Answer:
Velocity of plane is 100 mi/hr along northeast direction
Step-by-step explanation:
From the question it is given that Initial velocity of plane is 150 mi/hr along east north direction and wind is blowing at 50 mi/hr along southwest direction
since the velocity of wind and plane is exactly opposite
⇒ relative velocity of plane with respect to wind is given by
[tex]v_r_e_l = v_p - v_w[/tex] where [tex]v_p[/tex] is the velocity of plane = 150mi/hr and [tex]v_w[/tex] = velocity of wind = 50 mi/hr
Therefore, [tex]v_r_e_l = v_p - v_w[/tex] = [tex]v_r_e_l = 150 - 50 = 100 mi/hr[/tex] alond northwest direction
Therefore, velocity of plane is 100 mi/hr along northeast direction
By working with the velocity vectors, we will find that the direction of motion of the plane is 28.7 south of east.
Working with the velocity vectors:
First, we need to define our coordinate axis, I will define the x-axis as the east and the y-axis as the north.
We know that the plane travels at 150 mi/hr at 100° east of north, notice that if we measure from the positive x-axis, this is equivalent to an angle of -10°.
Then the x-component of the velocity is: 150mi/hr*cos(-10°) = 147.7 mi/hrThe y-component of the velocity is: 150mi/hr*sin(-10°) = -26 mi/hr.
So the vector is:
V = < 147.7 mi/hr, -26 mi/hr >
Now we know that the wind blowing at 50mi/hr at southwest, exactly southwest would be at an angle of 225°, so the components of the vector are:
x-component: 50mi/hr*cos(225°) = -35.4 mi/hry-component: 50mi/hr*sin(225°) = -35.4 mi/hr.So the vector is:
W = < -35.4 mi/hr, -35.4 mi/hr>
The sum of the vectors gives the total velocity of the plane in the wind, we will get:
V + W = < 147.7 mi/hr -35.4 mi/hr , -26 mi/hr -35.4 mi/hr >
V + W = <112.3 mi/hr, -61.4 mi/hr>
The direction of a vector <x, y> is given by:
θ = Atan(y/x)
Then in this case the direction of the plane is:
θ = Atan(-61.4 mi/hr/112.3 mi/hr) = -28.7°
So the direction of the plane is 28.7° south of east.
If you want to learn more about vectors, you can read:
https://brainly.com/question/17108011
What is the value of x in the equation 5.5x = 17.6?
1. 3.2
2. 12.1
3. 23.1
4. 96.8
Answer:
3.2
Step-by-step explanation:
divide 5.5 from both sides
x = 17.6/5.5 = 3.2
B. Find the value of X. Show your work, I’m not sure how to do this
Answer:
63°
Step-by-step explanation:
The sum of all interior angles of a triangle = 180°
Therefore:
x + 96° + 21° = 180°
x + 117 = 180
Subtract 117 from each side
x = 180 - 117
x = 63°
Answer all 6 questions and the topic is about ordering decimals.
Answer:
0.9, 0.75, 0.66, 0.62, 0.59
0.92, 0.85, 0.49, 0.38, 0.23
0.08, 0.11, 0.46, 0.51, 0.72
0.02, 0.1, 0.15, 0.33, 0.88
0.96, 0.79, 0.67, 0.4, 0.24
0.09, 0.28, 0.37, 0.4, 0.55
Add. (4y – z) + (–3y – 2z)
–12y + 2z
y – 3z
–y – 3z
–y – z
Find the y-component of this
vector:
Answer:
The y-component of the vector is approximately -67.844 meters.
Step-by-step explanation:
A vector [tex]\vec v[/tex] in rectangular form are defined by the following form:
[tex]\vec v = (r\cdot \cos \theta, r\cdot \sin \theta)[/tex] (1)
Where:
[tex]r[/tex] - Magnitude, measured in meters.
[tex]\theta[/tex] - Direction with respect to +x semiaxis, measured in sexagesimal degrees.
Please notice that the y-component of the vector corresponds to the second component of the definition. If we know that [tex]r = 101\,m[/tex] and [tex]\theta = 222.2^{\circ}[/tex], then the y-component of the vector is:
[tex]y = r\cdot \sin \theta[/tex] (2)
[tex]y = (101\,m)\cdot \sin 222.2^{\circ}[/tex]
[tex]y \approx -67.844\,m[/tex]
The y-component of the vector is approximately -67.844 meters.
what is the equation for -5x+6y=12 y=5/6x+2
Step-by-step explanation:
-5x + 6y = 12
y = 5/6x + 2
_______________-5x + 6y = 12
-5x + 6(5/6x + 2) = 12
-5x + 5x + 12 = 12
x real numbers
(x, y) = (x, 2 + 5/6 x)
Rearrange
2(a + c) = 5(a - b)
to make c the subject.
2a +2c= 5a - 5b
collect light terms.
take 2a on the other side
2c = 5a -2a-5b
2c = 3a - 5b
divide 2c's 2 on both sides
and
c = (3a - 5b)/2
give a brainliest please. tnx have a nice day.
Lula babysits for the two Finch children every Friday night. Mr. Finch pays her $4.25 per hour per child. Choose the correct expression to show how much money Lula will earn each Friday night she babysits.
Answer:
Lula babysists for Finch's children=2 Finch pays =$4.25 per child
Lula earns= 2×$4.25
= $8.50
orX=Finch per child
X=4.25
Lula earn each Friday night=
2X=$4.25×2 =$8.25
Step-by-step explanation:
SHOW YOUR WORK
7 divided by 20.79
9 divided by 24.93
Answer: 7 divided by 20.79= 0.3367003367
9 divided by 24.93= 0.36101083032
Hope this helped!
Answer: So Im basicaly just replying to get points sorry
Look i sure someone will answer it soon good luck buddy I have faith in you
Step-by-step explanation:
Can someone help me?
Answer:
The graph cannot represent a proportional relationship
Step-by-step explanation:
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form. In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin (0,0) . That means, ----> The x-intercept and the y-intercept of the line must to be the origin (0,0).
If the given line passes through the point (0,5), then the line does not pass through the origin. Therefore, the graph cannot represent a proportional relationship
Which fraction is equivalent to the decimal 0.68 with line on top?ILL GIVE WHO EVER BRAINLIEST
A. 31/45
B. 682/999
C. 62/99
D. 2/3
B)682÷999×100=68.268 which is the closest of all of them
I WILL GIVE BRAINLIEST I NEED HELP ASAP PLEASE!!!!
Using the new scale and starting from the origin, where will point A be?
Answer:
(9, 27)
Step-by-step explanation:
You multiply the current point A by 3 because that is the change in the new scale.
Find x where 2/3 of x added to 9 gives 30
Question 1 of 10 What is the value of the fourth term in a geometric sequence for which ay = 15 and r= 1/3? Express your answer as a fraction. Answer here
Answer:
The fourth term of given geometric sequence is 5/9
Step-by-step explanation:
The general formula for geometric sequence is given by:
[tex]a_n = a_1.r^{(n-1)}[/tex]
Here a_n is the nth term,
a_1 is the first term
and r is the common ratio.
It is given in the question that
[tex]a_1 = 15\\r = \frac{1}{3}[/tex]
Putting these values
[tex]a_n = 15 . (\frac{1}{3})^{n-1}[/tex]
For 4th term, we will put n=4
So,
[tex]a_4 = 15 . (\frac{1}{3})^{4-1}\\a_4 = 15 . (\frac{1}{3})^3\\a_4 = 15 . \frac{1}{27}\\a_4 = \frac{15}{27}\\a_4 = \frac{5}{9}[/tex]
Hence,
The fourth term of given geometric sequence is 5/9
Which choices are solutions to the following equation? Check all that apply. X^2-10x-5=9
Simplify 2 + 17x – 5x + 9.
A. 19x + 4
B. 12x + 11
C. 22x + 11
D. 15x - 4
B
add all the like terms together
9+2=11
17x+-5x=12x
HELP PLEASEE ANYBODY
Answer:
you didn’t provide a question
Step-by-step explanation:
Help Please!!! I have too turn in my assignment right now!!!
Answer:
11/18
Step-by-step explanation:
What is the solution to the following system densations?
Answer:
D. (2, 1)
Step-by-step explanation:
Given:
y = 6x - 11
-2x - 3y = -7
Required:
Find the solution.
Solution:
y = 6x - 11 ---› eqn. 1
-2x - 3y = -7 ----› eqn 2
Substitute y = (6x - 11) into equation 2.
-2x - 3(6x - 11) = -7
-2x - 18x + 33 = -7
-20x + 33 = -7
Subtract 33 from each side
-20x = -7 - 33
-20x = -40
Divide both sides by -20
x = -40/-20
x = 2
Substitute x = 2 into equation 1.
y = 6x - 11 ---› eqn. 1
y = 6(2) - 11
y = 12 - 11
y = 1
The solution is very (2, 1)
Which statement about the point (2, 0) is true?
It is on the origin.
It is in Quadrant I.
It is on the x-axis.
It is on the y-axis.
Answer:
the true statement is that it's on the x-axis. you can tell because the point has a 0 for the y-value. meaning the point has to be sitting on the x-axis.
Step-by-step explanation:
Answer:
It is on the x-axis.
Step-by-step explanation:
whats 5/35 in simpplest form
Answer:
5/35 = 1/7
hope it helps you
Answer:
5/35 in the simplest form is 1/7
Step-by-step explanation:
Gerbils can develop gastrointestinal tract issues as they get older that may cause severe diarrhea and dehydration. A researcher wishes to conduct a study to find which of two antibiotics, Antibiotic A or Antibiotic B, is more effective in improving gastrointestinal tract health. A total of 300 Gerbils that are at least 1 years old will be randomly selected from zoos in the state of Florida. The researcher will get consent from all owners, treat the gerbils for ten months and evaluate changes in gastrointestinal health.
Part A: How would the study benefit from adding a control group?
Part B: What is the best way to randomly place the gerbils into the Antibiotic A, Antibiotic B, and control groups?
Part C: The researcher wants to use a blocking variable to place gerbils into groups instead of doing it randomly. He decides to block either by breed or zoo. Explain which would be the best blocking method.
Answer:
Answer is explained below.
Step-by-step explanation:
a)
Adding control group will definitely benefit the study, as it will behave as the reference, or a benchmark for comparison. In order to compare and study the effects of the treatment control group is the one to compare with. So, in this way study would benefit by adding the control group, as it will become easier to know how much effective is the treatment as compared to the control group.
b)
Now, we have to randomly place the gerbils into the 1. Antibiotic A 2. Antibiotic B, and 3. control Groups
So, we have 3 groups to place gerbils randomly.
Now, we have to find the no. of replicates needed for 3 groups and 300 Gerbils.
n = t x r
n = 300
t = 3
r = ?
r = n/t
r = 300/3
r = 100 replicates will be needed.
First of all, we need to find the total number of experimental plots = n = 300
Secondly, we need to give each experimental plot a plot number in consecutive manner for example: we have 300 experimental plots
We can give numbers as 1,2,3,4,5 ...... 300
Thirdly, we need to give treatments a experimental plot picked from the random number table. For that, 300 divided by 3 = 100 numbers are to be achieved and put them in ascending or descending order.
c)
The best blocking method would be the blocking by breed of Gerbils. As in zoo, we know that, gerbils can develop gastrointestinal tract issues as they get older that may cause severe diarrhea and dehydration. But on the contrary, it gets better when it get old in case of breed of gerbils. Hence, the best blocking method would be the blocking by breed of gerbils instead by zoo.
Please help on this math problem
Answer:
1680 in^3
Step-by-step explanation:
SO you got the triangle
24*10=240
240/2=120
now we just need to find the area
There is a formula but I think this is easier
So theres a rectangle with a length of 14
So if you think of the triangle as the base, you just need 14 triangles stacked up to make up the volume
So 120*14=1680
So the volume is 1680
PLEASE ANSWER if a ball falls off a cliff that is 30 meters tall and down to the bottom of a pond that is 15 meters deep, what is the total distance traveled by the ball?
Answer:
30
Step-by-step explanation:
Determine the range of the following graph:
Answer:
Range: [-9, -4]
General Formulas and Concepts:
Math
Number LineAlgebra I
Range is the set of y-values that are outputted by function f(x)Step-by-step explanation:
According to the graph, the line's y-values span from -9 to -4. Since both are closed dot, they are inclusive in the range:
[-9, -4] or -9 ≤ y ≤ -4
HELPP now plssss!!!!!
A group of people was randomly selected and asked how many hours per day each person spends shopping online. The results of the survey are displayed in the following histogram:
Histogram with frequency on y-axis and hours on x-axis with bars starting on x. Bar at 1 goes to 5. Bar at 2 goes to 8. Bar at 3 goes to 8. Bar at 4 goes to 6. Bar at 5 goes to 4. Bar at 6 goes to 2. Bar at 7 goes to 3. Bar at 8 goes to 1. Bar at 9 goes to 2. Bar at 10 goes to 0. Bar at 11 goes to 1.
What percentage of the people surveyed spend less than 2 hours per day shopping online? (4 points)
12.5%
20%
32.5%
52.5%
Answer:
12.5
Step-by-step explanation:
took this test
This equation shows how Rocky the puppy's weight varies with age.
p = 3a + 2
The variable a represents Rocky's age in months, and the variable p represents Rocky's
weight if pounds. At how many months did Rocky weigh 17 pounds?
O months
Submit
Answer:
Age of Rocky = 5 months
Step-by-step explanation:
Given that:
Equation for calculating puppy's weight
p = 3a + 2
Here,
p = weight of puppy
a = age in months
We have to find the age if the weight is 17 pounds
Putting p=17 in given equation
17 = 3a + 2
17 - 2 = 3a
3a = 15
Dividing both sides by 3
[tex]\frac{3a}{3}=\frac{15}{3}\\a=5[/tex]
Hence,
Age of Rocky = 5 months
MACY AND BRIANNA ATE DINNER ATA RESTAURANT. THEIR MEAL COST 19.50. THEY LEFT A 15% TIP. CALCULATE THE TIP AND TOTAL COST FOR THEIR MEAL.
Answer:
Tip = 2.925 or about 2.93
Meal = 19.50
Total amount paid = 22.425 or about 22.43
Step-by-step explanation:
15% of 19.50 = 2.925
The amount for the meal is already given which is $19.50
Ace
Answer:
46.69
Step-by-step explanation:
40.60 • 15%=6.09
6.09 • 40.69= 46.69
x is 6 less than thrice of y.
Answer:
x = 3y - 6
Hope it helped u,
pls mark as the brainliest
^v^
Answer:
x is 6 less than thrice of y.[tex] \huge \boxed{x = 3y - 6}[/tex]