Natasha is 50 m due east of Michelle. Natasha walks 20 m due north, and Michelle walks 10 m due
south. Find the distance and bearing of Michelle from Natasha now.
Please use diagrams to explain.
Answers
Answer:
Let's define East as the positive x-axis and North as the positive y-axis.
If Michelle's initial position is (0, 0)m
We know that Nathasha is 50m due East of Michelle.
Then the position of Natasha is (50, 0)m
Now we know that Natasha walks 20m due North, then the new position of her's is:
(50, 0 + 20)m = (50, 20)m
While Michelle walks 10m due South (South would be the negative y-axis, then we subtract 10 meters)
Michelle's new position will be:
(0, 0 - 10)m = (0, -10)m
Now we want to know the distance and bearing of Michelle from Natasha.
First, remember that the distance between two points (a, b) and (c, d) is given by:
Distance = √( (a - c)^2 + (b - d)^2)
Then the distance between Michelle and Natasha is:
Distance = √( (50m - 0m)^2 + (20m - (-10m))^2)
Distance = √( (50m)^2 + (30m)^2) = 58.31m
Now to find the bearing you can see the image below:
Point B is Michelle's position and point A is Natasha's position.
To find the bearing, we can make a triangle rectangle as the one shown in the image:
Also remember the relation:
Tan(a) = (opposite cathetus)/(adjacent cathetus).
Where the opposite cathetus is the difference between the x-values of each position, this is:
opposite cathetus = 50m - 0m = 50m
And the adjacent cathetus is the difference between the y-values, this is:
adjacent cathetus = 20m - (-10m) = 30m
Then:
Tan(a) = 50m/30m
Tan(a) = 5/3
Now if we apply the inverse Tan function to both sides, Atan(x) we get:
Atan(Tan(a)) = Atan(5/3)
a = Atan(5/3) = 59°
So the bearing is of 59°.
Related Questions
17:56 Dawn is trying to find out how much weight she can push across the room. She is really trying to find her __________.
Answers
4.
You are given an isosceles trapezoid ABCD with median XY. Complete the following.
AX = 4, CD = __________
Answers
If isosceles trapezoid ABCD has a median XY then CD = 8 .
What is trapezoid?
A trapezοid is alsο knοwn as a trapezium is a fοur-sided pοlygοn οr a quadrilateral. It has οne set οf οppοsite sides which are parallel and a set οf nοn-parallel sides. The parallel sides are knοwn as the bases and the nοn-parallel sides are knοwn as the legs οf the trapezοid. A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
Given AX = 4
Now, AX = BX as XY is the meridian
i.e.
AB = 2AX
AB = 2(4)
AB = 8
We have given that the trapezoid is an isosceles trapezoid, which means
AB = CD
i.e.
CD = 8
Thus, If isosceles trapezoid ABCD has a median XY then CD = 8.
To learn more about trapezoid from the given link:
https://brainly.com/question/8643562
#SPJ1
what does your work show about the behavior of the standard deviation of a binomial distribution as the probability of a success gets closer to zero?
Answers
The probability of a success gets closer to zero is 15.
What is behavior of the standard deviation ?
The average squared difference between data points and their mean value is called variance, and it is the variance's square root that is used to calculate standard deviation. The symbol for standard deviation can be seen below.
Both the standard deviation and the variance are indicators of dispersion, but the standard deviation is more explicitly the typical distance between a data point and the mean. The majority of the data will be within one standard deviation of the mean. While the variance is not measured in the same units as the actual data, the standard deviation is
If mean deviation is 12, what is its standard deviation?
Lets look the problem .
Given ,
Mean deviation (MD) =12
Here is the inequality to calculate the standard deviation.
6QD=5MD=4SD ,
Where ,QD stands for the Quartile deviation.
SD stands for the standard deviation.
So,
Standard deviation =(5/4)*MD
=(5/4)*12
=15
To learn more about standard deviation visit:
https://brainly.com/question/23907081
#SPJ4
I need some help plz
Answers
- I’m pretty sure that is it... hope this works for ya!!
True or false? the interval [1,2] contains exactly two numbers - the numbers 1 and 2.
Answers
The answer is "false". The interval [1, 2] contains all the real numbers between 1 and 2 including the endpoints.
How to write and represent an interval?An interval notation is used for representing the continuous set of real values. This is the shortest way of writing inequalities.
Intervals are represented within the brackets such as square brackets or open brackets(parenthesis).
If the interval is within a square bracket, then the end values are included in the set of values.If the interval is within parenthesis, then the end values are not included in the set of values.The square brackets represent the inequalities - 'greater than or equal or 'less than or equalThe parenthesis represents the inequalities - 'greater than' or 'less thanFinding true or false:The given interval is [1, 2]
The given statement is - 'the interval [1, 2] contains exactly two numbers - the numbers 1 and 2'
The given statement is 'false'.
This is beacuse, an interval consists set of all the real values in between the two values given.
So, according to the definition, there are not only the end values but also many real values in between them.
Thus, the answer is "false". The interval [1, 2] consists of all the real values between 1 and 2 including 1 and 2.
Learn more about interval notation here:
https://brainly.com/question/10878781
#SPJ4
Dan invests £18790 into his bank account. He receives 4.9% per year simple interest. How much will Dan have after 3 years? Give your answer to the nearest penny where appropriate.
Answers
Answer:
$1278.23
Step-by-step explanation:
in each diagram below, line A is parallel to line B. in which diagram does the alternate interior angle postulate justify angle 1 being congruent to angle 2
Answers
Answer:
Step-by-step explanation:
a
DUE TOMORROW. Plz help
Answers
Answer:
V≈6.93
Step-by-step explanation:
AB=s(s﹣a)(s﹣b)(s﹣c)
V=ABh
s=a+b+c
2
Solving forV
V=1
4h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=1
4·4·﹣24+2·(2·2)2+2·(2·2)2﹣24+2·(2·2)2﹣24≈6.9282
1. According to the podcast, why and how is chicken the reason American trucks dominate the truck market in the United States? Briefly explain. 2. Name two reasons a party (e.g., a politician or an industry association) may want to impose a tariff? 3. Who are they usually trying to protect? Who would be hurt by a tariff on automobiles? Explain. 4. Describe how competition encourages innovation? In your answer to this question, include a discussion on why American trucks "basically stayed the same over the years. 5. Describe ways foreign companies tried to get around American-imposed tariffs on automobiles. 6. Do you think the methods you described in your previous answer are efficient for an economy? Why or why not? 7. Lastly, how can a tariff be used as a bargaining chip? In your opinion, is that a good reason to impose tariffs - why or why not?
Answers
1. Chicken became the key product that drove the creation of the Interstate Highway System, which led to the dominance of American trucks in the US truck market.
2. A party may want to impose a tariff to protect domestic industries from foreign competition or to generate revenue for the government.
3. A party is usually trying to protect domestic industries, but a tariff on automobiles would hurt both domestic consumers who would pay higher prices and foreign producers who would face reduced demand.
4. Competition encourages innovation by providing incentives for companies to improve their products and services to stay ahead of their rivals; American trucks stayed the same because they faced little competition due to protectionist policies.
5. Foreign companies tried to get around American-imposed tariffs on automobiles by establishing factories in the US, forming joint ventures with American companies, or exporting through third countries.
6. The methods used to get around tariffs can be efficient in the short term, but they may not be sustainable or desirable in the long term as they can lead to trade imbalances and undermine the competitiveness of domestic industries.
7. Tariffs can be used as a bargaining chip to negotiate better trade deals, but they should be imposed judiciously and only as a last resort to avoid damaging the economy and harming consumers.
1. In the podcast, chicken is cited as the reason why American trucks dominate the truck market in the United States.
This is because in the 1960s, the government imposed regulations on the trucking industry that limited the amount of weight a truck could carry.
To get around these regulations, the industry started using smaller trucks to transport goods, which were often not strong enough to handle the weight.
However, they found that if they put chicken on the back of the trucks, the weight of the cargo would distribute more evenly and the smaller trucks could handle the load.
This led to the development of the modern pickup truck, which is now a staple of the American automobile market.
2. Parties may want to impose tariffs for various reasons, such as to protect domestic industries and jobs from foreign competition, to raise revenue for the government, or to level the playing field in international trade.
Two specific reasons for imposing tariffs could be to protect national security interests or to address unfair trade practices by other countries.
3. Tariffs are usually imposed to protect domestic industries and jobs, and the parties that are being protected are typically the producers of the goods or services in question.
However, tariffs can also harm consumers who may have to pay higher prices for imported goods or may have fewer choices in the marketplace. For example, if a tariff is imposed on automobiles, domestic car manufacturers may benefit, but consumers may have to pay more for cars, and foreign automakers may lose market share.
4. Competition encourages innovation by creating incentives for companies to improve their products or services to gain a competitive advantage.
In the case of American trucks, the lack of competition may have contributed to their lack of innovation over the years. Since they dominated the market, there was little pressure to improve or innovate, and as a result, they have largely stayed the same.
However, the rise of foreign competition in recent years has led American truck manufacturers to invest more in innovation to stay competitive.
5. Foreign companies have tried to get around American-imposed tariffs on automobiles in various ways, such as by moving production to countries not subject to the tariffs, by exporting parts and assembling them in the United States, or by lobbying the government for exemptions or tariff reductions.
6. The methods used by foreign companies to get around tariffs may not be efficient for the economy as a whole because they can lead to higher costs and inefficiencies in the supply chain.
However, they may be necessary for individual companies to remain competitive in the short term.
Ultimately, a more efficient solution would be to address the root causes of the trade imbalances that lead to tariffs in the first place.
7. A tariff can be used as a bargaining chip by threatening to impose tariffs on imports from a country unless they make concessions in trade negotiations.
While this can be an effective strategy in certain situations, it can also lead to a trade war and harm both economies.
In general, tariffs should be used sparingly and as a last resort, and efforts should be made to address underlying trade issues through diplomacy and negotiation.
For similar question on regulations.
https://brainly.com/question/29618671
#SPJ11
a team of 15 workers picked 1,050 apples. each person picked the same number of apples. How many did each person pick?
Answers
Answer: Each worker picked 70 apples
Step-by-step explanation:
1050 apples divided by 15 workers
1050/15 = 70
a sample obtained in such a way that every element in the population has an equal chance of being selected is called a/an _______ sample.
Answers
The correct term for a sample obtained in such a way that every element in the population has an equal chance of being selected is a "random sample."
In a random sample, each member of the population has an equal probability of being chosen, providing a representative subset of the population. This sampling method helps to reduce bias and ensures that the sample is more likely to accurately reflect the characteristics of the entire population.
Random sampling is a fundamental principle in statistics and research, allowing for generalizations and inferences to be made about the population based on the characteristics observed in the sample. It is widely used in various fields, such as social sciences, market research, and opinion polls, to draw meaningful conclusions about a larger population.
To learn more about population click here:brainly.com/question/15889243
#SPJ11
Over the last 80 years, the average annual U. S. Inflation rate was about
a. 3. 6 percent, implying that prices have increased 16-fold.
b. 4 percent, implying that prices have increased 17-fold.
c. 4 percent, implying that prices have increased 16-fold.
d. 3. 6 percent, implying that prices increased about 17-fold
Answers
The correct option is C, Prices have increased about 16-fold over the last 80 years, assuming an average annual U.S. inflation rate of 4 percent.
The inflation rate is a measure of the rate at which the general level of prices for goods and services is rising over a period of time, usually a year. It is typically expressed as a percentage increase or decrease in the average price level of a basket of goods and services over a certain period of time.
Here, the price index is a weighted average of the prices of a specific set of goods and services. The inflation rate is a key indicator of the overall health of an economy, as high inflation can erode purchasing power and reduce the standard of living for individuals, while low or negative inflation can lead to economic stagnation or deflation. Governments and central banks closely monitor inflation rates to ensure that they remain within a targeted range, typically around 2-3% per year, through the use of monetary and fiscal policies.
To learn more about Inflation rate visit here:
brainly.com/question/30112292
#SPJ4
Adam had some candy to give to his three children. He first took seven pieces for himself and then evenly divided the rest among his children. Write an expression for how many pieces each child received. A. 7−c3 B. C−73 C. C−73 D. 7−c3
Answers
Answer : The expression will be
( c - 7 ) / 3
Step-by-step explanation:
Let's say Adam has c pieces of candy
He took ten pieces for himself which means we can write this as c-7
He then divided this amount between his 3 children (c-7)/3
Mail in female high school students reported how many hours they work each week in summer jobs the data is represented in the following box plots identify any values of data that might affect the systematical measures of spread and center
Answers
Answer:
poopooooo1p1p1p1pp11p1p1
can't anybody help me with this ik math sucks but help
Answers
Answer:
g
Step-by-step explanation:
Can someone please help me with this of identifying the domain and range!!!!
Answers
Question below, please help me
Answers
when the elevator at Franklin’s apartment building went out of service, Franklin walked up 15 flights of stairs. He stopped to rest after every 3 flights. How many times did Franklin stop to rest?
Answers
A circle has centre (-3,-4) and a point P(5,2) on its circumference. Determine the equation of the circle expressed in the form x²+y²+ax+by+c=0
Answers
The equation of the circle expressed in the form x²+y²+ax+by+c=0 is (x+3)² + (y+4)² - 100 = 0.
Center of the circle = (-3,-4)Point on the circumference of the circle = P(5,2) We know that the equation of the circle is given by: (x−a)²+(y−b)²=r² where the center of the circle is (a, b) and the radius is r.
Step 1: Find the radius of the circle using the distance formula Distance between the center of the circle and point
P = radius of the circle.
We get
r = √((-3-5)² + (-4-2)²)r = √64+36r = √100 = 10
Step 2:Find the equation of the circle substituting the center and the radius into the equation of the circle
(x−a)²+(y−b)²=r²(x-(-3))² + (y-(-4))² = 10²(x+3)² + (y+4)² = 100(x+3)² + (y+4)² - 100 = 0
For more question circle
https://brainly.com/question/26605972
#SPJ8
The sum of two positive numbers is 29. If one of them is 5 more than that of the other, find the numbers.
Answers
Answer:
12 and 17
Step-by-step explanation:
Let x represent the first number and y represent the second number.
x + y = 29
x = y + 5
Substitute the second equation into the first equation and solve for y.
y + y + 5 = 29
2y = 24
y = 12
Use this to calculate the value of x.
x = 12 + 5
x = 17
Therefore, the two numbers are 12 and 17.
Given (x – 1)2 = 50, select the values of x.
Answers
Answer: x=26
Step-by-step explanation:
(x-1) = 50/2
x-1 = 25
x = 25 +1
x = 26
X - 1 = 7.07
X = 8.07.
What is the equation of the vertical asymptote of g(x)=4log2(x−2) 5 ? enter your answer in the box.
Answers
The equation of the vertical asymptote of the function \(g(x)=4log_{2} (x-2)+5\) is x=2.
What is vertical asymptote of a function?Vertical asymptotes are vertical lines that represent the zeros of a rational function's denominator. Asymptotes can also occur in other situations, such as logarithms. It occurs at the x-value that is outside the domain of the function, therefore the graph can never cross it.
How to find vertical asymptotes from graph?There may be a vertical asymptote along the vertical line if a portion of the graph is about to turn vertical. At the point of x along which you discovered the vertical asymptote, the function's value changes to either ∞ or -∞. A vertical asymptote, however, must never touch the graph.
Graph the function \(g(x)=4log_{2} (x-2)+5\)
(x,y)= (3,5), (4,9), (6,13)
From graph we can see that the graph is turning to be vertical from x=2. So, the equation of vertical asymptote of the function is x=2.
To know more about vertical asymptotes, visit:
https://brainly.com/question/11743529
# SPJ4
The complete question is:
“What is the equation of the vertical asymptote of \(g(x)=4log_{2} (x-2)+5\)? enter your answer in the box.”
A drawing shows 12 apples and 4 bananas. Which is the ratio of bananas to apples?
Answers
The answer is 6:2. Since the greatest common denominator of both is 2 you divide it by both numbers to get the ratio.
George was able to solve 36 math problems in 15 minutes. Urban was able to solve 42 math problems in 20 minutes. Who was able to solve math problems at a greater rate? What was the rate?
Question 2 options:
A: George;
B: Urban;
C: George;
Answers
Answer:
Urban
Step-by-step explanation:
find the value of z for the probability statement: p (-z
Answers
Hi! I understand you're looking for the value of z in a probability statement. However, your question seems to be incomplete, as the probability statement is not fully provided. Please provide the complete probability statement (e.g., P(-z < Z < z) = p) so that I can assist you with finding the correct z-value.
I'm sorry, but I need more information to provide a complete answer. The probability statement you provided is incomplete. It should include a specific probability value and a direction (greater than or less than). For example, a complete probability statement could be: p(-z < -1.96) = 0.05, which means the probability of getting a score less than -1.96 standard deviations from the mean is 0.05. Once a complete probability statement is provided, we can use statistical tables or software to find the corresponding value of z.
Learn more about probability statement here:
brainly.com/question/14250268
#SPJ11
Write the equation of this line in y= mx + b form
Answers
Answer:
y=2x
Step-by-step explanation:
Slope (m): the formula for slope is y2-y1 over x2-x1 so it will be 2-(-2) over 1-(-1) and the result will be 2.
Y intercept: The Y intercept is 0 as shown in the graph
cual es la raiz cuadrada de 45
cual es la raiz cuadrada de 92
cual es la raiz cuadrada de 126
Answers
The square root of 45 ≈ 6.7082
The square root of 92 ≈ 9.5917
The square root of 126 ≈ 11.2249
How to solve
The square root of 45 is approximately 6.7082, which is derived from taking the square root of 45 \((\sqrt(45)).\)
For 92, the square root is approximately 9.5917 \((\sqrt(92))\).
As for 126, its square root is around 11.2249 \((\sqrt(126)).\)
These values are approximations because the square roots of 45, 92, and 126 are irrational numbers, meaning their decimal representation is non-repeating and non-terminating.
When working with these square roots in calculations, it is common to either use their approximate values or to keep them in square root form to maintain the highest level of precision.
Read more about square root here:
https://brainly.com/question/428672
#SPJ1
The Question in English
What is the square root of 45
what is the square root of 92
what is the square root of 126
In 2010, Fernando paid $1,810 in federal income tax. In 2011, he paid $816. What is the percent of decrease in the amount paid
Answers
Answer:
45% decrease.
Step-by-step explanation:
So, basically, write a fraction of the amount of decrease: 816/1,810. Change that to a decimal or simply convert the fraction to a percent. If you go the decimal way, convert the decimal to a percent. The result is 45%
pirya has picked 1 1/2 cups of raspberries, which is enough for 3/4 of a cake how many cups does she need for the whole cae
Answers
Pirya needs 1 1/2 cups of raspberries for 3/4 of a cake, so she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.
What is fraction?A fraction is a numerical representation of a portion of a total. It consists of two integers, a numerator and a denominator, separated by a line or slash. The numerator reflects the number of equal portions of the whole that are being considered, while the denominator represents the total number of equal parts in the whole. For instance, the fraction "1/2" denotes one of two identical pieces, or half, of the whole. Mathematicians frequently utilize fractions to represent quantities, ratios, and proportions. They are also used in everyday life to signify amounts, such as one-half of a pizza or one-third of a cups of sugar.
How to solve?
she needs 1 1/2 * (4/3) = 2 cups of raspberries for the whole cake.
To learn more about fraction, visit:
https://brainly.com/question/20593515
#SPJ4
s +9=25
Help me please