Simplify
5 x 52
leaving your answer in index form.

The Volume of largest Right Circular Cylinder that can be inscribed in Sphere of radius 3 cm is 65.3 cm³  .

Let the half height of of the cylinder be = h ;

we use h instead of [tex]\frac{h}{2}[/tex] for easier simplification ,

In order to find the Volume of cylinder , we multiply the area of  top with the total height of cylinder .

So , Volume = [tex]\pi \times (Radius Of Cylinder)^{2}\times (Height Of Cylinder)[/tex]

Volume = [tex]\pi \times (\sqrt{r^{2} -h^{2} } )^{2}\times (2h)[/tex];

Volume [tex]= 2\pi h(r^{2} -h^{2} )[/tex]

Now ,  we need the derivative of volume function and equate to 0. If we move the h inside parenthesis, we only need to use power rule to get  derivative.

So , we get , V = [tex]2\pi (r^{2} h-h^{3} )[/tex] ,

On simplifying further ,

we have ,

Volume of Largest Right Circular Cylinder  ⇒ [tex]\frac{4\sqrt{3} \pi r^{3} }{9}[/tex] ;

it is given that radius of sphere is = 3 cm ,

Substituting value of radius in Volume formula ,

we get ,

V =  [tex]\frac{4\sqrt{3} \times 3.14\times 3^{3} }{9}[/tex] ;

V = 65.2636 cm³

V ≈ 65.3 cm³.

Therefore , the volume of the largest right circular cylinder is 65.3 cm³.

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Answer:

➜ ∠4 = ∠2

➜ ∠2 + ∠3 = 180°

➜ ∠1 = ∠3

Step-by-step explanation:

     We can use vertical angles to prove the first statement true, ∠4 = ∠2.

     Next, ∠2 and ∠3 are supplementary angles, so if you add them together you will get 180 degrees. This statement is also true.

       Then, ∠1 and ∠2 are not complimentary angles. This statement is false.

       Lastly, we can use the same reasoning of the first one to prove this statement true as well. They are vertical angles, ∠1 = ∠3.

Answer:

5

Step-by-step explanation:

I just did it

The four types of problem solving can be named as Trial and Error , Algorithms , Inductive Reasoning and Deductive Reasoning .

What is Problem Solving ?

The Problem solving can be defined as the act of defining a problem , finding cause of problem, identifying, prioritizing and selecting the alternatives for solution and implementing it .

The four types of problem solving are :

(i) Trial and Error : It is defined as trying the different ways of doing something until we find the best solution .

(ii) Algorithms : The algorithm can be defined as a  set of step by step procedures which provides correct answer to a particular problem.

(iii) Inductive Reasoning : It is defined as a process where we come to a conclusion where a general statement is reached from specific result.

(iv) Deductive Reasoning : It is defined as a process where we get specific results from general statements .

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The original number is 25.

We know that,

The sum of the original number is 7 --(i)

When reversed, the value of the number is increased by 45 --(ii)

Therefore, adding (i) and (ii), we get:

7 + 45 = 52

Also, 5 + 2 = 7

Since 52 is the reversed number,

Therefore, the original number is 25.

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Polynomials form a system like to that of integers hence they are closed under the operations of addition and subtraction.

Exponents of polynomials are whole numbers.

Hence the resultant exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.

If an operation results in the production of another polynomial, the resulting polynomials will be closed.

The outcome of subtracting two polynomials is a polynomial. They are also closed under subtraction as a result.

The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and nominal means terms. This article will teach us about polynomial expressions, polynomial types, polynomial degrees, and polynomial properties.

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4x - 6 = x + 9

4x - x = 9 + 6

3x = 15

[tex]x = \frac{15}{3} \\ [/tex]

x = 5 ...

Answer:

[tex]x =5[/tex]

Step-by-step explanation:

[tex]4x - 6=x+9[/tex]

Subtract x from both sides

[tex]4x -6-x=x+9-x[/tex]

[tex]3x-6=9[/tex]

Add 6 to both sides

[tex]3x-6+6=9+6[/tex]

[tex]3x=15[/tex]

Divide both sides by 3

[tex]\frac{3x}{3} = \frac{15}{3}[/tex]

[tex]x = 5[/tex]

If a train travels 283. 8km in 4. 4 hours, the train travels 71km in 1 hour and the train travels 114.5km in 2.5 hours.

Based on the assumption that the train is traveling at a constant speed throughout its journey.

To find the speed the train travels , we divide the total distance by the total time:

speed = 283.8km/ 4.4 hours

speed = 64.5 km/h

To find the distance the train travels , we multiply the speed of the train by the total time:

Distance travelled in 1 hour = 64.5 km/ hour × 1 hour

Distance travelled in 1 hour = 64.5 km

Distance travelled in 2.5 hours = 64.5 km/hour x 2.5 hours

Distance travelled in 2.5 hours = 161.25km

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Answer:

-972

Step-by-step explanation:

The next number in the sequence would be the previous number multiplied by 3.

-4*3 = -12

-12*3 = -36

-36*3 = -108

-108*3 = -324

-324*3= -972

Hope this helps! :)

Answer:

90 cups

Step-by-step explanation:

Number of cups needed = 30 / (1/3) cups

                                          = 90 cups

Thought process:

1 cup -> 1/3 ounce

3 cups -> 1 ounce

? cups -> 30 ounce

Hence, ? = 30 x 3

                = 90

2x2+4x5=0 is a quadratic equation that can be solved. 2 x 2 + 4 x - 5 = 0. To find the answers, start with the quadratic formula.

Using the quadratic formula, determine the roots of the quadratic equations 2x2-3x-5= 0. The equation's roots must be located. As a result, the equation's roots are 5/2 and -1. Which equation with 2 as a root must be identified. As a result, 2 is not a root of x2-4x + 5= 0.

Since 2 is not a root, x2 + 3x-12= 0 cannot be solved. Thus, 2 is the root of the equation 2x2-7x + 6= 0. The roots of the quadratic equation ax2 + bx + c= 0 are real and equivalent if the discriminant is equal to zero (b2-4ac=0), a, b, and c are real values, and a0. The roots in this situation arex= -b/2a.

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Answer:

(-4, -8)

Step-by-step explanation:

Note that x in terms of y is x = 2y + 12.  Substitute 2y + 12 for x in the second equation:

5(2y + 12) + 3y = -44

or

10y + 60 + 3y = -44

Then 13y= -104, and y = -8

From the first equation we find x = 2(-8) + 12, or x = -16 + 12, or x = -4

Then the solution is (-4, -8)

Answer:

It should be 14400 square inches. Sorry if i'm wrong

Step-by-step explanation:

Find angle W first:

37 + 93 + W = 180 ---> W = 50°

Use sine law to find the length w:

w/(sin 50) = 31/(sin 37)

w = 31(sin 50/sin 37)

= 39.5

The total number of pairs of shoes produced should be 500 (the maximum possible production). The profit per day should be maximized, so we need to solve the following system of equations:

2x + 1y ≥ 100 (the number of high-grade shoes should be at least 100)

x + y = 500 (the total number of pairs of shoes produced should be 500)

Solving for x and y, we get:

x = 400 (high-grade shoes)

y = 100 (low-grade shoes)

Therefore, the factory should produce 400 pairs of high-grade shoes and 100 pairs of low-grade shoes for maximum profit.

To optimize a factory's production process to maximize profit, the factory should focus on increasing efficiency and reducing costs. This can be done by streamlining processes, automating tasks, and utilizing data-driven decision making. Additionally, the factory should focus on reducing waste, lowering overhead costs, and developing cost-saving strategies. Finally, the factory should focus on finding new markets and expanding its customer base to increase revenue.

The break-even point for a factory is the point where total revenue equals total costs. This can be calculated by subtracting the total variable costs (costs that change with production, such as raw materials and labor) from the total fixed costs (costs that are not affected by production, such as rent, insurance, and equipment). The difference is the break-even point, which is the total revenue needed to cover all costs and generate a profit.

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Answer:

these two apply:

10x + 12 = 38 and

10x = 26

Step-by-step explanation:

7x+6+3x+6 = 38

10x + 12 = 38

10x = 26

x = 2.6

Answer:

610,000

Step-by-step explanation:

Answer:

610,000

Step-by-step explanation:

614,952 rounded to the nearest ten thousand place is 610,000.

hope this helps and is right :) p.s. i rlly need brainliest.

The opposite of number 27 is -27

We know that the opposite of a number is nothing but the number which is at the same distance from 0 but in the opposite direction on a number line.

Here we have been givena number 27

Let a number 'p' be the opposite of number 27

If we plot 27 on the number line then we can observe that it is  located to the right of 0 on the number line.

So, from the definition of opposite of a number p would be at the same distance from 0  i.e., 27 units but in the opposite direction on a number line.

so, the number p would be -27

Therefore, -27 is opposite of 27

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Answer:

The answer is 13.5

Step-by-step explanation:

According to question we can say that 1% percent of people are ambidextrous.

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

Let 'x' represent the percentage of left-handed people.

Let y represent the percentage of right-handed people.

Let z represent the percentage of ambidextrous people.

x = y/100

100x = y

y/100 = 9( x/100 + z/100)

y = 9x + 9Z

10x = 9x + 9z

x = 9z

x+y+z = 100

11x + x/9 = 100

100x/9 = 100

x = 9

z = 1%

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Answer:

This is one of my specialties so sit back, relax while I work on this for 5 mins :)

Step-by-step explanation:

The formula is a^2 + B^2 = c^2

Sooo

7^2 + 5^2 = c^2

49 + 25 = 74

√74 = √c^2

8.60232526 = c

8.60232526 rounded to the nearest tenth is 8.6

So there you go. Hope it helps!!

Answer:

The answere is C

Step-by-step explanation:

x = 448, which is the greatest of these integers.

Positive, negative, and zero are all examples of integers.

The Latin word "integer" signifies "whole" or "intact."

As a result, fractions and decimals are not included in integers.

All whole numbers and negative numbers are considered integers.

This means that if we combine negative numbers with whole numbers, a collection of integers results.

An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.

Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043. a collection of numbers, denoted by the symbol Z.

According to our question-

added together =1341

x +  x-1 + x-2 =1341

3x-3  = 1341

3x = 1344

x = 448

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The solution of the equation is x = 6, y = 0.

1. Subtract the two equations:

   x3y6 - 2x3y12 = 0

2. Simplify both sides of the equation:

   x3y - 2x3y = 0

3. Simplify further calculations:

   x3(y - 2y) = 0

4. Factorize the expression:

   x(y - 2y) = 0

5. Solve for x:

   x = 0

6. Substitute x = 0 into either equation:

   3y = 6

7. Solve for y:

   y = 2

8. Substitute y = 2 into either equation given above:

   x = 6

The solution of the equation is x = 6, y = 2.

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Answer:

I'm pretty sure it's 97

Step-by-step explanation:

I made three shapes 2 rectangle and 1 triangle

8/10 liters of water she spilled. This can be solved using the concept of fraction.

A fraction is a piece of the entire. The number is stated in arithmetic as a quotient, which signifies the numerator divided by the denominator. Both are integers in a straightforward fraction. The numerator or denominator of a complex fraction is a fraction. A suitable fraction has a numerator that is smaller than its denominator.

Three main fractional kinds exist. They come in three varieties: appropriate fractions, incorrect fractions, and mixed fractions. The numerator and denominator words are known as fractions. We define its kinds in light of these two words.

Given that,

There were 57/10 liters of water in a bucket than she spilled some so she added another 15/10, now she get:

(57/10) + (15/10) = 72/10

After that, there was 64/10 liters of water in the bucket, now she spilled:

(72/10) - (64/10) = 8/10

So, 8/10 liters of water she spilled.

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The value of ES will be;

⇒ ES = 10.63 units

Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.

Given that;

The coordinate of E = (- 3, - 4)

The coordinate of S = (4,  4)

Now,

Since, The coordinate of E = (- 3, - 4)

The coordinate of S = (4,  4)

Hence, The value of ES is find as;

⇒ ES = √ (4 - (-3))² + (4 - (-4))²

         = √ 7² + 8²

         = √ 49 + 64

         = √ 113

         = 10.63

Thus, The value of ES = 10.63 units

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When the two lines makes angle of 90 degree , then the lines are known as Perpendicular Lines .

What are Perpendicular Lines ?

Two lines are said to be perpendicular to each other if the straight line  makes an angle of 90 degree with another line. 90 degree is also called a Right Angle and is represented by a little square between two perpendicular lines .

when the two lines intersect at a right angle, they are said to be perpendicular to each other.

For Example : In a football field all the four corners of a football field are perpendicular to each other.

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Reasonable algorithms expand at polynomial rates or less quickly. Unreasonable algorithms expand exponentially. Even for relatively small problem sizes, the time to solve an unreasonable algorithm increases very quickly.

When the algorithm takes an excessively long time, we say that the number of steps is an exponential function of the size of the input (or some other function that is larger than any polynomial). Simply increasing the input size (n) by 1 doubles the number of steps for an algorithm that runs in 2n time.

Depending on the polynomial, polynomial time can be further decomposed. Algorithms with a runtime of approximately n2 operate in quadratic time. (If the input size is doubled, the number of steps is quadrupled.) In practise, polynomial time algorithms that take longer than cubic (n³) time are uncommon.

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This is a coordinate pair of a point. 2 and 3 denotes X and Y coordinate respectively.

The system that is used to represent the location of points in the space is termed as coordinate system. There are two types of coordinate system such as polar and cartesian. In case system there are two reference axes which are perpendicular to each other.

In the cartesian system points are represented with respect to a vertical axis named Y axis and a horizontal axis named X axis.

We stated earlier that in the cartesian system a location of a point is identified by a pair of numerical terms.

So, 2, 3 indicates a pair of numerical terms. 2 denotes the X coordinate of the point and 3 denotes the Y coordinate of that point.

In the next, the distance of the point from X axis is 3 unit and distance from Y axis is 2 unit.

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Complete question is: In the point (2,3) which point denotes the y-coordinate.