5. If R(2.2) and S(5.4) i. Calculate the magnitude of RS ii. Express RS in the form (K,D), where K is the magnitude and Q the bearing.
Answers
Answer:
We have:
R = (2, 2)
S = (5, 4)
RS is the segment that connects R with S.
So RS is just the distance between R and S.
Remember that the distance between two points (a, b) and (c, d) is given by:
[tex]distance = \sqrt{(a - c)^2 + (b - d)^2}[/tex]
Then the distance between S and R is
[tex]distance = \sqrt{(5 - 2)^2 + (4 - 2)^2} = \sqrt{3^2 + 2^2} = \sqrt{13}[/tex]
Then:
RS = √13
ii) Now we want to express RS in the form (K, Q)
where K is the magnitude (we already know that it is √13) and Q is the bearing, which is measured with respect to the horizontal axis.
To interpret the bearing, let's look at the image below:
We can use the relation:
Tan(θ) = (opposite cathetus)/(adjacent cathetus)
where the opposite cathetus is just the difference between the y-values:
Opposite cathetus = 4 - 2 = 2
And the adjacent cathetus is the difference between the x-values:
Adjacent cathetus = 5 - 2 = 3
Then we have:
Tan(θ) = 2/3
If we apply the inverse tangent equation to both sides, we get:
Atan(tan(θ)) = Atan(2/3)
θ = Atan(2/3) = 33.69°
The bearing is 33.69°
then:
RS = (√13, 33.69°)
Related Questions
Determine the domain of the function (f o g)((x) where:
Answers
Answer: You have the correct answer. It's choice B
Domain = [tex]\left(-\infty, \frac{2}{5}\right)[/tex]
Nice work.
=========================================================
Explanation:
The domain of g(x) is found by setting 2-5x greater than or equal to 0 and solving for x. We're doing this to ensure that 2-5x is not negative.
[tex]2-5x \ge 0\\\\2 \ge 5x\\\\5x \le 2\\\\x \le \frac{2}{5}[/tex]
So we can plug in any number smaller than 2/5, or we can plug in 2/5 itself, into the g(x) function to get some output.
However, notice that if x = 2/5, then g(x) = 0. This then would feed into the f(x) function and lead to a division by zero error. Therefore, x = 2/5 must be kicked out of the domain of (f o g)(x). We keep everything else that we found earlier.
In short, the domain as an inequality is [tex]x < \frac{2}{5}[/tex], which is the same as saying [tex]-\infty < x < \frac{2}{5}[/tex] and that converts to the interval notation [tex]\left(-\infty, \frac{2}{5}\right)[/tex]
We don't use a square bracket because we don't want to include the endpoint 2/5.
What number had an experimental probability that matched its theoretical probability
Answers
Answer:
here
https://decabonner.weebly.com/uploads/1/6/4/8/1648294/day_1_-_practice_wksht_-_basic_probability_key.pdf
Avani is trying to find the height of a radio
antenna on the roof of a local building. She
stands at a horizontal distance of 21 meters
from the building. The angle of elevation
from her eyes to the roof (point A) is 42°,
and the angle of elevation from her eyes to
the top of the antenna (point B) is 51°. If
her eyes are 1.5 meters from the ground,
find the height of the antenna (the distance
from point A to point B). Round your
answer to the nearest meter if necessary.
Answers
Answer:
The height of the antenna is 7.0 m
Step-by-step explanation:
Let the height of the antenna be represented by x, and the distance from Avani's eyes to the top of the building A by y. And let z = x + y, so that:
Tan 42 = [tex]\frac{y}{21}[/tex]
y = Tan 42 x 21
= 0.9004 x 21
= 18.9084
y = 18.91 m
Also,
Tan 51 = [tex]\frac{z}{21}[/tex]
z = Tan 51 x 21
= 1.2349 x 21
= 25.9329
z = 25.93 m
Therefore,
x = z - y
= 25.93 - 18.91
= 7.02
x = 7.02 m
The height of the antenna is 7.0 m
Find the equation of the line through (6,8) which is parallel to the line y=4x−6.
Give your answer in the form y=mx+b.
Answers
Answer:
[tex]y=4x-16[/tex]
Step-by-step explanation:
Hi there!
What we need to know:
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope of the line and b is the y-intercept (the value of y when x is 0)Parallel lines always have the same slope1) Determine the slope (m)
[tex]y=4x-6[/tex]
4 is in the place of m, making it the slope. Because parallel lines have the same slope, the slope of the line is therefore 4. Plug this into [tex]y=mx+b[/tex]:
[tex]y=4x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=4x+b[/tex]
Plug in the given point (6,8) and solve for b
[tex]8=4(6)+b\\8=24+b[/tex]
Subtract 24 from both sides to isolate b
[tex]8-24=24+b-24\\-16=b[/tex]
Therefore, the y-intercept of the line is -16. Plug this back into [tex]y=4x+b[/tex]:
[tex]y=4x-16[/tex]
I hope this helps!
Answer:
y=4x−16
Step-by-step explanation:
Because we want a parallel line to the given one, we know it needs to have the same slope. Therefore, the new line must be y=4x+b for some b. Knowing that the line goes through the point (6,8), we can plug this in and solve for b:
y=4x+b
8=4(6)=b
b=-16
So the equation of the line is y=4x−16.
hello! i hope your day is going great! whats 4x 2/1/2??
Answers
Answer:
4
Step-by-step explanation:
1/2=0.5
2/0.5=1
4x1=4
Jacob needs 48 ounces of tomatoes for the spaghetti sauce. He is choosing between two brands of tomatoes.
A 2-column table with 2 rows. Column 1 is labeled Brand A with entries 8 ounces, 2 dollars and 99 cents. Column 2 is labeled brand B with entries 16 ounces, 4 dollars and 99 cents.
Find the unit rate for each brand. Round to the nearest cent (hundredth). Brand A costs per ounce. Brand B costs per ounce.
PLS HELP
Answers
Answer:
$0.37 and $0.31
Step-by-step explanation:
Answer:
Step-by-step explanation:
PLEASE ANSWER ASAP FOR BRAINLEST!!!!!!!!!!!!!!!!!
Answers
Answer: 216
Step-by-step explanation:
We have 3 sets of 6 options.
6x6x6
6x6x6=216
Find x
Find Angle CBD
Find Angle D
Answers
Answer:
[tex]thank \: you[/tex]
The values in the table represent a linear function. What is the common difference of the associated arithmetic sequence
Answers
21-4=17
4+17=21
21+17=38 and so on..
3x+5y=14 and 6x-4y=9
Answers
Answer:
Step-by-step explanation:
Bấm máy tính hệ phương trình là ra
An online survey company wants to know if customer age is important in deciding to subscribe. The company has gathered a random sample of 1000 people from the population and asked each person whether he or she would subscribe to a service. Perform all the steps of a hypothesis test with a = 0.05 to determine whether or not an individual would subscribe to a service and age are independent.
Age
Under 18 18-34 35 and Over Total
Yes 120 262 237 619
No 41 103 237 381
Total 161 365 574 1000
Answers
Answer:
service subscription and age are not independent
Step-by-step explanation:
The appropriate statistical test to adopt for the above problem is the Chisquare test.
The hypothesis :
H0 : service subscription and age are independent
H1 : service subscription and age are not independent
Observed values :
Under 18 18-34 35 and Over Total
Yes__ 120 __262 __237__ 619
No___ 41 ___103 __237 __381
Total 161 365 574 1000
χ² = (Observed - Expected)²/Expected
Expected Values:
99.659 __ 225.935 __ 293.406
61.341 ___ 139.065 __ 180.594
The Chisquare values :
4.15172__ 5.7569__ 10.8438
6.74518_ 9.35307 __ 17.6176
χ² = 4.15172 + 5.7569 + 10.8438 + 6.74518 + 9.35307 + 17.6176 = 54.46827
Degree of freedom = (row-1)*(column-1) = (2-1)*(3-1) = 1*2 = 2
Pvalue at df = 2 ; Pvalue = 0
α = 0.05
Pvalue < Α ; Hence, we reject H0 ; and conclude that service subscription and age are not independent
HELP ME PLEASE I REALLY NEED HELP I DONT KNOW HOW TO DO THIS CAN SOMEONE PLEASE HELP I WOULD REALLY APPRECIATE IT PLEASE AND THANK YOU
Answers
9514 1404 393
Answer:
{-12, -8, 0, 8}
Step-by-step explanation:
The range is the set of y-values that correspond to the given set of x-values. I like to figure them "all at once", since the math is repetitive.
f(x) = -2x +6
f({-1, 3, 7, 9}) = -2{-1, 3, 7, 9} +6 = {2, -6, -14, -18} +6
f({-1, 3, 7, 9}) = {8, 0, -8, -12}
The range for the given domain is {-12, -8, 0, 8}.
When x= 1, then y=
Just how ?
Answers
Josie and her brothers and sisters measured their heights and found the mean averageThe mean was 150cmJosie forgot her height. Can you work out Josie's height? 150cm, 170cm, 140cm, 155cm
Answers
Answer:
135 cm
Step-by-step explanation:
Let Jose's height = x
The mean of their heights = 150
Given the Heights:
150cm, 170cm, 140cm, 155cm
The mean is the sum if the heights divided by the number of people
Here :
(150 + 170 + 140 + 155 + x) / 5 = 150
(615 + x) / 5 = 150
615 + x = 750
x = 750 - 615
x = 135 cm
solving quadratic equation using the completing the square method. (a)-6h²+5h+2=0
Answers
...........................................................................................................................................................................................................................................................................................................................................................................
[tex]-6h^{2}+5h+2=0\\h^{2} -\frac{5}{6} h-\frac{1}{3} =0\\h^{2} -\frac{5}{6} h+(\frac{5}{12} )^{2} -(\frac{5}{12} )^{2}-\frac{1}{3} =0\\(h-\frac{5}{12} )^{2} =\frac{1}{3} +(\frac{5}{12} )^{2}\\(h-\frac{5}{12} )^{2} =\frac{73}{144} \\[/tex]
[tex]h-\frac{5}{12} = \sqrt{\frac{73}{144}} \\h=\sqrt{\frac{73}{144}} +\frac{5}{12}[/tex]
or
[tex]h-\frac{5}{12} = -\sqrt{\frac{73}{144}} \\h=-\sqrt{\frac{73}{144}} +\frac{5}{12}[/tex]
Combine the following complex numbers.
(16 − 6i) − (2 − 3i)
Answers
Answer:
14 - 3i
Step-by-step explanation:
Distribute the minus sign amongst the second equation:
(16 - 6i) - (2 - 3i) = 16 - 6i - 2 + 3i
Solve:
16 - 6i - 2 + 3i:
16 - 2 - 6i +3i
14 - 3i
Hope this helps!
Help plssssss I really need the answer asap! I’d really appreciate it
Answers
This is the question
Answers
Answer:
x= 3
Step-by-step explanation
Answer:
the answer is x = 3, but i gave you the explanation to figure it out on your own.
Step-by-step explanation:
x = 3
27 + 5/8 = 32
Which of the Following is a solution to 7x-6y=19
(-5,-3)
,(7,5),
(-4,0)
(1,-2)
Answers
Answer:
(1,-2)
Step-by-step explanation:
Choose any value for x that is in the domain to plug into the equation.
Choose 0 to substitute in for x to find the ordered pair.
(0, -19/6)
Choose 1 to substitute in for x to find the ordered pair.
Remove parentheses.
y= -19/6 + 7(1)/6
Simplify
y=2
Use the
x and y values to form the ordered pair.
(1,−2)
What is 3+7x(-3)(-3)÷-5
Answers
Answer:
-37.8
Step-by-step explanation:
Answer:-37.8
Step-by-step explanation:
Plz help me solve this
Answers
If someone helps me I’ll give brainless
Answers
Answer:
128
Step-by-step explanation:
The two angles form a straight line so they add to 180
2m+62 + 3m +143 = 180
Combine like terms
5m+205=180
Subtract 205 from each side
5m+205-205=180-205
5m = -25
Divide by 5
5m/5 = -25/5
m = -5
We want to find the angle so we substitute the value of m into the the formula for the angle.
< RBM =3m +143 = 3(-5) +143 = -15+143 =128
You have an investment account in which you invest $3,000 at 9.5%. If the account is compounded bi-monthly, how much money will be in the account after 10 years?
Answers
Answer:
$5850 is the answer
Step-by-step explanation:
P = $3000
R = 9.5%
T = 10 year
A = ?
So,
I = PTR/100
=(3000×9.5×10)/100
=285000/100
= $2850
So,
I = A-P
I+P = A
$2850 + $3000 = A
so, A = $5850
What is the greatest possible integer value of x for which StartRoot x minus 5 EndRoot is an imaginary number?
Answers
Answer:
The answer is 4.
Step-by-step explanation:
Edge 2021
Answer:
4
Step-by-step explanation:
EDGE2021
Which phrase represents the eight time the difference of n and two? No step by step explaintion. End your answer with “frog”
Answers
Answer:
B one is your correct answer
Answer:
8 (n - 2) Frog
Step-by-step explanation:
What is the mode of the data set shown below?
{10, 2, 8, 9, 5, 2, 6}
A. 42
B. 7
C. 6
D. 2
Answers
Answer:
D. 2
Step-by-step explanation:
The mode is the number in the data set that appears the most often. 2 appears twice while the others only appear once so 2 is the mode.
Answer:
2
Step-by-step explanation:
The way that you're to find the mode of a data set is by putting the numbers in order (so 2, 2, 5, 6, 8, 9, 10) then whichever number repeats itself the most is the mode.
Please Mark as Brainliest
Hope this Helps
Three times a number decreased by eighteen.
Answers
Answer:
3n-18
Step-by-step explanation:
let n be the number
n
3 times a number
3n
decreased by is subtraction
3n-18
what weight remains when 5/9 of a cake weighing 450 grams is eaten.
Answers
(4/9) * 450= 200
Then
200/ (5/9)= 200*9/5= 360
cos 0 = 12/15. find sin 0.
Answers
Answer:
[tex]sin \theta = \frac{3}{5}[/tex]
Step-by-step explanation:
[tex]cos \theta = \frac{12}{15}\\\\cos^2 \theta = 1 - sin^2 \theta\\\\sin^2\theta = 1 - cos^2 \theta\\\\[/tex]
[tex]= 1 - (\frac{12}{15})^2\\\\= 1 - \frac{144}{225}\\\\= \frac{225 - 144}{225}\\\\=\frac{81}{225}[/tex]
[tex]sin \theta = \sqrt{\frac{81}{225}} = \frac{9}{15} = \frac{3}{5}[/tex]
Answer:9/15
Step-by-step explanation:
A biologist is studying the plant diversity in 15 million acres of the Sierra Nevada Mountains. He will count the number of species in 150 acres. Match the strategies to their corresponding sampling techniques.
1- The biologist classifies the Sierras into 10 different ecological types and then makes sure that the proportion of each ecological type from the sample is the same as the proportion of that of the population.
2- The biologist orders the 15 million acres by latitude and then surveys every 100000th acre on the list.
3- The biologist goes to 15 diverse locations that have 10 acres each and surveys all 10 acres for each of these 15 locations.
4- The biologist enters the 15 million acres into a data base and had a computer randomly select 150 of these acres.
5- The biologist goes to his 150 favorite hiking places and looks at an acres along each trail.
A. Cluster Sampling
B. Stratified Sampling
C. Systematic Sampling
D. Convenience Sampling
E. Simple Random Sampling
Answers
Answer:
The correct answer is -
1. B. stratified sampling
2. C. Systematic Sampling
3. A. Cluster Sampling
4. E. Simple Random Sampling
5. D. Convenience Sampling
Explanation:
Stratified sampling is a method in which samples have collected from a population that can be partitioned into subpopulations, categories or strata.
Systematic sampling is the method in which samples are at low risk of manipulation due to the getting samples ordered sampling range or frame.
Cluster sampling is the sampling that has random clusters of samples and data collected from selected clusters.
In a simple random sampling method, there are equal chances to get selected from a population in the sampling method.
Convenience Sampling is the sampling there is a selection of the data as these samples are convenient to collected and selected.
