

24

Step-by-step explanation:

add all of them up

Answer:

I got you

Step-by-step explanation:

it's c -103 cause you first have to get 180 degrees

From the word problem given, it will take Grace 0.05 hours and Kelly 4.05 to complete the task

To solve this problem, we need to write an equation for the word problem.

Let x = time it takes for Kelly

let y = time it takes for Grace

From the problem;

y = x - 4 ...eq(i)

Since they can complete the work in 20 hours;

1/x + 1/y = 20 ...eq(ii)

Solving for both equations

From equ(ii)

1/x + 1/(x - 4) = 20

Solving for x;

x = 4.05 or x = 0.049

Put the value in and solve for y

y = x - 4

y = 4.05 - 4 = 0.05 or y = 0.0049 - 4 = insignificant

The value of y = 0.5 hours

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Answer:

The answer to the question provided is choice A, 4.

The value of m which makes the inequality true is, 4

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 3m - 4 < 11

Now,. We can simplify as;

⇒ 3m - 4 < 11

⇒ 3m < 11 + 4

⇒ 3m < 15

⇒ m < 5

Thus, The value of m which makes the inequality true is, 4

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I apologize, but there seems to be some confusion in your question. The function given, y = ∫√25sin^2t - 1 dt, is not a curve but rather an indefinite integral expression. In order to find the length of a curve, we need a function defined explicitly in terms of x (or y) and its bounds. Could you please provide more information or clarify your question?
To find the length of the curve given by y = ∫√(25sin^2(t) - 1) dt from 0 to π/2, we need to calculate the definite integral.

First, let's set up the integral:

Length = ∫√(25sin^2(t) - 1) dt, with bounds from 0 to π/2

Unfortunately, this integral cannot be solved analytically using elementary functions. You will need to use a numerical method, such as the Trapezoidal Rule or Simpson's Rule, to approximate the value of the integral, and thus find the length of the curve.

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The equation of the attached graph is

The equation is written by the general formula

y = A cos (Bx + C) + D

where:

A = amplitude.

B = 2π/T

where T = period

C = phase shift.

D = vertical shift.

A = amplitude

A = (maximum - minimum) / 2

Using the graph,

maximum = 1

minimum = -1

A = [1 - (-1)] / 2 = 2/2 = 1

B = 2π/T

where T = 2π

B = 2π/(2π) = 1

C = phase shift = 0

D = vertical shift

D = 1 - 1 = 0

substituting results to

y = 1 cos (1x + 0) + 0

this is written as

y = 1 cos (1x) + 0

y = cos (x)

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Answer: 6 chocolates

Step-by-step explanation:

Keilantra had 24 chocolates to begin with, and she ate six lots of three. so the first step is 6 x 3 = 18. Now that we know how many chocolates Keilantra ate, we need to figure out how many chocolates she has left. So we take our product (18) and we subtract it from the total (24). So we end up with 24 - 18 = 6.

Therefore , the solution of the given problem of unitary method comes out to be  it is consistently a constant proportion or percentage of the preceding value.

The task can be completed using the well-known minimalist technique, actual variables, and any essential components from the very first Diocesan specialised question. In response, customers can be given another opportunity to use the item. If not, significant effects on our comprehension of algorithms will disappear.

Here,

According to the students' responses, all instances of exponential decay share the following characteristics:

They begin with a baseline value. (y-intercept).

They get smaller with time. (or successive periods).

They get closer to a horizontal asymptote, which stands for the function's minimum or limit value.

The graphs also demonstrate that, although the rate of decay—or the rate at which values decrease—can vary from circumstance to circumstance,

it is consistently a constant proportion or percentage of the preceding value.

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The weight of Lucy's dog, written in expanded notation, is 9 kilograms and 0.75 kilograms.

Expanded notation is a way of writing a number as the sum of each digit multiplied by its place value. In this case, the number is 9.75. The digit 9 is in the tens place, so it represents 9 tens or 90. The digit 7 is in the ones place, so it represents 7 ones or 7.

The digit 5 is in the tenths place, so it represents 5 tenths or 0.5. The digit 7 is in the hundredths place, so it represents 7 hundredths or 0.07. Therefore, the weight of Lucy's dog in expanded notation is 90 kilograms plus 7 kilograms plus 0.5 kilograms plus 0.07 kilograms, which simplifies to 9 kilograms and 0.75 kilograms.

Mathematically, we can represent the given number as 9.75 = 9 x 10 + 7 x 1 + 5 x 0.1 + 7 x 0.01 = 90 + 7 + 0.5 + 0.07 = 9.57. Thus, the weight of Lucy's dog written in expanded notation is 9 kilograms and 0.75 kilograms.

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Answer:

Angle Q measures 55°, so angle M measures 55°.

39 + 55 + x = 180

94 + x = 180

x = 86

The set of all points in quadrant I not including the axis's can be represented by the following system of inequalities:

x > 0

y > 0

Inequalities are useful in modeling situations where there are constraints or limitations. For  illustration, in real- life  scripts, there may be limited  coffers or capacity, or certain variables must fall within a specific range. Systems of inequalities are  frequently used to represent these constraints or limitations graphically.   One common  operation of systems of inequalities is in optimization problems, where the  thing is to maximize or minimize a particular function subject to certain constraints.

In these situations, the  doable region, or the set of all points that satisfy the constraints, is  frequently represented as a shadowed region on a graph. The optimal  result is  also  set up by  relating the point( s) within this region that maximize or minimize the function.

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The correct comparison of the numbers is:

678,200 > 678,194 > 678,227

Therefore, the answer is the last option, "678,200 > 678,194 > 678,227".

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The area of the sector is approximately 73.14 square centimeters.

The formula to calculate the area of a sector is given by A = (θ/2) × r^2, where θ is the central angle measure in radians, and r is the radius of the circle.

Substituting the given values in the formula, we get A = (4/7π/2) × 16^2

Simplifying this expression, we get A = (8/7) × 16^2 × π/2

A = 128π square centimeters/7

Using the approximation π ≈ 3.14, we can calculate the value of A as follows:

A ≈ (128 × 3.14) square centimeters/7 ≈ 573.44 square centimeters/7 ≈ 73.14 square centimeters (rounded to two decimal places)

Therefore, the area of the sector is approximately 73.14 square centimeters.

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To find three positive integers x, y, and z that satisfy the given conditions, we need to use the concept of maximizing a function subject to certain conditions. Solving for y and z, we have y = 15 and z = 16.

In this case, we want to maximize the function P= xy^2z, subject to the condition that the sum of x, y, and z is 32.
To maximize P, we need to find the values of x, y, and z that make P as large as possible. One way to do this is to use the method of Lagrange multipliers, which involves finding the critical points of a function subject to a constraint.
In this case, we have the function P= xy^2z and the constraint x+y+z=32. Using Lagrange multipliers, we can set up the following equations:
∂P/∂x = λ∂(x+ y+ z)/∂x
y^2z = λ
∂P/∂y = λ∂(x+ y+ z)/∂y
2xyz = λ
∂P/∂z = λ∂(x+ y+ z)/∂z
xy^2 = λ
x+y+z=32
Solving these equations simultaneously, we get:
y^2z/x = 2xyz/y = xy^2/z = λ
Simplifying, we get:
y^2z/x = 2yz = xy^2/z
Rearranging, we get:
x = 2y^3/z
y = (x/2z)^(1/3)
z = (x/4y^2)^(1/3)
Substituting these expressions for x, y, and z into the constraint x+y+z=32, we get:
2y^3/z + (x/2z)^(1/3) + (x/4y^2)^(1/3) = 32
Solving this equation for x, y, and z, we get:
x = 16
y = 4
z = 2
Therefore, the three positive integers x, y, and z that satisfy the given conditions are x=16, y=4, and z=2. These values make P= xy^2z a maximum, since any other values of x, y, and z that satisfy the constraint x+y+z=32 would yield a smaller value of P.

To find three positive integers x, y, and z that satisfy the given conditions, we need to consider the following:
1. The sum of x, y, and z is 32: x + y + z = 32
2. The product P = xy^2z is a maximum.
First, let's express z in terms of x and y using the sum condition:
z = 32 - x - y
Now, substitute this expression for z into the product P:
P = xy^2(32 - x - y)
To maximize P, we should make y as large as possible, since it has the largest exponent in the product formula. Let's allocate the majority of the remaining sum to y. For example, if x = 1, we get:
1 + y + z = 32
Solving for y and z, we have y = 15 and z = 16. Now let's check the product:
P = (1)(15^2)(16) = 3600
This is one possible solution for x, y, and z that gives a maximum product P with the given conditions. The three positive integers are x = 1, y = 15, and z = 16, and the maximum product P = 3600.

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The property was not explicitly used in this example, but it is worth noting that adding 0 to any number leaves it unchanged (i.e., a + 0 = a).

The properties that were used to simplify the expression 4 + 3(9 + 2) into 37 are:

Distributive property: The expression was rewritten as 4 + (3 × 9) + (3 × 2) by distributing the 3 over the parentheses.

Associative property: The order of the terms (3 × 9) and (3 × 2) was rearranged without changing the result because of the associative property of multiplication.

Commutative property: The order of the terms 4, 27, and 6 was rearranged without changing the result because of the commutative property of addition.

Identity property: The property was not explicitly used in this example, but it is worth noting that adding 0 to any number leaves it unchanged (i.e., a + 0 = a).

The properties used to simplify the expression are Associative property of addition, Commutative property of addition, and Distributive property and Identity property of addition. Therefore, the correct option is A, C, E and F.

The properties used to simplify the expression are as follows.

1. Distributive property (E): 4 + 3(9 + 2) = 4 + (3 × 9) + (3 × 2)

This property is applied when a number is multiplied with the sum of two or more numbers. In this case, the number 3 is distributed over the numbers 9 and 2.

2. Identity property of addition (F): 4 + 27 + 6 = 4 + 6 + 27

This property states that adding zero to any number does not change its value. Although this property isn't explicitly shown in the given steps, it is implied by the fact that we can rearrange the terms in the addition without changing their value.

3. Commutative property of addition (C): 4 + 6 + 27 = 10 + 27

This property states that changing the order of numbers in an addition does not change the sum. Here, the numbers 4 and 6 were rearranged to make it easier to add them together.

4. Associative property of addition (A): (10 + 27) = 37

This property states that the grouping of numbers in an addition does not affect the sum. In this case, the parentheses are unnecessary since the numbers were already grouped correctly.

In summary, the properties used to simplify the expression are: A) Associative property of addition, C) Commutative property of addition, and E) Distributive property and F) identity property of addition.

Note: The question is incomplete. The complete question probably is: The real number properties can be used to simplify numerical expressions. in this section, you will identify which properties were used to simplify several expressions. Which properties were used to simplify the following expression? select all that apply.

4 + 3(9 + 2)

4 + (3 × 9) + (3 × 2)

4 + 27 + 6

4 + 6 + 27

10 + 27

37

A) associative property of addition B) associative property of multiplication C) commutative property of addition D) commutative property of multiplication E) distributive property F) identity property of addition G) identity property of multiplication

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The percentage of the model is shaded is 45% if the total number of square is 80 option (H) is correct.

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

Total No. of squares = 10×8 = 80

Total No. of squares shaded = 36

Percentage of the model is shaded = (36/80)×100

= 0.45×100

= 45%

Thus, the percentage of the model is shaded is 45% if the total number of square is 80 option (H) is correct.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

If A car accelerates away from the starting line at 3. 6 m/s2 and has a mass of 2400 kg, Therefore, the net force acting on the vehicle is 8640 N.

The net force acting on the vehicle can be calculated using Newton's second law of motion, which states that the force applied to an object is equal to its mass multiplied by its acceleration:

Net force = mass x acceleration

In this case, the mass of the car is 2400 kg and the acceleration is 3.6 m/s^2. Thus, we can calculate the net force as:

Net force = 2400 kg x 3.6 m/s^2

Net force = 8640 N

Therefore, the net force acting on the vehicle is 8640 N.

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Answer:

So Monica is 9 years old.

To find Amita's age, we substitute x into the expression for Amita's age:

Amita's age = 9 + 3 = 12

Therefore, Amita is 12 years old.

A square pyramid with the maximum volume that can fit inside a cube has a same base as a cube ( 30 cm x 30 cm ) . The height of the pyramid is also same as a side length of a cube ( h = 30 cm ).

    The volume of the pyramid:

    V = 1/3 · 30² · 30 = 1/3 · 900 · 30 = 9,000 cm³

    The maximum volume of the pyramid is 9,000 cm³.

The pool is draining at a rate of 1.36% per hour according to Inayah's claim.

According to Inayah's claim, the pool is experiencing a draining at a rate of 1.36% per hour. This means that for every hour that passes, the pool's water level decreases by 1.36% of its total volume.

Understanding the rate at which a pool is draining is essential for monitoring and managing water levels. If the rate of drainage is accurate, it can help estimate how long it would take for the pool to reach a certain level or completely drain. Additionally, it aids in determining the necessary actions to maintain the pool's water balance and prevent potential issues such as overflow or inadequate water supply.

It is crucial to verify the accuracy of the claim by monitoring the pool's water level over a specific period. This can be done by measuring the change in water volume or using other reliable methods to ensure the drainage rate aligns with the claimed percentage.

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The primary reason many present-day African nations struggled to unite their people is F. Because many African peoples have strong tribal ties.

The strong tribal identities and loyalties that exist among various ethnic groups inside African states today are one of the main causes of the effort to bring people together. Through colonisation, many African nations were developed, and many of them contained numerous groups with various cultural, linguistic, and ethnic origins.

Therefore, as a result, it has been challenging to forge a strong sense of national identity among many individuals who still identify primarily with their own tribe or ethnic group. This has occasionally resulted in disputes and hostilities amongst various diverse groups, impeding efforts to create a community that is more unified.

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Applying the triangle inequality theorem, the possible length of side AC is: C. 18 inches.

The triangle inequality theorem states that lengths of the two sides of a triangle, when added together must be greater than the third side of any given triangle.

Therefore, to determine the possible length of side AC, we can use the triangle inequality theorem, stated above and applying this to triangle ABC, we have the following:

AC < AB + BC

AC < 12 + 20

AC < 32

This implies that, length of side AC must be less than 32 inches. Thus, the answer is: C. 18 inches.

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The population of the world in 1955 based on the model q(t) = 2.500[tex]e^{0.0168t}[/tex] is 2.54 billion.

The model q(t) = 2.500[tex]e^{0.0168t}[/tex] represents the world population in billions

Here, t represents the years after 1955 and e is exponential constant its value is approximately 2.718.

Here the population is growing exponentially means population is growing at faster rate.

To find the population of the world in 1955 we will take

t = 1

on putting the value of t in the given function q(t)

q(t) = 2.500e[tex]e^{0.0168(1)[/tex]

on solving the function q(t) we get

q(t) ≈ 2.54

so, the population of the world in 1955 is 2.54 billion

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The equation defines a linear function is A y = 2x/4 + 12

A y = 2x/4 + 12 is the equation that defines a linear function because it can be simplified to y = 1/2x + 12,

Which has a constant slope of 1/2 and a constant rate of change.

The other options are not linear functions because they involve exponents or do not have a constant slope.

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Answer:

  (x, y) = (1, 3)

Step-by-step explanation:

You want to solve this system of equations by substitution:

We can solve the first equation for an expression in x:

  x = (1.1 -0.3y)/0.2 = (11 -3y)/2

Substituting for x in the second equation gives ...

  0.7(11 -3y)/2 -0.5y +0.8 = 0

  7.7 -2.1y -y +1.6 = 0 . . . . . . . . . multiply by 2, eliminate parentheses

  -3.1y +9.3 = 0 . . . . . . . . . . . . collect terms

  y -3 = 0 . . . . . . . . . . . . . . . divide by -3.1

  y = 3 . . . . . . . . . . . . . . . add 3

  x = (11 -3(3))/2 = 2/2 = 1 . . . . . find x

The solution is (x, y) = (1, 3).

__

Additional comment

A graphing calculator confirms the solution.

The region bounded by the given curves is a triangle with vertices at (0,0), (1,1), and (1,0). When this region is revolved around the line y=3, we obtain a solid with a hole in the middle.
To find the volume of this solid, we can use the method of cylindrical shells. Imagine slicing the solid into thin cylindrical shells with radius r and height Δy. The volume of each shell is approximately 2πrΔy times the thickness of the shell.

The distance between the axis of rotation (y=3) and the line y=1 is 2 units. Therefore, the radius of each cylindrical shell is r = 3 - y. The height of each shell is Δy = dx, where x is the distance from the y-axis.

To set up the integral, we need to express x in terms of y. Since the region is bounded by y=x and y=1, we have x=y for 0<=y<=1. Therefore, the integral for the volume of the solid is:
V = ∫[0,1] 2π(3-y)x dx
 = 2π ∫[0,1] (3-y)y dx

Evaluating this integral, we get:
V = 2π [3y^2/2 - y^3/3] from 0 to 1
 = 2π (3/2 - 1/3)
 = 2π/3

Therefore, the volume of the solid obtained by rotating the region bounded by y=x, y=1 about y=3 is (2/3)π cubic units.

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