I need help asap!!! (Measurement)

By definition of volume of cone, The radius of cone is,

⇒ r = 2.1 cm

Since, We know that;

The area that any three-dimensional solid occupies is known as its volume.

And, These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

We have to given that;

Volume of cone is,

⇒ V = 120.73 cubic centimeters

And, Height of cone = 8.9 cm

Since, We know that;

Volume of cone is,

V = πr²h/3

Where, r is radius of cone and h is height of cone.

Hence, WE can Substitute all the values, we get;

V = πr²h/3

Here, V = 120.73 , h = 8.9

So,

V = 3.14 × r² × 8.9

120.73 = 27.95r²

r² = 4.31

r = 2.07

r = 2.1

Therefore, The radius of cone is,

⇒ r = 2.1 cm

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Answer:

X >= 6.7

Step-by-step explanation:

So first of all, what you need is write out the equation from the given prompt

x + 2.7 >= 9.4
Next, what you really want to do is

Subtract 2.7 both side
x >= 9.4 - 2.7
x >= 6.7

Answer:

True choices are 1, 2, 5

Step-by-step explanation:

As per diagram, the circles are equal.

Since the distance AB is the radius of both circles:

So the answer choices:

1. AC = BC

2. AC = BD

3. CD = AB

4. ABCD is a square

5. ABD is an equilateral triangle

6. CD = AB + AB

To determine if vector u belongs to the null space of matrix A, we need to perform matrix-vector multiplication between A and u. The null space of a matrix consists of all vectors that, when multiplied by the matrix, result in the zero vector. If A * u = 0, where 0 is the zero vector, then u belongs to the null space of matrix A.

To answer your question, we first need to understand what the null space of a matrix is. The null space of a matrix A, denoted as null(A), is the set of all vectors x such that Ax = 0. In other words, the null space of a matrix is the set of solutions to the homogeneous equation Ax = 0.
Now, if we want to know whether a vector u belongs to the null space of a matrix A, we need to check whether Au = 0. If Au = 0, then u belongs to the null space of A.
So, to answer your question, we need to check whether Au = 0. If it does, then u belongs to the null space of A. If it doesn't, then u does not belong to the null space of A.
The null space of a matrix is an important concept in linear algebra because it helps us understand the behavior of linear transformations and the properties of matrices. The null space is also closely related to the rank of a matrix, which is the dimension of the column space of the matrix. The rank-nullity theorem states that the rank of a matrix plus the dimension of its null space equals the number of columns in the matrix. This theorem is a fundamental result in linear algebra and has many important applications in fields such as engineering, physics, and computer science.

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The graph of the inequality y ≥ (1/2)x - 1 and x - y > 1 is attached. Shannon's graph is correct.

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Inequalities are used for the non equal comparison of numbers and variables.

Given the inequalities:

y ≥ (1/2)x - 1     (1)

and

x - y > 1     (2)

The graph of the inequality is attached. Shannon's graph is correct.

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Answer:

  95

Step-by-step explanation:

Let x represent the ones digit. The tens digit will be higher, because reversing the digits results in a lower number. Its value is (14 -x). The given relation is ...

  (10(14-x) +x) -(10x +(14 -x)) = 36 . . . . reversing the digits gives 36 less

  140 -9x -9x -14 = 36 . . . . eliminate parentheses

  90 = 18x . . . . . . . . add 18x-36

  5 = x . . . . . . ones digit

  14-5 = 9 . . . tens digit

The original number is 95.

__

Check

  95 -59 = 36

_____

Additional comment

The difference in value when the digits of a 2-digit number are reversed is always 9 times the difference in the digits. This means the difference in the digits is 36/9 = 4. Since the sum of digits is 14, the two digits are (14+4)/2 = 9 and (14-4)/2 = 5. 95 is the number of interest.

The solutions to a "sum and difference" problem are half the sum and half the difference of the given sum and difference. That is how we know the larger digit is (1/2)(14 + 4), for example.

We worked this "the hard way" using the above equation. It can actually be worked in your head if you're familiar with these generic solutions.

The product of (2x+7) and (x – 5) is option C) 2x^2 - 3x - 35.

What is FOIL method. give a description

FOIL method is a mnemonic technique used to multiply two binomials. The term "FOIL" stands for First, Outer, Inner, Last, and refers to the order in which the terms in each binomial are multiplied.

To use the FOIL method, you start by multiplying the first terms of each binomial, then the outer terms, the inner terms, and finally the last terms. The resulting terms are then combined using addition or subtraction as needed.

Finding the product of given two terms :

The product of (2x+7) and (x – 5) can be found by using the FOIL method.

we multiply the first terms, then the outer terms, then the inner terms, and finally the last terms:

\((2x + 7) \times (x - 5) = 2x^2 - 10x + 7x - 35\)

\((2x + 7) \times (x - 5) = 2x^2 - 3x - 35\)

Therefore, the answer is option C) \(2x^2 - 3x - 35\).

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Answer:

I think w=6

Step-by-step explanation:

Source: trust me

Answer:

6

Step-by-step explanation:

The length of the rectangle is nine feet less than five times the width. This means that L = 5w - 9. The perimeter, or 2w + 2L, is 54. We can substitute L with 5w - 9 to solve the equation for w.

2w + 2(5w - 9) = 54

2w + 10w - 18 = 54

12w = 72

w = 6

Answer: 7 tens and 6 ones

Step-by-step explanation: 76 is two numbers, with a 7 in the tens place and a 6 in the ones place.

76 can be represented as 7 tens and 6 ones or as 6 tens and 16 ones. This involves understanding the place value of digits in a number and knowing that a ten can be broken down into ones.

The number 76 can be broken down into tens and ones in multiple ways. First, let's understand what tens and ones mean in the context of a number. In the number 76, '7' is the tens place, and '6' is the ones place, meaning there are 7 tens (70) and 6 ones (6) making up 76.

One way to show 76 with tens and ones is to say that there are 7 tens and 6 ones. This is a very direct method where we just count the number of tens and ones in the number.

Another way we could break down 76 is to say there are 6 tens and 16 ones. This method involves taking one of the tens and breaking it down into 10 ones, giving us a total of 6 tens and 16 ones.

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The inequality is: 14.2 + 14.2 + x < 51.3

x < 22.9

We are given the following:

Perimeter of the triangle < 51.3 in.

The sides are 14.2 in., x in., and 14.2 in.

Therefore, we would have the following inequality:

14.2 + 14.2 + x < 51.3

Solve for x

28.4 + x < 51.3

x < 51.3 - 28.4

x < 22.9

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Answer:

0.48

Explanation:

4.8 is greater than 0.48.

Answer:

x= 23

y=7

Step-by-step explanation:

x-y=16

4y-5=x

4y-5-y=16

3y-5=16 add 5 to both sides

3y=21 divide by 3 on both sides

y=7

x-7=16 substitute back in

x=23 added 7 to both sides

so x=23 and y=7

23-7=16

Answer:

(x-0)²+(y-0)²=16

Step-by-step explanation:

The formula for the equation of a circle is (x-a)²+(y-b)²=r², with a,b=center coordinates, and r=radius.

Hope this helps!

We need to write the standard equation of circle with , center (0,0) and radius 4 unit . The Standard equation of the circle is:

\(\longrightarrow ( x - h)^2 + (y -k)^2 = r^2\)

\(\longrightarrow( x -0)^2 + (y-0)^2 = 4^2\)

\(\longrightarrow \bold{x^2 + y^2 = 16 }\)

• Hence the equation of the circle is \(x^2 + y^2 = 16\).

1. Homogeneous solution is \(\rm y_h(t) = c_1e^{(1/2t)} + c_2te^{(1/2t)\).

2. Particular solution: \(\rm y_p(t) = 80e^{(1/2t)\).

3. General solution: \(\rm y(t) = y_h(t) + y_p(t) = c_1e^{(1/2t)} + c_2te^{(1/2t)} + 80e^{(1/2t)\).

1. Find the homogeneous solution:

The characteristic equation for the homogeneous equation is given by \($4r^2 - 4r + 1 = 0$\). Solving this equation, we find that the roots are \($r = \frac{1}{2}$\) (double root).

Therefore, the homogeneous solution is \($ \rm y_h(t) = c_1e^{\frac{1}{2}t} + c_2te^{\frac{1}{2}t}$\), where \($c_1$\) and \($c_2$\) are constants.

2. Find the particular solution:

Assume the particular solution has the form \($ \rm y_p(t) = u(t)e^{\frac{1}{2}t}$\), where u(t) is a function to be determined. Differentiate \($y_p(t)$\) to find \($y_p'$\) and \($y_p''$\):

\($ \rm y_p' = u'e^{\frac{1}{2}t} + \frac{1}{2}ue^{\frac{1}{2}t}$\)

\($ \rm y_p'' = u''e^{\frac{1}{2}t} + u'e^{\frac{1}{2}t} + \frac{1}{4}ue^{\frac{1}{2}t}$\)

Substitute these expressions into the differential equation \($ \rm 4(y_p'') - 4(y_p') + y_p = 80e^{\frac{1}{2}}$\):

\($ \rm 4(u''e^{\frac{1}{2}t} + u'e^{\frac{1}{2}t} + \frac{1}{4}ue^{\frac{1}{2}t}) - 4(u'e^{\frac{1}{2}t} + \frac{1}{2}ue^{\frac{1}{2}t}) + u(t)e^{\frac{1}{2}t} = 80e^{\frac{1}{2}}$\)

Simplifying the equation:

\($ \rm 4u''e^{\frac{1}{2}t} + u(t)e^{\frac{1}{2}t} = 80e^{\frac{1}{2}}$\)

Divide through by \($e^{\frac{1}{2}t}$\):

\($4u'' + u = 80$\)

3. Solve for u(t):

To solve for u(t), we assume a solution of the form u(t) = A, where A is a constant. Substitute this solution into the equation:

\($4(0) + A = 80$\)

\($A = 80$\)

Therefore, \($u(t) = 80$\).

4. Find the particular solution \($y_p(t)$\):

Substitute \($u(t) = 80$\) back into \($y_p(t) = u(t)e^{\frac{1}{2}t}$\):

\($y_p(t) = 80e^{\frac{1}{2}t}$\)

Therefore, a particular solution of the differential equation \($4y'' - 4y' + y = 80e^{\frac{1}{2}}$\) that does not involve any terms from the homogeneous solution is \($y_p(t) = 80e^{\frac{1}{2}t}$\).

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Answer:

9a) 6 1/5

b) 6 4/7

c) 1 1/0

d) 4 1/8

e) 1 1/3

f) 3 1/6

10a) 15 years old

b) 14 1/6 years old

11) 8/3 = 2 2/3

7/5 = 1 2/5

2 2/3 + 1 2/5 = 4 1/15

12a) They ate 3 11/12 pizzas

b) They ate 1 1/3 more cheese pizzas than veg

The area of each triangle using the formula A = 1/2bh would be 2000 meters sq.

The area of the triangle is defined as the product of half the base and the height of the triangle.

The area of the triangle = 1/2 x b x h

We have been given the base of triangle b, 100m and the height of the triangle h, 40m , we are asked to find the area.

We know that Area of triangle = ½ × b × h

Area = ½ × 100 × 40

Area =50 × 40

Area = 2000 meters sq.

Hence, the area of each triangle using the formula A = 1/2bh would be 2000 meters sq.

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The complete question is

The height of the triangle is 40m and the base is b = 100m.  find the area of each triangle using A=1/2bh

Step-by-step explanation:

b = 42

c = 138

plz mark my answer as brainlist plzzzz if you find it useful .

Absolute humidity in conjunction with other factors, such as relative humidity and dew point temperature, can help provide a comprehensive understanding of the atmospheric conditions and their implications.

The term you are looking for is "absolute humidity." Absolute humidity is the mass of water vapor in a given amount of air expressed in grams per cubic meter (g/m3). This measurement represents the actual amount of moisture present in the air, regardless of the temperature or pressure. It is essential to understand and monitor absolute humidity for various applications, such as meteorology, environmental studies, and indoor air quality management. In contrast to relative humidity, which describes the percentage of moisture in the air compared to the maximum amount it can hold at a given temperature, absolute humidity provides a more accurate and direct representation of the water vapor content in the air. By measuring absolute humidity, scientists and professionals can better assess and predict weather patterns, manage heating, ventilation, and air conditioning (HVAC) systems, and ensure optimal conditions for health and comfort. It is important to note that absolute humidity can change as air temperature and pressure change, even if the amount of water vapor remains constant. This is because the air's capacity to hold water vapor depends on its temperature and pressure.

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When reading a buret with graduated markings at every 0.1 ml, your recorded volume should read to a) hundredths place.

A burette is a long tube-shaped glass instrument with scale lines like a measuring pipette or measuring cup with the same cross section from top to bottom. At the bottom of this tool is equipped with a faucet as a place for the solution to come out at the mouth of the burette.

The function of the burette is as a tool to measure the solution based on the volume released. The burette size usually has a volume of 25 / 50 ml.

If the burette is being used, it must be supported firmly with a stand equipped with clamps to clamp the burette. Make sure that when clamping the burette in the stand and clamp the position of the burette must be perpendicular so that the scale reading is correct and does not cause paralax errors.

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The reformulated problem includes the original variables x₁, x₂, x₃, and the additional slack variables s₁, s₂, and s₃. The objective function and constraints remain the same, but the problem has been transformed into an equality form suitable for applying the big-M method or other linear programming techniques.

To reformulate the given linear programming problem using the big-M method, we introduce additional binary variables and big-M constants. The reformulated problem is as follows:

maximize 2x₁ + x₂ + x₃

subject to:

x₂ + x₃ + s₁ = 5

x₁ - x₂ + s₂ = 1

x₁ + x₂ + 3x₃ + s₃ = 25

x₁, x₂, x₃, s₁, s₂, s₃ ≥ 0

where s₁, s₂, and s₃ are slack variables, and we choose a large positive constant M to represent infinity.

Introducing slack variable s₁ for the inequality constraint x₂ + x₃ ≥ 5:

We add s₁ to the left-hand side of the inequality to transform it into an equation: x₂ + x₃ + s₁ = 5.

Introducing slack variable s₂ for the inequality constraint x₁ - x₂ ≥ 1:

We subtract s₂ from both sides of the inequality to transform it into an equation: x₁ - x₂ + s₂ = 1.

Introducing slack variable s₃ for the inequality constraint x₁ + x₂ + 3x₃ ≤ 25: We subtract s₃ from the left-hand side of the inequality to transform it into an equation: x₁ + x₂ + 3x₃ + s₃ = 25.

Since all variables in the original problem are non-negative (x₁, x₂, x₃ ≥ 0), we explicitly state this in the reformulation.

Therefore, the reformulated problem includes the original variables x₁, x₂, x₃, and the additional slack variables s₁, s₂, and s₃. The objective function and constraints remain the same, but the problem has been transformed into an equality form suitable for applying the big-M method or other linear programming techniques.

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Incomplete question:

Reformulate the following LP by the big-M method (only the reformulation is required, no need to solve the LP).

maxₓ 2x₁ + x₂ + x₃

s.t.

x₂+x₃ ≥ 5

x₁ - x₂ ≥ 1

x₁ + x₂+ 3x₃ ≤ 25

x₁, x₂, x₃  ≥0

Answer:

A

Step-by-step explanation:

Answer:

8 >_ 3 +x

Step-by-step explanation:

X = 5 and any numbers below 5

Answer:

8 ( > or equal to) n + 3

Step-by-step explanation:

I hope this helps :)

Answer:

y = 3x - 10

Step-by-step explanation:

Answer:

120%

Step-by-step explanation:

Given that,

The diameter of the raw cookie is 2 1/2 inches i.e. 5/2 inches

After baking the cookie, the diameter is 5 1/2 inches i.e. 11/2inches

We need to find by what factor does the cookie expand.

\(x=\dfrac{5\dfrac{1}{2}-2\dfrac{1}{2}}{2\dfrac{1}{2}}\times 100\\\\=\dfrac{\dfrac{11}{2}-\dfrac{5}{2}}{\dfrac{5}{2}}\times 100\\\\=120\%\)

So, the cookie will expand 120%.

Answer:

220%

Step-by-step explanation:

to the test got answer correct

Answer:

The mathematical problem that forms the basis of most modern cryptographic algorithms is the difficulty of factoring large prime numbers.

Step-by-step explanation:

The problem that forms the basis of most modern cryptographic algorithms is the difficulty of factoring large integers into their prime factors. This is known as the integer factorization problem. It is believed to be a computationally hard problem, meaning that it would take an impractically long time to factor very large integers using classical computers. Many cryptographic algorithms, such as RSA, rely on this problem for their security.

The power series expansion of the function \(3(1 - x/4)^{2/3}\) is 3 - (2x)/9 + (x²)/36 - (x³)/108 + ... It is obtained using the binomial series formula by substituting t = -x/4 and r = 2/3.

To expand the function \(3(1 - x/4)^{2/3}\)as a power series using the binomial series, we can use the general formula for the binomial series

\((1 + t)^r\) = 1 + rt + (r(r-1)t²) / 2! + (r(r-1)(r-2)t³) / 3! + ...

In this case, we have t = -x/4 and r = 2/3. Substituting these values into the binomial series formula, we get:

\(3(1 - x/4)^{2/3}\)= 3 * [1 + (-x/4) * (2/3) + ((2/3)((2/3)-1)(-x/4)²) / 2! + ((2/3)((2/3)-1)((2/3)-2)(-x/4)³) / 3! + ...]

Simplifying the terms, we have

\(3(1 - x/4)^{2/3}\)= 3 * [1 - (2/3)(x/4) + (2/3)(1/3)(x²/16) - (2/3)(1/3)(4/9)(x³/64) + ...]

Expanding further and simplifying the coefficients, we get

\(3(1 - x/4)^{2/3}\) = 3 - 2x/9 + (x²)/36 - (x³)/108 + ...

Therefore, the power series expansion of the function \(3(1 - x/4)^{2/3}\)is 3 - 2x/9 + (x²)/36 - (x³)/108 + ...

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The (d/c) should be an element of N. Hence, the conditions required for cR-1d are d/c is an element of N.

A relation R is defined on N by aRb if a/b is an element of N. For c,d that is an element of N, under

Given that, the Natural numbers set is N.The inverse of relation R is given by R⁵-1.

A pair (c, d) is included in R^-1 if (d, c) is a part of R.

The inverse of R is that it is created when the order of the pairs of R are reversed.

A relation is defined as a connection between two or more objects. In other words, we can say that it is a way to relate or associate two or more variables.

The conditions required for cR-1d can be defined as follows:

Given that the relation R is defined on the Natural numbers set, aRb where a/b is an element of N, we can find the conditions for cR-1d.

It can be said that the relation R is based on the division between the two numbers.

It means that it checks whether the division of two numbers is a natural number or not. So, if we have a pair (c, d) in R⁵-1, then (d, c) should be a part of R.

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It appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

Here, we have,

given that,

min t_i

x₁ = x₂-u

x₂ = u

-1 ≤ u ≤ 1, (x₁, x₂) are arbitrary starting point.

and origin  (0,0) be the begging of the coordinate.

also given that, (x₁, x₂)→ (0,0)

so, min t_i at origin (0,0) = t

Therefore, the generality condition of the situation does not met.

so, we get,

The given system can be represented by the following equations:

x₁' = x₂ - u

x₂' = u

To analyze the behavior of the system, we can examine the dynamics of each variable separately.

For x₁:

x₁' = x₂ - u

The equation implies that the rate of change of x₁ is dependent on x₂ and the input u. The term (-u) acts as a control input that can affect the dynamics of x₁. If we choose an appropriate control input u, we can manipulate the rate of change of x₁ and potentially minimize the time required to reach the origin.

For x₂:

x₂' = u

The equation for x₂ indicates that the rate of change of x₂ is solely determined by the input u. The variable x₂ can be directly controlled by the input u, allowing us to influence its behavior and potentially expedite convergence.

Based on the given equations, it appears that the system dynamics can be manipulated through the control input u to minimize the time required for convergence to the origin (0,0).

By carefully selecting the control input, it is possible to achieve the shortest time to reach the origin from any arbitrary starting point (x₁, x₂).

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