volume of cones and spheres questions

Answer:

A: area of one additional plan exceeds 624 square feet ...... it does not

Step-by-step explanation:

let's lay out the six additional plans:

plan                         width                  length                  area

6                                26                       24                          624

7                                 28                      22                           616

8                                30                       20                           600

9                                32                       18                             576

10                              34                         16                            544

11                                36                       14                             504

A: one additional plan (plan 6) does not exceed 624. so this incorrect

B: one of the plans (plan 11) is less than 544. this is correct.

C: area of plan 6 = area of plan 5. this is correct.

D: Plan 7 area (616) is less than area of plan 6 (624). this is correct.

So, A is incorrect

The requried measures of DEF and x are 82° and 90° respectively.

In a quadrilateral, the sum of the opposite angle is 180°,
So,
98 + y = 180
y = 180 - 98
y =  82°

Similarly,
x + x = 180
2x = 90
x = 90°

Thus, the requried measures of DEF and x are 82° and 90° respectively.

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The vertex of the function f(x)=(x-3)²-2 is (3, -2).

13) The given function is f(x)=x²+1.

Rewrite in vertex form and use this form to find the vertex (h, k).

(0, 1)

14) The given function is f(x)=(x-3)²-2.

Rewrite in vertex form and use this form to find the vertex (h, k).

(3, -2)

15) The given functions are f(x)=x² and f(x)= -1/2 x²

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Horizontal Shift: None

Vertical Shift: None

Reflection about the x-axis: Reflected

Reflection about the y-axis: None

Vertical Compression or Stretch: Compressed

16) The given functions are f(x)=x² and f(x)= x²-1

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Horizontal Shift: None

Vertical Shift: Down 1 Units

Reflection about the x-axis: None

Reflection about the y-axis: None

Vertical Compression or Stretch: None

Therefore, the vertex of the function f(x)=(x-3)²-2 is (3, -2).

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Using the tangent of the angle from trigonometric ratio, the value of x is 4.0

In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent. These ratios are written as sin, cos, tan, sec, cosec(or csc), and cot in short.

sin θ = opposite / hypothenuse

cos θ = adjacent / hypothenuse

tan θ = opposite / adjacent

To solve this problem, we can use the tangent of the angle.

tan θ = opposite / adjacent

tan 20 = x / 11

Cross multiply both sides;

x = 11 tan 20

x = 4.0

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The integer 15 would best represent points given for good behavior.

We have,

In situation B,

The integer 15 represents a positive quantity or value that is given or awarded to individuals for exhibiting good behavior.

It can be interpreted as a form of positive reinforcement or recognition for demonstrating desirable conduct.

For example, in a reward system implemented in a classroom or organization, students may earn points for following rules, completing tasks, or displaying positive behaviors.

Each point signifies progress or achievement, and when students accumulate a certain number of points, they may be eligible for rewards or incentives.

The integer 15, in this context, serves as a numerical representation of the rewards or points associated with good behavior.

It indicates a positive outcome and reinforces the desired conduct by providing tangible recognition or benefits.

Thus,

The integer 15 would best represent points given for good behavior.

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The data in the table represent a direct variation

The equation is y = 5x

From the question, we have the following parameters that can be used in our computation:

x  1 3 4 7

y 5 15 20 35

In the above table of values, we can see that

As the x values, the y values increase

This means that the table of values represent a direct variation

The equation is a direct variation

So, we have

y = kx

The value of k is calculated as

k = 5/1

So, we have

k = 5

This means that

y = 5x

Hence, the equation is y = 5x

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The height of the cylinder is 20 meters.

To find the height of the cylinder, we can use the formula for the volume of a cylinder, which is given by V = πr^2h, where V represents the volume, r represents the radius, and h represents the height.

In this case, we are given the radius as 4 meters and the volume as 803.84 cubic meters. We can substitute these values into the formula to solve for the height.

803.84 = π * 4^2 * h

Simplifying further, we have:

803.84 = 16πh

To isolate h, we can divide both sides of the equation by 16π:

h = 803.84 / (16π)

Using the approximation of π as 3.14, we can calculate:

h ≈ 803.84 / (16 * 3.14)

h ≈ 50.99

Therefore, the height of the cylinder is approximately 50.99 meters.

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Tyler's age when he was inaugurated is given as follows:

50.3 years old.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 54.6, \sigma = 6.3[/tex]

The z-score associated with the 25th percentile is given as follows:

Z = -0.675.

Hence Tyler's age is obtained as follows:

-0.675 = (X - 54.6)/6.3

X - 54.6 = -0.675 x 6.3

X = 50.3.

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If the number of research papers in Dr. Carey's area of expertise is increasing by 3% every year and 34,176 research papers were published this year, then approximately 35,168 research papers will be published two years from now.

To calculate the number of research papers that will be published two years from now, we need to apply the 3% annual increase for two consecutive years to the initial count of 34,176 papers.

First, we calculate the increase for the first year:

Increase = 34,176 * 3% = 34,176 * 0.03 = 1,025.28 (approximately)

Next, we add this increase to the initial count to get the count after one year:

Count after one year = 34,176 + 1,025.28 = 35,201.28 (approximately)

Now, we calculate the increase for the second year based on the count after one year:

Increase = 35,201.28 * 3% = 35,201.28 * 0.03 = 1,056.04 (approximately)

Finally, we add this increase to the count after one year to get the count after two years:

Count after two years = 35,201.28 + 1,056.04 = 36,257.32 (approximately)

Therefore, approximately 36,257 research papers will be published two years from now.

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The number of tickets were sold are; 150 for adult tickets and 250 for child tickets

There are 400 seats in the auditorium which means that there are 400 tickets to be sold and the total ticket sales were 2600 dollars.

Since there were adult tickets for 9 each and child tickets for 5 dollars each.

9x + 5y = 2600

x + y = 400

Solving;

9x + 5(400-x) = 2600

9x + 2000 - 5x = 2600

4x = 600

x = 150

Then y = 250

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The F test is a statistical test used to compare variances between two or more groups of data. It is often used in ANOVA (analysis of variance) to determine whether the means of three or more groups are significantly different. D. the raw score populations are normally distributed and the variances of the raw score populations are the same

Assumptions underlying the use of the F test include the normal distribution of raw score populations and the equality of variance between groups. The first assumption, that raw score populations are normally distributed, is important because the F test assumes that the population variances are normally distributed. If the distribution of the raw score population is not normal, the F test may not be appropriate.

The second assumption, that the variances of the raw score populations are equal, is also important. The F test assumes that the variance of the populations is equal, and if this assumption is violated, it may lead to inaccurate results. Therefore, the correct answer to the question is D, as both assumptions are required for the F test to be used accurately. If either assumption is not met, it may be necessary to use a different statistical test to analyze the data.

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a) The probability that a patient testing positive for HIV with this test is infected with it is approximately 73.96%

b) With this test, there is a 26.04% chance that a patient who tests positive for HIV is not actually infected.

c) The probability that a patient testing negative for HIV with this test is infected with it is approximately 0.18%.

d) The probability that a patient testing negative for HIV with this test is not infected with it is approximately 99.82%.

Gonna determine how likely something is gonna occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

Let's denote the events as follows:

A = Patient is infected with HIV

B = Patient tests positive for HIV

Given information:

P(A) = 0.08 (probability of a patient being infected with HIV)

P(B|A) = 0.98 (probability of testing positive given the patient is infected with HIV)

P(B|A') = 0.03 (probability of testing positive given the patient is not infected with HIV)

We need to find:

a) P(A|B) = Probability that a patient testing positive for HIV is infected with it.

b) P(A'|B) = Probability that a patient testing positive for HIV is not infected with it.

c) P(A|B') = Probability that a patient testing negative for HIV is infected with it.

d) P(A'|B') = Probability that a patient testing negative for HIV is not infected with it.

We can use Bayes' theorem to find these probabilities:

a) P(A|B)=P(B|A)*P(A)/P(B)

b) P(A'|B)=P(B|A')*P(A')/P(B)

c) P(A|B') = P(B'|A) * P(A) / P(B')

d) P(A'|B') = P(B'|A') * P(A') / P(B')

To find P(B), we can use the law of total probability:

P(B)=P(B|A)*P(A)+P(B|A')*P(A')

First, let's calculate P(B):

P(B)=P(B|A)*P(A)+P(B|A')*P(A')

     = 0.98 * 0.08 + 0.03 * (1 - 0.08)

     = 0.0784 + 0.0276

     = 0.106

Now, we can calculate the probabilities:

a) P(A|B)=P(B|A)*P(A)/P(B)

          = 0.98 * 0.08 / 0.106

          = 0.0784 / 0.106

          ≈ 0.7396 (or 73.96%)

b) P(A'|B)=P(B|A')*P(A')/P(B)

           = 0.03 * (1 - 0.08) / 0.106

           = 0.0276 / 0.106

           ≈ 0.2604 (or 26.04%)

c) P(A|B') = P(B'|A) * P(A) / P(B')

          = (1 - P(B|A)) * P(A) / (1 - P(B))

          = (1 - 0.98) * 0.08 / (1 - 0.106)

          = 0.02 * 0.08 / 0.894

          ≈ 0.0018 (or 0.18%)

d) P(A'|B') = P(B'|A') * P(A') / P(B')

           = (1 - P(B|A')) * (1 - P(A)) / (1 - P(B))

           = (1 - 0.03) * (1 - 0.08) / (1 - 0.106)

           = 0.97 * 0.92 / 0.894

           ≈ 0.9982 (or 99.82%)

Therefore:

a) The probability that a patient testing positive for HIV with this test is infected with it is approximately 73.96%

b) The probability that a patient testing positive for HIV with this test is not infected with it is approximately 26.04%.

c) The probability that a patient testing negative for HIV with this test is infected with it is approximately 0.18%.

d) The probability that a patient testing negative for HIV with this test is not infected with it is approximately 99.82%.

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Therefore, the probability that Sergio's number is larger than the sum of the two numbers chosen by Tina is 11/15, or about 0.733.

We can approach this problem by finding the probability of Sergio's number being less than or equal to the sum of Tina's numbers, and then subtracting this probability from 1.

The total number of ways for Tina to select two distinct numbers from the set is 6 choose 2, which is 15. Each pair of numbers has an equal chance of being selected, so we can assume that each pair has probability 1/15 of being selected.

Now, for each pair of numbers Tina selects, there is a range of numbers that Sergio can select such that his number is greater than the sum of Tina's numbers. Specifically, Sergio's number must be greater than the smaller of Tina's numbers and less than or equal to the largest number in the set.The length of this shaded region is 6 - 2 = 4. Therefore, the probability of Sergio's number being greater than the sum of Tina's numbers for a given pair of numbers is 4/6 = 2/3.

The probability of Tina selecting any particular pair of numbers is 1/15, so the probability of Sergio's number being greater than the sum of Tina's numbers for that pair is (2/3)(1/15) = 2/45.

To find the total probability, we sum up the probabilities for all pairs of numbers:

(2/45) + (2/45) + (2/45) + (2/45) + (2/45) + (2/45) = 12/45 = 4/15

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The area of the shape in the figure, obtained by finding the areas of the component figures is; 31

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

The areas of the squares can be found by summing the areas of the each unit squares where available as follows;

The number of squares in the rows 3 to 9 = 25 squares

The area for the squares in the  rows 3 to 9 = 25 square centimeters

The area of the parallelogram = Base length × Height

The base length  =  3 cm

The height of the parallelogram  = 2 cm

Area of the parallelogram = 3 cm × 2 cm = 6 cm²

The area of the figure = 25 + 6 = 31

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To test these hypotheses, appropriate statistical methods such as a t-test or z-test can be employed, depending on the sample size and whether the population standard deviation is known

In this scenario, the appropriate null and alternative hypotheses can be formulated based on the objective of the hypothesis test. Let's consider the mean running time of the flashlight battery as the parameter of interest.

Null Hypothesis (H0): The mean running time of the flashlight battery is equal to 8 hours.

Alternative Hypothesis (Ha): The mean running time of the flashlight battery has changed, either increased or decreased, as a result of the production method change.

Symbolically, the hypotheses can be represented as:

H0: μ = 8 (mean running time is equal to 8 hours)

Ha: μ ≠ 8 (mean running time is not equal to 8 hours)

Here, μ represents the population mean running time of the flashlight battery. The null hypothesis assumes that the mean running time remains unchanged at 8 hours, while the alternative hypothesis allows for any deviation from this value.

. These tests would help analyze the sample data and provide evidence to either accept or reject the null hypothesis in favor of the alternative hypothesis.

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in the past, the mean running time for a certain type of flashlight battery has been 8 hours. the manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has changed as a result. what are the appropriate null and alternate hypotheses?

Answer:

If the hummingbird is filmed at 140 frames in one second, and the film is played at 10 frames per second, then the film would play for 14 seconds.

Step-by-step explanation:

Using dimensional analysis:

140 frames / (10 frames /sec)  =  14 seconds

The minor arc is QS and the measure of the arc is 98°

An arc is a smooth curve joining two endpoints. It can also be defined as the portion of a circumference of a circle. The circumference of a circle will be divided into minor arc and major arc.

The major arc is the arc that bounds the big sector and the minor arc is the arc that bounds the small sector.

A sector is an area bounded radii and an arc

Therefore the minor arc is arc SQ and the measure of the arc is also 98°. This is because the angle substended by the arc is equal to the measure of the arc.

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The parallel vectors to CD are:

Here we have the vector:

CD = 4a - 3b

Where a and b are vectors.

A vector V will be parallel to CD if we can find a scalar number k such that we can write the vector as:

V = k*CD

The second option:

V = 20a - 15b

We can rewrite this as:

V = 20a - 15b = 5*(4a - 3b)   this vector is parallel.

The third one is:

V'  =10a - 20b + 2a + 11b

V' = 12a - 9b = 3*(4a - 3b)  this vector is parallel.

V'' = (-8a + 6b) = -2*(4a - 3b)  this vector is parallel.

V''' = a - (3/4)b = (1/4)*(4a - 3b)  this vector is parallel.

These are all the parallel vectors.

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The correlation between average 2007 price and number of 2007 is 0.207

To compute the correlation between the average 2007 price and the number of 2007 wins for the 16 National League baseball teams, we can use the formula for Pearson's correlation coefficient.

First, we need to calculate the following sums:

Sum of prices (ΣX) = 19.68 + 17.07 + 34.30 + 17.90 + 14.72 + 16.70 + 26.66 + 20.09 + 18.11 + 25.28 + 26.73 + 17.08 + 20.83 + 24.53 + 29.78 + 20.88 = 387.47

Sum of wins (ΣY) = 90 + 84 + 85 + 72 + 90 + 71 + 73 + 82 + 83 + 88 + 89 + 68 + 89 + 71 + 78 + 73 = 1296

Sum of products of prices and wins (ΣXY) = (19.68 * 90) + (17.07 * 84) + (34.30 * 85) + (17.90 * 72) + (14.72 * 90) + (16.70 * 71) + (26.66 * 73) + (20.09 * 82) + (18.11 * 83) + (25.28 * 88) + (26.73 * 89) + (17.08 * 68) + (20.83 * 89) + (24.53 * 71) + (29.78 * 78) + (20.88 * 73) = 24839.87

Sum of squared prices (ΣX^2) = (19.68)^2 + (17.07)^2 + (34.30)^2 + (17.90)^2 + (14.72)^2 + (16.70)^2 + (26.66)^2 + (20.09)^2 + (18.11)^2 + (25.28)^2 + (26.73)^2 + (17.08)^2 + (20.83)^2 + (24.53)^2 + (29.78)^2 + (20.88)^2 = 19151.7899

Sum of squared wins (ΣY^2) = (90)^2 + (84)^2 + (85)^2 + (72)^2 + (90)^2 + (71)^2 + (73)^2 + (82)^2 + (83)^2 + (88)^2 + (89)^2 + (68)^2 + (89)^2 + (71)^2 + (78)^2 + (73)^2 = 94518

Using these sums, we can calculate the correlation coefficient (r):

r = (n * ΣXY - ΣX * ΣY) / sqrt((n * ΣX^2 - (ΣX)^2) * (n * ΣY^2 - (ΣY)^2))

where n is the number of data points, which in this case is 16.

Substituting the values:

r = (16 * 24839.87 - 387.47 * 1296) / sqrt((16 * 19151.7899 - (387.47)^2) * (16 * 94518 - (1296)^2))

Calculating this expression gives us:

r ≈ 0.207

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If those two given angles combined = 180, then u and v are parallel.

(91 + x) + 95 = 180

186 + x = 180

x = 180-186

x = -6

When x = -6, lines u and v are parallel.

A graph of the system of inequalities is shown on the set of axes below

No, (6, 3) is not a solution to the system of inequalities.

In order to graphically determine the solution for this system of linear inequalities on a coordinate plane, we would make use of an online graphing calculator to plot the given system of linear inequalities while taking note of the point of intersection;

y ≤ -3x/4 + 5            ......equation 1.

3x - 2y > 4       ......equation 2.

Based on the graph shown (see attachment), we can logically deduce that the solution for this system of linear equations is the point of intersection of each lines on the graph that represents them, which is represented by this ordered pair (3, 2).

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The midrange of a distribution, defined as the average of the maximum and minimum values, is not robust to outliers and extreme skew. It is influenced by extreme values, resulting in an inflated or deflated measure of central tendency. Therefore, it is not a reliable statistic in the presence of outliers and extreme skew.

The midrange is calculated by taking the average of the maximum and minimum values in a distribution. While it provides a simple measure of central tendency, it is sensitive to outliers and extreme skew.

Outliers are extreme values that fall far outside the typical range of the data. When outliers are present, they can significantly affect the maximum and minimum values, leading to an inflated or deflated midrange. For example, if there is a single extremely large or small value, the midrange will be pulled towards that extreme, giving a distorted representation of the central tendency.

Similarly, extreme skewness, where the distribution is heavily skewed towards one tail, can also impact the midrange. In such cases, the minimum or maximum value may be heavily influenced by the skewed portion of the distribution, leading to an inaccurate estimate of the central tendency.

In contrast, robust measures of central tendency, such as the median or trimmed mean, are less affected by outliers and extreme skew. They are designed to be more resistant to extreme values and provide a more reliable estimate of the typical value in a distribution.

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There is no meaningful difference in the weights of the two types of rings

From the question, we have the following parameters that can be used in our computation:

Platinum = 8.21 grams

Gold = 8.61 grams

The difference in these weights is

Difference = 8.61 grams - 8.21 grams

Evaluate the difference

Difference = 0.4 grams

This value approximates to 0

This means that there is no meaningful difference in the weights

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The probability of taking 2 different types of sandwiches is 0.691

From the question, we have the following parameters that can be used in our computation:

The total number of sandwiches is

4 + 5 + 2 = 11

So, the probability of taking the same types of sandwiches is

P(Same) = (4/11 * 3/10) + (5/11 * 4/10) + (2/11 * 1/10)

This means that the probability of taking 2 different types of sandwiches is

P(Different) = 1 - [(4/11 * 3/10) + (5/11 * 4/10) + (2/11 * 1/10)]

Evaluate

P(Different) = 0.691

Hence, the probability is 0.691

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In the item procurement importance matrix, the item described as low risk, low value is referred to as a non-critical item.

The item procurement importance matrix is a tool used in procurement management to categorize items based on their importance and risk. It helps in determining the appropriate procurement strategies and allocation of resources. The matrix typically categorizes items into four quadrants based on their value and risk levels: critical, strategic, non-critical, and bottleneck.

A non-critical item is characterized by low risk and low value. These items are generally of lesser importance in terms of their impact on the overall procurement process. They may include non-essential or low-cost items that are easily replaceable or have minimal consequences if they experience delays or disruptions in the supply chain.

Therefore, in the item procurement importance matrix, the item described as low risk, low value is categorized as a non-critical item.

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Step-by-step explanation:

Depends on how you read it :

x = the number

1/2 x -2 = 4

x = 12             <==== I suspect this is the answer wanted

or  

1/2 ( x-2)  = 4

x = 10  

4to9, 4:9, and 4\9 are all different ways to  the same ratio of 4 to 9. Ratios are a fundamental concept in mathematics, and they are used in various fields such as finance, physics, and engineering.

"Reio" is not a known mathematical term or concept. However, the three expressions you provided, 4to9, 4:9, and 4\9, represent different ways to write a ratio.

A ratio is a mathematical comparison of two or more quantities, often written in the form of a fraction or with a colon. It is used to describe the relationship between the quantities being compared.

The expression 4to9, also written as 4:9, represents a ratio of 4 to 9. This means that there are 4 units of one quantity for every 9 units of another quantity. The ratio can be simplified by dividing both the numerator and denominator by their greatest common factor, if any.

The expression 4/9, written with a forward slash, represents the same ratio as 4 to 9. This is because a ratio can be expressed as a fraction, where the numerator represents one quantity and the denominator represents the other quantity.4to9, 4:9, and 4\9 are all different ways to write the same ratio of 4 to 9. Ratios are a fundamental concept in mathematics, and they are used in various fields such as finance, physics, and engineering.

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Answer: Credit cards

Step-by-step explanation:

(you can search it up as well)

Therefore, the projectile goes approximately 6.9 × 10^6 meters or 6,900 kilometers high.

Let's first convert the initial speed from km/hr to m/s to be consistent with the unit of acceleration due to gravity.

1.30×10^4 km/hr = (1.30×10^4 × 1000 m/km) / (3600 s/hr) = 3611.11 m/s

We can use the kinematic equation: Δy = v0t + 1/2at^2 to determine the maximum height reached by the projectile. At the highest point, the velocity is zero, so we can use the fact that v = v0 + at = 0 to find the time it takes to reach the maximum height.

v0 = 3611.11 m/s (initial velocity)

a = -9.81 m/s^2 (acceleration due to gravity)

t = -v0/a = -3611.11/(-9.81) = 367.97 s (time to reach maximum height)

Now we can use the time to find the maximum height reached:

Δy = v0t + 1/2at^2 = 3611.11 × 367.97 + 1/2 × (-9.81) × (367.97)^2 ≈ 6.9 × 10^6 meters

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