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Answer:

[tex]q > 20[/tex]

Step-by-step explanation:

[tex] - q < - 13 - 7[/tex]

[tex]q > 20[/tex]

The slopes of AB and CD are neither equal nor negative reciprocals of each other, we can conclude that AB and CD are neither parallel nor perpendicular.

To determine if AB and CD are parallel, perpendicular, or neither, we need to find the slopes of both lines.

The slope of AB can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (8, 4) and (x₂, y₂) = (4, 3).

mAB = (3 - 4) / (4 - 8) = -1/4

The slope of CD can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (4, -9) and (x₂, y₂) = (2, -1).

mCD = (-1 - (-9)) / (2 - 4) = 8 / (-2) = -4

If the two lines are parallel, their slopes must be equal. However, mAB = -1/4 and mCD = -4, so the two lines are not parallel.

If the two lines are perpendicular, their slopes must be negative reciprocals of each other. That is, mAB x mCD = -1.

However, mAB x mCD = (-1/4) x (-4) = 1, which is not equal to -1. Therefore, the two lines are not perpendicular either.

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The sum of the perimeters of all squares is 80 ft.

What is perimeter?

Perimeter is the distance around the outer boundary of a two-dimensional shape, such as a rectangle, square, triangle, or circle. It is the total length of all the sides of the shape.

Starting with a square with a perimeter of 40 ft, we can find the length of one side by dividing the perimeter by 4:

[tex]\frac{40ft}{4} = 10ft[/tex]

So, the original square has a side length of 10 ft.

Connecting the midpoints of the sides of this square creates a new square with half the side length of the original square. Each side of this new square is the hypotenuse of a right triangle with legs equal to half the side length of the original square (i.e., 5 ft).

Using the Pythagorean theorem, we can find the length of each side of the new square:

[tex]s^2 = (5 ft)^2 + (5 ft)^2[/tex]

[tex]s^2 = 50 ft^2[/tex]

[tex]s = \sqrt{50}ft[/tex]

So, the second square has a side length of [tex]\sqrt{50}ft[/tex], which is approximately 7.07 ft.

Continuing this process, each subsequent square will have half the side length of the previous square. Therefore, the side length of the third square will be half the side length of the second square, which is:

[tex]\frac{1}{2}[/tex] * [tex]\sqrt{50}ft[/tex] = [tex]\sqrt{25}ft[/tex] = 5 ft.

The side length of the fourth square will be half the side length of the third square, which is: [tex]\frac{1}{2}[/tex] * 5 ft = 2.5 ft. And so on.

The perimeters of the squares are:

The perimeter of the first square is 40 ft.

The perimeter of the second square is 4 * [tex]\sqrt{50}ft[/tex], which is approximately 28.28 ft.

The perimeter of the third square is 4 * 5 ft = 20 ft.

The perimeter of the fourth square is 4 * 2.5 ft = 10 ft.

We can see that the perimeter of each subsequent square is half the perimeter of the previous square. So, the series for the perimeters of the squares is a geometric series with a first term of 40 ft and a common ratio of 1/2.

Using the formula for the sum of an infinite geometric series, we can find the sum of the perimeters of all squares:

S = a / (1 - r)

where a is the first term (40 ft) and r is the common ratio (1/2). Plugging in these values, we get:

S = 40 ft / (1 - 1/2)

S = 80 ft

Therefore, the sum of the perimeters of all squares is 80 ft.

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The identity of cos (2π-x) = -cosx

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

for example;

cos 2 θ + sin 2 θ = 1

1 + cot 2 θ = csc 2 θ

1 + tan 2 θ = sec 2 θ

For cos(2π -x)

π = 180°

2π = 2× 180

= 360°

Therefore cos ( 360-x) will have the identity -cos x.

This is because 360° has an equivalent as 0 in trigonometry.

Therefore cos( 0-x)

= -cosx

therefore the identity of cos (2π-x) is -cos(x).

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Answer:

33

Step-by-step explanation:

First, you multiply 3 into the other equation (remember, anytime there is a parentheses by each like there is shown, it will be multiplication.) So -3 * -7 is 21 because a negative and a negative is a positive. Then -3 * -4 which is 12. Add 21 and 12 together and you get 33!

I hoped this helped <3

According to the given information, it will take Hector 15 weeks to reach 10 km if he starts at 2.5 km and adds 0.5 km every week.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equals sign (=), where each side contains an expression that may contain variables, constants, or mathematical operations. The goal of solving an equation is to find the value(s) of the variable(s) that make the equation true.

The equation that correctly determines how many weeks it will take Hector to reach 10 km is 0.5x + 2.5 = 10, where x is the number of weeks.

To verify, we can solve for x:

0.5x + 2.5 = 10

0.5x = 10 - 2.5

0.5x = 7.5

x = 7.5/0.5

x = 15

Therefore, it will take Hector 15 weeks to reach 10 km if he starts at 2.5 km and adds 0.5 km every week.

The other equations are not equivalent to Hector's weekly addition of 0.5 km:

0.5 – 2.5 = 10x is not equivalent because it does not involve adding 0.5 every week.

2.5x + 0.5 = 10 is not equivalent because it does not take into account Hector's starting distance of 2.5 km.

2.5x – 0.5 = 10 is not equivalent because it does not involve adding 0.5 every week and it also does not take into account Hector's starting distance of 2.5 km.

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Volume of Sphere B is 8 times greater than the volume of Sphere A

What does sphere refer to?

A sphere is symmetrical and round in form. All of its surface points are equally spaced from the centre, making it a three-dimensional solid. Depending on the radius, it has a surface area and a volume. No faces, corners, or edges exist on it.

                            It is sometimes referred to as the second cousin of a circle, the sphere is a three-dimensional form. Round, without boundaries, and solid in shape, a sphere is spherical. Examples of spherical shapes include a playing ball, a balloon, and even light bulbs.

Sphere A:  V = 4π (2³)/3 = 32π/3

Sphere B:  V = 4π (4³)/3 = 4π(64)/3 = 256π/3

volume of Sphere B / volume of Sphere A =  (256π/3)/(32π/3) = 8

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Answer:

angle=80 degrees

Step-by-step explanation:

if we know the arc is 160 degrees than we know we want to find the interior angle, then we must divide 160/2 to get the measure of the indicated angle.

Answer:

[tex]32x-16[/tex]

Step-by-step explanation:

[tex](2x+3)^{2} - (2x-5)^{2}[/tex]

expand the equation.

[tex](2x+3)(2x+3) - (2x-5)(2x-5)[/tex]
then distribute.
[tex](4x^{2} +6x + 6x+9) - (4x^2 - 10x - 10x + 25)[/tex]

finally simplify the equation.

= [tex]32x-16[/tex]

Therefore , the solution of the given problem of unitary comes out to be

option A is correct option.

The task can be finished by combining the data expression obtained to use this nanosection methodology with in all supplemental data from two people who employed a particular variable tactic. In plain English, this indicates that, if the desired result occurs, either the stated individual will be known or, in fact, the colour by both enormous processes would be skipped. A refundable fee of Rupees ($1.01) may be necessary for forty pens.

Here,

Given :

there is a relationship between a person’s age and their preference for a particular style of dress.

So,

The question can be included in the interview

and so,

option A. The questions are acceptable because the researcher is studying the relationship between age and preferred dress style.

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A. The questions are acceptable because the researcher is studying the relationship between age and preferred dress style.

What is probability?

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence.

conducting a research study, it is important to carefully consider the questions being asked in the survey to ensure that they are relevant to the research question and that they do not cause any harm or offense to the participants. In the case of the clothing designer's survey, asking about age and dress size is relevant to the study's goal of investigating the relationship between age and preferred dress style. Therefore, including these questions in the survey is acceptable.

However, it is also important to consider the potential concerns or discomfort that some participants may have about answering these questions. To address these concerns, the survey questions should be worded in a respectful and non-intrusive manner.

Therefore, A. The questions are acceptable because the researcher is studying the relationship between age and preferred dress style.

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Answer:

4                      [Yes, really]

Step-by-step explanation:

(8/64)^-2/3      [Wow]

(1/8)^-2/3         [Simplify 8/64 to 1/8]]

(8^-1)^-2/3      [Reformat (1/8) to 8^-1]

8^(-1*(-2/3))      [Rule of exponents: When an exponent is raised to another exponent,  multiply the exponents.]

8^(2/3)             [Simplify (-1(-2/3)) to (2/3)]

64^(1/3)            [8^(2/3) means square the 8 and then take the cube root]

4                      [The cube root of 64 is 4 (4*4*4 = 64]

Answer: B - A kitten who is just born is predicted to weigh 4.05 ounces

Step-by-step explanation:

In the case of the example given, the finance charge is $5.32, which is the amount of money that will be charged for borrowing the money for the given period.

Finance charges refer to the fees and interest associated with borrowing money or making a purchase on credit. Finance charges are usually expressed as a percentage of the total amount borrowed or purchased, and they are calculated based on the interest rate and the length of the loan term. In the case of the example given, the finance charge is $5.32, which is the amount of money that will be charged for borrowing the money for the given period. The finance charge is calculated by multiplying the interest rate by the amount borrowed and then dividing it by the total number of days in the loan term.

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To determine which company would give Amy a stable long-term investment, we need to compare the standard deviations of the stock prices for both companies. A lower standard deviation indicates that the stock price is more stable and has less variability.

From the given information, we can see that the standard deviation of stock prices for Garden Statues Express is $1.05, while the standard deviation of stock prices for Masterful Pocketwatches is $9.83. This means that Garden Statues Express has a much lower standard deviation, and thus a more stable stock price, compared to Masterful Pocketwatches.

Therefore, if Amy is looking for a stable long-term investment, she should consider investing in Garden Statues Express.

If 87¹/₂ percent of milk is water and a gallon consists of 16 cups, the number of cups of water in a gallon of milk is 14 cups.

A value expressed in percentage implies that it is the quotient multiplied by 100.

The quotient is the result of the division operation involving a portion and the whole value.

The number of cups in a gallon of milk = 16

The percentage of the content that is water = 87¹/₂%

87¹/₂% of 16 = 14 cups (16 x 87¹/₂%)

Thus, we can state that out of 16 cups in a gallon of milk, water consists of 14 cups, which is 87¹/₂ per cent.

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The inequality that represents this situation is (x × y) + (z x n) ≥ $300 and the quantities are true for h when the value is 36.

To find the value of h (the number of hours Chris needs to work), we can rearrange the inequality as follows:

Base wage x Number of hours worked ≥ $300 - Bonus per book x Number of books sold

Number of hours worked ≥ ($300 - Bonus per book x Number of books sold) / Base wage

Now, let's substitute the values we know into this equation. We know that Chris earns a base wage of $7.50 per hour and a $2 bonus for each book sold. We also know that she sold 15 books. Therefore:

Number of hours worked ≥ ($300 - $2 x 15) / $7.50

Number of hours worked ≥ ($300 - $30) / $7.50

Number of hours worked ≥ $270 / $7.50

Number of hours worked ≥ 36

So, the inequality that represents this situation is:

Base wage x Number of hours worked + Bonus per book x Number of books sold ≥ $300

Now, let us consider that x refers the Base wage, y refers the Number of hours worked, z refers the Bonus per book and n refers the Number of books sold, then the resulting inequality is

=>  (x × y) + (z x n) ≥ $300

And the true value of h (the number of hours Chris needs to work) is at least 36 hours.

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For the isolated term the value of f/2  is -2.5

Given the equation f/2+9=4, we need to isolate the term f/2 to solve for the value of f. To do so, we need to perform the same operation on both sides of the equation in order to keep it balanced.

One way to isolate f/2 is to subtract 9 from both sides of the equation. This would give us:

f/2 = -5

By subtracting 9 from both sides, we removed the constant term from the left side of the equation. This operation did not affect the capacity of the equation, as we simply moved a constant value from one side to the other.

Another way to isolate f/2 is to multiply both sides of the equation by 2. This would give us:

f + 18 = 8

By multiplying both sides by 2, we eliminated the denominator on the left side of the equation, and the capacity of the equation remained unchanged.

Next, to isolate the term f, we need to perform the same operation on both sides of the equation, but this time with a different set of values.

To isolate f, we can subtract 18 from both sides of the equation. This would give us:

f = -10

By subtracting 18 from both sides, we removed the constant term from the right side of the equation, and the capacity of the equation remained the same.

We can also isolate f by dividing both sides of the equation by 2. This would give us:

f/2 = -2.5

By dividing both sides by 2, we eliminated the numerator on the left side of the equation, and the capacity of the equation remained unchanged.

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Answer:

Your question is not fully completed. People can't solve it because it is not fully completed.

Step-by-step explanation:

Therefore , the solution of the given problem of expressions comes out to be  x ≈ 0.6309.

Calculations that combine joining, removing, and random subdivision must be done with ever-changing factors. They could accomplish the following if they united: An programme, some data, and a mathematical problem. Formulas, components, and arithmetic operations like adds, subtractions, mistakes, and groupings can all be found in a declaration of truth.

Here,

We can rewrite this equation as follows in order to answer it using the properties of logarithms:

We can now use a substitution to simplify the problem. Let y = 8^x.

By finding x, we obtain:

=>  y = (6³ˣ))/8

This equation can be made simpler by applying the formula 8 = 23:

=> y = (6³ˣ))/(2³)

=> y = (3³ˣ)/(2³)

=> 6³ˣ - (3³ˣ)/(2³) = 0

=> (6³ˣ)*(2³) - (3³ˣ) = 0

=> (2³)/(3³ˣ) - 1 = 0

=> log((2³)/(3³ˣ)) = log(1)

=> log(2³) - log(3³ˣ) = 0

Simplifying, we get:

=> 3log(2) - 3xlog(3) = 0

By multiplying both parts by 3log(3), we obtain:

=> x = (log(2))/(log(3))

Using a calculator, we can calculate this expression to four decimal places:

=>  x ≈ 0.6309

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Answer:

range = 60

Step-by-step explanation:

the range of the data set is the difference between the largest and smallest values in the set.

the largest value = 140 ( denoted by the line on furthest right )

the smallest value = 80 ( denoted by line on left )

range = 140 - 80 = 60

When these two numbers are subtracted, the difference is 2 3/4, which is the total change in the volume of water in the birdbath after two days. This can be written as a mixed number, which would be 2 3/4.

The total change in the volume of water in the birdbath after two days can be determined by subtracting the starting volume of water (1 1/2) from the ending volume of water (4 1/4).

The total change in the volume of water in the birdbath after two days is an important figure to calculate in order to understand the amount of water that has been added or removed from the birdbath. To calculate this figure, one must subtract the starting volume of water from the ending volume of water. In this scenario, the starting volume of water was 1 1/2 and the ending volume of water was 4 1/4. When these two numbers are subtracted, the difference is 2 3/4, which is the total change in the volume of water in the birdbath after two days. This can be written as a mixed number, which would be 2 3/4. This figure is important to know as it can help one determine how much water has been added or removed from the birdbath over a certain period of time.

the complete question is :

A birdbath is filled to the top. On Day 1, the volume of water in the bowl decreases by 7/8 cup. On Day 2, the volume in the bowl decreases by 3/4 cup. What number represents the total change in the volume of water in the bowl after two days? Write your answer as a mixed number.

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The measure of angle B on the straight line is 22 degrees

When two angles lie along a straight line, they form a straight angle which measures 180 degrees.

The statement from the question can be represented as

m∠A = 4(m∠B + 17.5°)

But we know that the sum of the measures of angles A and B is 180 degrees, since they form a straight angle.

m∠A + m∠B = 180°

Substitute the known values in the above equation, so, we have the following representation

4(m∠B + 17.5°) + m∠B = 180°

Simplifying this equation, we get:

5m∠B + 70° = 180°

Subtracting 70 degrees from both sides, we get:

5m∠B = 110°

Dividing both sides by 5, we get:

m∠B = 22°

Therefore, the measure of angle B is 22 degrees.

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The expressions for the dimensions of the rectangular composite figure, indicates;

a) The simplified expression for the shaded region is; (3·x + 36) cm²

b) x = 17

c) Please find attached the drawing of the figure, showing the dimensions, created with MS Word

d) The area of the shaded region cannot be 39 cm², because that will make the length of the small rectangle -1 cm.

A composite figure is a figure that comprises of two or more simpler figures.  

The figure can be considered as a composite figure, comprising of a small rectangular unshaded region within a shaded larger rectangle.

The area of the shaded region is the difference between the area of the large rectangle and the area of the unshaded rectangle, which can be found as follows;

Area of a rectangle = Length × Breadth

Length of the large rectangle = (x + 5) cm

Breadth of the large rectangle = 6 cm

Area of large rectangle = 6 cm × (x + 5) cm = (6·x + 30) cm²

Area of the unshaded area = 3 cm × (x - 2) cm = (3·x - 6) cm²

Area of the shaded region, A, is therefore;

A = (6·x + 30) cm² - (3·x - 6) cm² = (3·x + 36) cm²

b) The shaded area = 87 cm², therefore;

(3·x + 36) = 87

3·x = 87 - 36 = 51

x = 51/3 = 17

c) The dimensions of the figures are therefore;

x = 17

Please find attached the drawing of the shape created with MS Word

d) The area of the shaded region is; (3·x + 36)

Therefore, if the area of the shaded region is 39, we get;

(3·x + 36) = 39

x = (39 - 36)/3 = 1

x = 1

The length of the unshaded region is; (x - 2)

The length of the unshaded region becomes; (1 - 2) = -1, which is not a natural number and therefore, not possible

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As a result, 67° is the measure of ∠B.

Due to the fact that a triangle contains three sides, three angles, & three vertices, it's a complete, two-dimensional object. A triangle is indeed a polygonal element. Triangle ABC can be seen in the image above. Triangle illustrations. Triangles can be found on a variety of everyday objects, such as sandwiches, traffic signs, clothes hangers, and pool table racks.

Given:

∠A = 32°

∠C = 81°

∠B =?

The sum of all the angles in a triangle, as we all know, is 180 degrees.

∴ ∠A +∠B + ∠C = 180°

⇒ 32° + ∠B + 81° = 180°

⇒ ∠B + 113° = 180°

⇒ ∠B = 180° - 113°

⇒ ∠B = 67°

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Answer:

(-4, -2)      x=−4,  y=−2

Step-by-step explanation:

A2AGE, A2HT, A2WGT, A2FTL, A2HC, A2CC, A2NC, A2WC, A2SW, A2SH, A2SKH, A2SEH, A2NHT, A2PPD, A2ARM, A2WH, A2GND

The ANSUR II study was conducted in 2012 and consisted of body measurements from 6068 U.S. Army personnel. In the data set, AGE is in years, WEIGHT is in kilograms (kg), GENDER is identified as 1=male and 0=female, WRITING HAND is 1=right and 2=left and 3=both, and the other body measurements are in millimeters (mm). The following data list names are provided for TI-83/84: A2AGE, A2HT, A2WGT, A2FTL, A2HC, A2CC, A2NC, A2WC, A2SW, A2SH, A2SKH, A2SEH, A2NHT, A2PPD, A2ARM, A2WH, A2GND.

The first five rows of the data set are provided here for reference:

AGE HEIGHT WEIGHT FOOT LENGTH HEAD CIRC CHEST CIRC SHOULDER WIDTH SITTING HT ARM SPAN WRITING HAND GENDER (1=M)
41 1776 81.5 273 583 1074 493 928 1782 1 1
35 1702 72.6 263 568 1021 479 884 1745 2 1
42 1735 92.9 270 573 1120 544 917 1867 2 1
31 1655 79.4 267 576 1114 518 903 1708 1 1
21 1914 94.6 305 566 1048 524 919 2035 1 1

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Answer:

the mean is 13

Step-by-step explanation:

the mean is all the numbers added (130) divided the number of numbers in the set(10)

If the company has limited resources or is not particularly concerned with precision, it may decide to forego the additional information and rely on its prior probabilities to make decisions

Bayes TheoremBayes Theorem is a statistical technique that enables one to find the probability of an event given another event that is known to have happened. The theorem states that the probability of an event A happening given that another event B has already occurred is equivalent to the probability of event B happening given that event A has already occurred multiplied by the probability of A happening divided by the probability of B happening. The revised decision tree can be produced to make a decision. However, before that, we need to find the sum of getting a Raise report for each outcome of the prior probabilities. This is shown in the table below:Consultant`s Prediction (in %)Actual Market OutcomePrior ProbabilitiesRiseStableFallRaise0.60.70.20.10.70.140.1260.0280.0140.20.30.20.60.240.0600.0180.1260.03 0.03150.0060.00210.07Total 0.34 0.36 0.30 1.00To revise the consultant's prediction using Bayes theorem, we can use the following formula:P(Stable | Raise) = (P(Raise | Stable) * P(Stable)) / (P(Raise | Stable) * P(Stable) + P(Raise | Rise) * P(Rise) + P(Raise | Fall) * P(Fall)) = (0.140 * 0.30) / (0.140 * 0.30 + 0.126 * 0.34 + 0.028 * 0.36) = 0.2906 or 29.06%The probability of getting a stable report given a raise report is 29.06%. This value can also be calculated for getting a fall report given a raise report using the same formula, which gives a probability of 24.51%.To make a decision on whether to use the consultant firm or not, we can use the revised decision tree. The tree shows that the probability of getting a raise report is only 34%, and given that we get a raise report, the probability of getting a stable report is 29.06% while the probability of getting a fall report is 24.51%.If the company decides to use the consultant firm, they will have to pay for the additional information. This cost needs to be weighed against the benefits of having this information, which will depend on the goals and priorities of the company. If the company values precision and accuracy in its decision-making process and is willing to pay for it, then it may choose to use the consultant firm. However, if the company has limited resources or is not particularly concerned with precision, it may decide to forego the additional information and rely on its prior probabilities to make decisions.

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Answer:

  (i)  25.83 m

  (ii)  178.9 m

  (iii) 4.592 s

Step-by-step explanation:

You want the greatest height, the range, and the time of flight of a particle launched at 45 m/s at an angle of arcsin(0.5) from the horizontal.

The vertical speed is the speed in the direction of launch multiplied by the sine of the angle from the horizontal. Here, it is ...

  (45 m/s)(sin(arcsin(0.5))) = 22.5 m/s

The maximum height is the height at which all of the initial vertical kinetic energy is converted to potential energy:

  h = v²/(2g)

  h = (22.5 m/s)²/(2·9.8 m/s²) ≈ 25.83

The maximum height is about 25.83 meters.

The time of flight is twice the time it takes to reach the maximum height. That time is the height divided by the average vertical speed, which average is half the initial vertical speed.

  T = 2 × (25.83 m)/(11.25 m/s) ≈ 4.592 s

The time of flight is about 4.592 seconds.

The range is the product of the time of flight and the horizontal speed. The horizontal speed is the speed in the launch direction multiplied by the cosine of the angle from the horizontal.

  cos(α) = √(1 -sin(α)²) = √(1 -(1/2)²) = √(3/4)

  R = (45 m/s)√(3/4)·4.592 s = 178.949 m

The horizontal range of the particle is about 178.9 meters.

Therefore , the solution of the given problem of angle comes out to be the particle's horizontal range is approximately 178.9 metres.

A tilt is a form in Euclidean geometry made up of two sides, but rather cylindrical faces, that divide at the barrier's centre and apex. At their junctions, two rays may combine to form an angle. Angle is another outcome of two entities interacting. Dihedral shapes best describe them. A two-dimensional curve can be created by arranging two line beams in various configurations at their ends.

Here,

Lateral momentum

The launch speed is compounded by the sine of the angle from the horizontal to obtain the vertical speed. This is it...

=> 22.5 m/s = (45 m/s)(sin(arcsin(0.5)))

I The tallest person

The height at which all of the original vertical kinetic energy is transformed into potential energy is known as the maximum height.

=> h = v²/(2g) (2g)

=> h = (22.5 m/s)²/(2·9.8 m/s²) ≈ 25.83

The highest point is roughly 25.83 metres high.

(ii) Flight time

The duration of flying is twice as long as the time required to ascend to the highest point. The height divided by the average vertical speed, which is half of the original vertical speed, yields that time.

=> T = 2 × (25.83 m)/(11.25 m/s) ≈ 4.592 s

The journey lasts for approximately 4.592 seconds.

=> (iii) Scope

The range is calculated by multiplying the flight duration by the horizontal speed. The cosine of the angle from the horizontal compounded by the speed in the direction of launch gives the horizontal speed.

=>Cos(x) = (1 - sin(x)2) = (1 -(1/2)2) = Cos(x) = (3/4)

=> R = (45 m/s)√(3/4)·4.592 s = 178.949 m

The particle's horizontal range is approximately 178.9 metres.

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