Answers
Rounding to the nearest hundredth, the arc length of one slice is approximately 53.67 feet.
What is arc length?Arc length is the distance along the curved line or arc of a circle, measured in linear units such as centimeters, feet, or meters. It is calculated as the product of the radius of the circle and the angle subtended by the arc at the center of the circle, expressed in radians.
Here,
Since the circle is divided into eight equal slices, each slice is 360/8 = 45 degrees. The arc length of one slice can be calculated using the formula:
Arc length = (angle/360) x 2πr
where angle is the central angle in degrees, r is the radius of the circle, and π is the constant pi.
In this case, the diameter of the circle is 137 feet, so the radius is half of that, or 68.5 feet.
Substituting the given values into the formula, we get:
Arc length = (45/360) x 2 x 3.14 x 68.5
Arc length = 0.125 x 2 x 3.14 x 68.5
Arc length = 0.785 x 68.5
Arc length = 53.67 feet
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Related Questions
HELP MARKING BRAINLEIST
Answers
Answer:
r = 2
center: ( -7,0 )
Step-by-step explanation:
4negative slope equations, 2undefined slope equations, and 2zero slope equations (y=mx+b)
Answers
Answer:
negative
y=-x
y=-2x+6
y=(-1/2)x+1
y=-5x+20
undefined
x=4
x=-3
zero slope
y=2
y=-100
Write down the equations of six lines that increase in steepness
Answers
Answer:
Step-by-step explanation:
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
the average car can go 25 miles on one gallon of gas. You can write an equation to show the relationship between the amount of gas you buy and how far you can travel
Answers
Answer:
Step-by-step explanation:
the inword
Kylie brought 5 pears to soccer practice to share with her teammates. She cuts each pear into thirds. How many slices of pears does she have to share with her teammates? Which equations can you use to solve the problem? Select two equations. A. 5 × 3 = 15 B. 1 5 × 1 3 = 1 15 C. 1 5 × 3 = 3 5 D. 5 ÷ 1 3 = 15 E. 1 3 ÷ 5 = 1 15
Answers
Answer: a and d
Step-by-step explanation:
1 pear = 3 slices
5 pears = 15 slices
5x3=15
OR
5/1/3=15
Equation A and Equation D are the two equations that Kylie can use to solve the problem.
This is a simple mathematics problem.
Kylie has five pears. She cuts each of her pears into thirds, i.e., three slices of each pear.
So, now Kylie will do the same for each pear she has:
Total Slices with Kylie = 5 x 3
Total Slices with Kylie = 15
Equation D can also be used to define the situation of Kylie. Total pears with her are five and each pear is divided into thirds, i.e., 1/3
Total Slices with Kylie = 5 ÷ 1/3
Total Slices with Kylie = 15
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Select the correct answer. Sides of three square rooms measure 14 feet each, and sides of two square rooms measure 17 feet each. Which expression shows the total area of these five rooms? A. (3 × 14^2) + (2 × 17^2) B. (2 × 14^3) + (2 × 17^2) C. (3 × 17^2) + (2 × 14^2) D. (3 × 14^2) × (2 × 17^2) Reset Next
Answers
The correct expression showing the total area of the five rooms is A. (3 x 14²) + (2 x 17²), which simplifies to 1918 square feet.
What is expression?An expression is a combination of numbers, symbols, and operators (such as addition, subtraction, multiplication, and division) that represent a mathematical calculation. An expression can be a single number, a variable, or a combination of both, and can be used to represent mathematical formulas, equations, or relationships.
In the given question,
C. (3 × 17²) + (2 × 14²)
To find the total area of the five rooms, we need to add the area of each room. The area of a square is found by squaring the length of one side.
For the three rooms with sides of 14 feet each, the area of each room is:
14^2 = 196 square feet
So the total area of these three rooms is:
3 × 196 = 588 square feet
For the two rooms with sides of 17 feet each, the area of each room is:
17^2 = 289 square feet
So the total area of these two rooms is:
2 × 289 = 578 square feet
Therefore, the total area of all five rooms is:
588 + 578 = 1166 square feet
Option C, (3 × 17²) + (2 × 14²), gives the correct expression for this calculation.
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what minus 1 1/2 equals 3 3/4
Answers
Answer:
5 1/4
Step-by-step explanation:
In a 10-kilometer race, there are no race
monitors for the first kilometer. After
that, there are race monitors every
0.25 kilometer, including at the finish
line. How many race monitors are there
Answers
Therefore, there are 37 race monitors in the entire 10-kilometer race.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It usually contains one or more variables, and the goal is to find the value of the variable(s) that satisfies the equation. An equation can be written in various forms, such as standard form, slope-intercept form, or general form, depending on the type of equation and the information given. Equations are used in many areas of mathematics, science, and engineering to model and solve problems.
Here,
There are race monitors every 0.25 kilometers, so we can divide the race into segments of 0.25 kilometers.
The first segment is from 1 kilometer to 1.25 kilometers. Since there are no monitors for the first kilometer, we only need to count the monitors from 1 kilometer to the finish line.
To find the number of monitors from 1 kilometer to the finish line, we can subtract 1 from the total distance of the race and then divide by 0.25 (since there is a monitor every 0.25 kilometers after the first kilometer):
(10 - 1) / 0.25 = 36
So there are 36 race monitors from 1 kilometer to the finish line. But since there are no monitors for the first kilometer, we need to add 1:
36 + 1 = 37
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three hundred students in a school were asked to select their favorite fruit from a choice of apples, oranges, and mangoes. this table lists the results. if a survey is selected at random, what is the probability that the student is a girl who chose apple as her favorite fruit? answer choices are rounded to the hundredths place.
Answers
The probability that a student selected at random is a girl who chose apple as her favorite fruit is 0.32, or 32% rounded to the nearest hundredth.
To calculate the probability that a student is a girl who chose apple as her favorite fruit, we need to use the information provided in the table. First, we need to find the total number of girls who participated in the survey, which is the sum of the number of girls who chose apples, oranges, and mangoes as their favorite fruit, i.e., 46 + 41 + 55 = 142.
Next, we need to find the number of girls who chose apples as their favorite fruit, which is 46. Therefore, the probability that a student is a girl who chose apple as her favorite fruit is given by:
Probability = Number of girls who chose apples / Total number of girls in the survey
Probability = 46 / 142
Probability = 0.32
This means that out of all the girls who participated in the survey, 32% of them chose apple as their favorite fruit.
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Complete question is:
three hundred students in a school were asked to select their favorite fruit from a choice of apples, oranges, and mangoes. this table lists the results.
Boys Girls
Apple 66 46
Orange 52 41
Mango 40 55
if a survey is selected at random, what is the probability that the student is a girl who chose apple as her favorite fruit?
if nurse susan jones day includes seven trips from the nursing pod to each of the 12 rooms back and forth, 20 trips to the central medical supply, six trips to the break room, and 12 trips to the pod linen supply, how many miles does she walk during her shift? what are the differences in the travel times between the two nurses for the random day?
Answers
Nurse Susan Jones would walk a total of 16,000 feet or approximately 3.03 miles during her shift.
Without knowing the travel times of the two nurses, it is not possible to determine the differences in their travel times for a random day.
Assuming that each trip from the nursing pod to a room and back is approximately 50 feet and each trip to the central medical supply, break room, and linen supply is approximately 100 feet, nurse Susan Jones would walk a total of:
- 7 trips to each of the 12 rooms = 7 x 12 x 2 x 50 feet = 8,400 feet
- 20 trips to the central medical supply = 20 x 2 x 100 feet = 4,000 feet
- 6 trips to the break room = 6 x 2 x 100 feet = 1,200 feet
- 12 trips to the pod linen supply = 12 x 2 x 100 feet = 2,400 feet
Therefore, nurse Susan Jones would walk a total of 16,000 feet or approximately 3.03 miles during her shift.
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Nurse Susan Jones would walk nearly 34.4 miles during her shift.
Assuming that Nurse Susan Jones walks an average of 0.2 miles per round trip, she would walk approximately 34.4 miles during her shift (7 trips x 12 rooms x 2 round trips x 0.2 miles per round trip + 20 trips x 2 round trips x 0.2 miles per round trip + 6 trips x 2 round trips x 0.2 miles per round trip + 12 trips x 2 round trips x 0.2 miles per round trip).
Unfortunately, there is not enough information provided to calculate the differences in travel times between two nurses on a random day. It would depend on factors such as the number and location of rooms each nurse is responsible for, the location of the medical supply and break room, and any additional tasks or responsibilities each nurse has during their shift.
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Write the equation of the line that passes through the point (0, 4) and is parallel to the line with equation y=5x+3
Answers
Sorry if my english is a bit weird, i hope that helped!
in the faculty lecture, dr. salon mentioned a survey that was taken in the slums in nairobi. from this survey, how long did the average person live in the slums?
Answers
Without specific data from the survey, I cannot provide the exact average length of time a person lived in the slums. I can be found by collecting data and finding average.
In general, surveys can be used to gather information on a population's characteristics and experiences, including their life expectancy. If the survey conducted in the slums of Nairobi included questions about life expectancy or mortality rates, the average lifespan of the individuals surveyed could be calculated using the data collected. It's important to note that the average lifespan in the slums may differ from that of other areas in Nairobi or other regions of the world.
Based on the information provided, Dr. Salon mentioned a survey conducted in the slums of Nairobi. To determine how long the average person lived in the slums, we would follow these steps:
1. Collect the data: The survey would gather information about the length of time people lived in the slums.
2. Calculate the average: Add up the total number of years all respondents lived in the slums and divide by the total number of respondents.
Without specific data from the survey, can't provide the exact average length of time a person lived in the slums. Please provide more information or refer back to Dr. Salon's lecture for the results of the survey.
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a scientist claims that the mean gestation period for a fox is more than 48.9 weeks. if a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted? g
Answers
The rejection of the null hypothesis in a hypothesis test that claims the mean gestation period for a fox is more than 48.9 weeks implies there is sufficient evidence to support the claim, indicating a statistically significant difference between the observed sample mean and the hypothesized mean.
If a hypothesis test is performed that rejects the null hypothesis that the mean gestation period for a fox is 48.9 weeks or less, it means that there is sufficient evidence to support the claim that the mean gestation period for a fox is more than 48.9 weeks.
The rejection of the null hypothesis implies that the observed sample mean is significantly different from the hypothesized mean, and this difference is unlikely to have occurred by chance alone. The statistical test used to evaluate the hypothesis would have produced a p-value less than the significance level, indicating that the evidence against the null hypothesis is strong.
Therefore, the scientist can conclude that there is evidence to support their claim that the mean gestation period for a fox is more than 48.9 weeks, and this finding could have important implications for understanding fox reproductive biology and management.
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the mean life of a television set is 97 months with a variance of 169 . if a sample of 59 televisions is randomly selected, what is the probability that the sample mean would be less than 100.9 months? round your answer to four decimal places.
Answers
The probability that the sample mean would be less than 100.9 months is approximately 0.9600.
We can use the central limit theorem to approximate the sampling distribution of the sample mean as a normal distribution with a mean of 97 months (the population mean) and a standard deviation of σ/√n, where σ is the population standard deviation and n is the sample size.
The standard deviation of the sampling distribution can be calculated as follows
σ/√n = √(169)/√59 = 2.065
Therefore, the z-score corresponding to a sample mean of 100.9 months is
z = (100.9 - 97) / 2.065 = 1.75
Using a standard normal distribution table or calculator, we can find that the probability of obtaining a z-score less than 1.75 is approximately 0.9599.
Therefore, the probability that the sample mean would be less than 100.9 months is approximately 0.9599.
Rounding this to four decimal places, we get
P(x < 100.9) ≈ 0.9600
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In an all boys school, the heights of the student body are normally distributed with a mean of 71 inches and a standard deviation of 4.5 inches. Out of the 1912 boys who go to that school, how many would be expected to be between 61 and 70 inches tall, to the nearest whole number?
Answers
The range of heights between 66 inches and 76 inches indicates the center 95% of males' heights from this school.
What do we mean by interval?All the numbers between two specific integers are referred to as an interval.
All actual values between those two are included in this range.
The class interval is calculated by deducting the upper limit from the class' lower limit.
The following is the formula for the class interval: Upper limit - Lower limit equals the class interval.
Let x represent the heights of the male students at this institution.
The Empirical Rule states that given the mean and standard deviation:
1) Approximately 68% of the x values fall within the range of the mean plus or minus one standard deviation.
2) Nearly 95% of the x values fall within the range of the mean plus or minus two standard deviations.
3) Nearly 99.7% of the x values fall within a range of 3 standard deviations either above or below the mean.
Considering the data provided:
mean = 71 inches
Standard deviation = 2.5 inches
We want to know where 95% of the x values fall. The variation from the mean is 2 standard deviations. Therefore,
2 standard deviations = 2 × 2.5 = 5 inches
Heights:
71 - 5 = 66 inches and
71 + 5 = 76 inches
Therefore, the range of heights between 66 inches and 76 inches indicates the center 95% of males' heights from this school.
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Complete question:
In an all-boys school, the heights of the student body are normally distributed with a mean of 71 inches and a standard deviation of 2.5 inches. Using the empirical rule, determine the interval of heights that represents the middle 95% of male heights from this school.
Chase is moving and must rent a truck. There is an initial charge of $35 for the rental plus a fee of $2.50 per mile driven. Make a table of values and then write an equation for C,C, in terms of m,m, representing the total cost of renting the truck if Chase were to drive m miles.
Answers
The required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.
What is the equation?Equation: A declaration that two expressions with variables or integers are equal.
In essence, equations are questions and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.
A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.
A formula would be 3x - 5 = 16, for instance.
The equation would be:
C is the total cost and m is the miles driven.
We know that:
Charge of the truck: $35
Charge per mile: $2.50
Then, form the equation as follows:
C = 35 + 2.50m
Therefore, the required equation in the given situation is C = 35 + 2.50m where C is the total cost and m is the number of miles driven.
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Convert the polar coordinates (6, -π/3) to Cartesian coordinates. Leave answers in fractional form. Use the "/" key as the fraction bar.
Answers
the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).
What is a fraction?
A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator and denominator.
To convert these polar coordinates to Cartesian coordinates (x, y), we use the following formulas:
x = r cos(θ)
y = r sin(θ)
Substituting the given values, we get:
x = 6 cos(-π/3) = 6 × (1/2) = 3
y = 6 sin(-π/3) = 6 × (-√3/2) = -3√3
Therefore, the Cartesian coordinates of the point represented by the polar coordinates (6, -π/3) are (3, -3√3).
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Solve for X, please write an explanation.
Answers
Step-by-step explanation:
2x+20 and 2x-4 are supplementary angles...they form a straight line and thus = 180 degrees when added together
2x+20 + 2x-4 = 180 simplify
4x + 16 = 180 subtract 16 from both sides
4x = 164 divide both sides by 4
x = 41 degrees
tell whether the ordered pair is a solution of the inequality. 2z less than 15; z =11
Answers
The ordered pair (z, 11) is not a solution of the inequality.
Explain inequality
An inequality is a statement that compares two values, expressing that one value is greater than or less than the other, or that they are not equal. Inequalities are represented using symbols such as < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to). They are used to describe relationships between numbers, variables, and expressions.
According to the given information
To determine whether the ordered pair (z, 11) is a solution of the inequality 2z < 15, we need to substitute z = 11 into the inequality and see if it is true or false:
2z < 15
2(11) < 15
22 < 15 (this is false)
Since 22 is not less than 15, the ordered pair (z, 11) is not a solution to the inequality.
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Amy is sewing some pants for herself. This is the rule for how much fabric she needs to buy. • Measure from your waist to the finished length of thepants • Double this measurement • Add 8inches 1. Amy’s measurement from her waist to the finished length of the pants is 35inches. How many inches of fabric does sheneed?
Answers
Amy needs 78 inches of fabric for her pants if she follows the given rule.
Define inches ?
An inch is a unit of length that is equal to exactly 2.54 centimeters. It is commonly used in the United States and other countries that use the Imperial system of measurement.
To determine how much fabric Amy needs for her pants, we can use the rule provided to us. The first step is to measure from the waist to the finished length of the pants, which in this case is 35 inches.
Next, we need to double this measurement, which gives us 2 * 35 = 70 inches. This is because we need to account for the fabric that will make up both the front and back of the pants.
Finally, we need to add 8 inches to the doubled measurement, which gives us 70 + 8 = 78 inches. This additional 8 inches is to account for any seams, hems, or other finishing touches that may be required to complete the pants.
Therefore, Amy needs 78 inches of fabric for her pants.
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the ratio of a time a student spends on their art project to time spent on their science project is 3:4.The total amount of time the student spends on projects for these 56 min.How much does the students spend on projects for each subject
Answers
Answer: the student spends 24 minutes on their art project and 32 minutes on their science project.
Step-by-step explanation:
Answer:
The student spends 24 minutes on their art project, and 32 minutes on their science project
Step-by-step explanation:
To solve this problem, we can utilise the unitary method, a process by which we find the value of a single unit, from the value of multiple units and thus, the value of multiple units from the value of a single unit.
If the total number of units in the ratio is (3+4)=7, then 7 units = 56 mins.
If 7 units = 56 mins,
then 1 unit = 56/7 mins = 8 mins.
Therefore, 3 units = 8×3 = 24 mins,
and 4 units = 8×4 = 32 mins.
Thus, the student spends 24 minutes on their art project, and 32 minutes on their science project
4.7. the time it takes a printer to print a job is an exponential random variable with the expectation of 12 seconds. you send a job to the printer at 10:00 am, and it appears to be third in line. what is the probability that your job will be ready before 10:01?
Answers
The probability of exponential random variables that your job will be ready before 10:01 is approximately 0.0693, or about 6.93%.
We can use the cumulative distribution function (CDF) of the exponential distribution to solve this problem. Let X be the random variable representing the time it takes to print a job. Then, X follows an exponential distribution with parameter λ = 1/12, since the expectation of X is 12 seconds.
The probability that your job will be ready before 10:01 is equal to the probability that the printer finishes the first two jobs in less than 1 minute since your job is third in line.
Let Y be the random variable representing the time it takes to print the first job. Then, Y also follows an exponential distribution with parameter λ = 1/12.
The probability that the first job is finished before 10:01 is given by:
P(Y < 60) = 1 - [tex]$e^{(-\lambda t)}$[/tex] = 1 - [tex]e^{(-(1/12)(60))}[/tex] = 0.3935
Similarly, the probability that the second job is finished before 10:01 is also 0.3935, since it is also an exponential random variable with the same parameter. Therefore, the probability that your job will be ready before 10:01 is:
P(X < 60) = P(Y < 60) × P(Y < 60) × P(X < 60) = 0.3935² × (1 - [tex]$e^{(-\lambda t)}$[/tex]) = 0.0693
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On a trip, you had to change your money from dollars to euros.
You got 450
euros for 600
dollars.
What is a unit rate that describes the exchange?
Answers
Answer: 0.75 euros = 1 dollar
Step-by-step explanation:
Unit rate
450 euros ----> 600 dollars
450/600 = 0.75
0.75 euros = 1 dollar
Uni rate for the exchange of dollars to euros is 0.75 euros/dollars.
Explanation :[tex]\implies[/tex] To find the unit rate of exchange from dollars to euros, divide the amount of euros Monica received by the amount of dollars she paid:
[tex]\largearrow{\sf{\boxd{\boxed{Unit \ change = \dfrac{Number \ of \ euros \ you \got}{Number \ of \ dollars \ you \ have} }}}}[/tex]
[tex]\implies{\sf{Unit \ change = \dfrac{\cancel{450}}{\cancel{600}} }}[/tex]
[tex]\implies{\sf{Unit \ change = 0.75 }}[/tex]
As a result, the unit rate for the exchange of dollars to euros is 0.75 euros/dollar.
what is the range and domain of y = 3x^2 + 2?
Answers
The domain of the function is (-∞, ∞) and the range of the function is [2, ∞).
Define range!In mathematics, the range of a function refers to the set of all possible output values (dependent variable) that the function can produce for its corresponding input values (independent variable).
According to question:The given function is y = 3x² + 2.
The domain of a function is the set of all possible values of the independent variable (x) for which the function is defined. Since the given function is a polynomial function, it is defined for all real numbers.
Therefore, the domain of the function y = 3x² + 2 is (-∞, ∞), which means that the function is defined for all real values of x.
The range of a function is the set of all possible values of the dependent variable (y) that the function can take. In this case, the function is a quadratic function with a leading coefficient of 3, which means that the parabola opens upwards and its vertex is at the point (0,2).
Since the minimum value of the function is 2, the range of the function is [2, ∞).
Therefore, the domain of the function is (-∞, ∞) and the range of the function is [2, ∞).
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help me please help answer the question below Do not round
Answers
Answer:
0.1296
Step-by-step explanation:
0.6*0.6=0.36
0.6*0.36=0.216
0.6*0.216=0.1296
a recent survey revealed that 30% of us households own one or more cats. you visit 50 random households. what is the mean number of households that will have one or more cats? 15 what is the standard deviation of the number of households that will have one or more cats? 3.2 round your answer to 1 decimal place. suppose that 10 of the 50 random households had one or more cats. would you consider this unusual?
Answers
1. The mean number of households that will have one or more cats is 15.
2. This means that getting 10 or fewer households with cats out of 50 is not extremely unusual, as there is a 5.3% chance of it happening by random chance alone.
The mean number of households that will have one or more cats can be calculated as:
Mean = (30/100) x 50 = 15
Therefore, the mean number of households that will have one or more cats is 15.
The standard deviation can be calculated using the formula:
Standard deviation = [tex]\sqrt{(npq)}[/tex]
where n is the sample size (50), p is the probability of success (30/100 = 0.3), and q is the probability of failure (1 - p = 0.7).
Standard deviation = sqrt(50 x 0.3 x 0.7) = 3.08
Rounding to 1 decimal place, the standard deviation is 3.1.
If 10 of the 50 random households had one or more cats, we can calculate the z-score as:
z = (x - μ) / σ
where x is the observed number of households with cats (10), μ is the mean (15), and σ is the standard deviation (3.1).
z = (10 - 15) / 3.1 = -1.61
Looking up the z-score in a standard normal distribution table, we find that the probability of getting a z-score of -1.61 or lower is 0.053.
This means that getting 10 or fewer households with cats out of 50 is not extremely unusual, as there is a 5.3% chance of it happening by random chance alone.
However, it is somewhat lower than the expected value of 15, which suggests that the sample may not be fully representative of the population.
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Determine the domain of the following graph:
21098
11
76
4
+32
2
1
-12-11-10-9-8-7-6-5-4-3-2-1
5
ܐ ܣ ܣ ܟ ܬ ܬ { ܣ ܣ
-2
-3
-4
-5
-6
-9
-7
-10
-8
-11
-12
2 3 4 5 6 7 8 9 10 11 12
Answers
The domain of the following graph is equal to [-11. -3]
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function is defined.
How to identify the domain any graph?In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-11, -3].
Range = [-5, 0].
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which of the following is true with regards to statistical analysis? which of the following is true with regards to statistical analysis? bivariate analysis is a special form of multivariate analysis. it examines the relation between two or more variables. regression analysis is a univariate analysis. multivariate analysis examines the relationship between one, two or more variables. univariate analysis involves the analysis of a single variable.
Answers
The correct option is: "Univariate analysis involves the analysis of a single variable."
The following statement is true with regards to statistical analysis:
Univariate analysis involves the analysis of a single variable.
The other statements are not entirely accurate:
Bivariate analysis is a form of multivariate analysis that examines the relationship between two variables, but multivariate analysis can involve more than two variables.
Regression analysis is a multivariate analysis technique that examines the relationship between one dependent variable and one or more independent variables.
Multivariate analysis involves the examination of the relationship between two or more variables, not necessarily one, two, or more.
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Determine two coterminal angles (one positive and one negative) for each angle. Give your answers in radians. (Enter your answers as a comma-separated list.)
(a)
3/4
Answers
The two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.
What is coterminal angles ?Coterminal angles are two or more angles that have the same initial and terminal sides, but differ by a multiple of 360 degrees or 2π radians. In other words, coterminal angles are angles that overlap each other when drawn in standard position (with their initial side on the positive x-axis).
To find two coterminal angles with 3/4 radians, we can add or subtract multiples of 2π radians (which is equivalent to a full circle).
One positive coterminal angle is obtained by adding 2π radians to 3/4 radians:
3/4 + 2π = 3/4 + 8π/4 = 3/4 + 2π
Simplifying, we get:
3/4 + 2π = (3π + 4)/4
Therefore, one positive coterminal angle is (3π + 4)/4 radians.
One negative coterminal angle is obtained by subtracting 2π radians from 3/4 radians:
3/4 - 2π = 3/4 - 8π/4 = 3/4 - 2π
Simplifying, we get:
3/4 - 2π = (-5π + 4)/4
Therefore, one negative coterminal angle is (-5π + 4)/4 radians.
Hence, the two coterminal angles for 3/4 radians are (3π + 4)/4 and (-5π + 4)/4 radians.
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During a snowstorm, Annabelle tracked the amount of snow on the ground. When
the storm began, there were 3 inches of snow on the ground. Snow fell at a constant
rate of 1 inch per hour until another 4 inches had fallen. The storm then stopped for 6
hours and then started again at a constant rate of 2 inches per hour for the next 5
hours. As soon as the storm stopped again, the sun came out and melted the snow for
the next 7 hours at a constant rate of 2 inches per hour. Make a graph showing the
inches of snow on the ground over time using the data that Annabelle collected.
Answers
The graph will have a horizontal line from 4 to 15 hours (since there is no change in snow depth during that time) and two downward sloping lines from 0 to 4 hours and from 15 to 22 hours (representing snowfall and snow melt, respectively)
How to draw a graph?To make a graph of the inches of snow on the ground over time, we can use the following steps:
We can divide the time into different intervals based on the snowfall, the break in the storm, and the snow melt. We have:
Snowfall for the first 4 hours (at a rate of 1 inch per hour).Break in the storm for 6 hours.Snowfall for the next 5 hours (at a rate of 2 inches per hour).Snow melt for the next 7 hours (at a rate of 2 inches per hour).We can then calculate the inches of snow on the ground at the end of each interval, starting with the initial 3 inches of snow. We have:
After 4 hours of snowfall: 3 + 4(1) = 7 inches of snow on the ground.After 10 hours (4 hours of snowfall + 6 hours of break): 7 inches of snow on the ground.After 15 hours (10 hours + 5 hours of snowfall): 7 + 5(2) = 17 inches of snow on the ground.After 22 hours (15 hours + 7 hours of snow melt): 17 - 7(2) = 3 inches of snow on the ground.We can now plot these points on a graph with time (in hours) on the x-axis and inches of snow on the y-axis. The graph will have four points: (0,3), (4,7), (15,17), and (22,3).
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