The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.
A plane that travels a distance [tex]r[/tex], in kilometers, with a bearing of [tex]\theta[/tex] sexagesimal degrees can be represented in standard position by means of the following expression:
[tex]\vec r = r\cdot (\sin\theta, \cos \theta)[/tex] (1)
We can obtain the resulting vector ([tex]\vec R[/tex]) by the principle of superposition:
[tex]\vec R = \Sigma_{i=1}^{n} [r_{i}\cdot (\sin \theta_{i}, \cos \theta_{i})][/tex] (2)
If we know that [tex]r_{1} = 5\,km[/tex], [tex]\theta_{1} = 0^{\circ}[/tex], [tex]r_{2} = 6\,km[/tex], [tex]\theta_{2} = 60^{\circ}[/tex], [tex]r_{3} = 4\,km[/tex] and [tex]\theta_{3} = 120^{\circ}[/tex], then the resulting vector is:
[tex]\vec R = 5\cdot (\sin 0^{\circ}, \cos 0^{\circ}) + 6\cdot (\sin 60^{\circ}, \cos 60^{\circ}) + 4\cdot (\sin 120^{\circ}, \cos 120^{\circ})[/tex]
[tex]\vec R = (5\sqrt{3}, 6) \,[km][/tex]
The magnitude of the resultant is found by Pythagorean theorem:
[tex]\|\vec R\| = \sqrt{R_{x}^{2}+R_{y}^{2}}[/tex]
And the bearing is determined by the following inverse trigonometric relationship:
[tex]\theta_{R} = \tan^{-1} \left(\frac{R_{y}}{R_{x}}\right)[/tex] (3)
If we know that [tex]R_{x} = 5\sqrt{3}\,km[/tex] and [tex]R_{y} = 6\,km[/tex], then the magnitude and the bearing of the resultant is:
[tex]\|\vec R\| = \sqrt{(5\sqrt{3})^{2}+6^{2}}[/tex]
[tex]\|\vec R\| \approx 10.536\,km[/tex]
[tex]\theta_{R} = \tan^{-1} \left(\frac{6}{5\sqrt{3}} \right)[/tex]
[tex]\theta_{R} \approx 34.715^{\circ}[/tex]
The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.
To learn more on vectors, we kindly invite to check this verified question: https://brainly.com/question/21925479
What is the 7th term in the sequence below?
-19, -7, 5, 17, .....
Select one:
a.65
b.29
c.101
d.53
Answer:
53
Step-by-step explanation:
—19 + 12 = —7
—7 + 12 = 5
5 + 12 = 17
.
.
.
so the n term of the sequence will be: 12n — 31
so 7th term will be: 12 × 7 — 31 = 53
Answer:
d. 53
Step-by-step explanation:
increases 12 units at each step:
17 + 12 = 29
29 +12 = 41
41 + 12 = 53 (7th term)
Hope this helps
Can anyone help! me 30 points
Answer:
the first one and the last one
Step-by-step explanation:
Hope it will helps you ❤️❤️❤️
Please mark me as a brainliest
ALGEBRA Ben Shield's credit card uses the unpaid-balance method to compute the finance charge at a monthly periodic rate of 1.875%. During the monthly billing cycle, Ben charged $238.75, made a payment of $300.00, and had a finance charge of $7.99. Find his unpaid balance, previous balance, and new balance.
The new balance is a credit of $ 48.78.
Since Ben Shield's credit card uses the unpaid-balance method to compute the finance charge at a monthly periodic rate of 1.875%, and during the monthly billing cycle, Ben charged $ 238.75, made a payment of $ 300.00, and had a finance charge of $ 7.99, to find his new balance, the following calculations must be performed:
Finance charge + new purchases + previous balance - payments = X 238.75 x 1.01875 + 7.99 - 300 = X 243.22 + 7.99 - 300 = X 251.21 - 300 = X -48.78 = X
Therefore, the new balance is a credit of $ 48.78.
Learn more about maths in https://brainly.com/question/3554632
3 + 6 x (5 + 4) ÷ 3 -7?
Answer:
Answer: 14
Step-by-step explanation:
[tex]{ \rm{3 + 6 \times (5 + 4) \div 3 - 7}} \\ \\ = { \rm{3 + (6 \times 9) \div 3 - 7}} \\ \\ = { \rm{3 + (54 \div 3) - 7}} \\ \\ = { \rm{14 }}[/tex]
If x is increasing at a
rate of 2 units per second,
find the rate of change of theta
at the instant when x= 12 units.
Answer:
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex] at [tex]x=12[/tex]
Step-by-step explanation:
[tex]\frac{dx}{dt}=2[/tex]
[tex]\frac{d\theta}{dt}=?[/tex]
[tex]x=12[/tex]
[tex]cos(\theta)=\frac{adjacent}{hypotenuse}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]\frac{d}{dt}cos(\theta)=\frac{d}{dt}\frac{x}{13}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}\frac{dx}{dt}[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{1}{13}(2)[/tex]
[tex]-sin(\theta)\frac{d\theta}{dt}=\frac{2}{13}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]cos(\theta)=\frac{x}{13}[/tex]
[tex]cos(\theta)=\frac{12}{13}[/tex]
[tex]\theta=cos^{-1}(\frac{12}{13})[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(\theta)}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13sin(cos^{-1}(\frac{12}{13}))}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-13(\frac{5}{13})}[/tex]
[tex]\frac{d\theta}{dt}=\frac{2}{-5}[/tex]
[tex]\frac{d\theta}{dt}=-\frac{2}{5}[/tex]
The value of θ is given by the inverse sine function, from which the rate of
change of θ with respect to x can be derived.
The rate of change of θ at the instant when x = 12 units is -0.4 rad/sReasons:
[tex]\displaystyle \frac{dx}{dt} = \mathbf{2 \ units \ per \ second}[/tex]
[tex]\displaystyle cos(\theta) = \frac{x}{13}[/tex]
[tex]\displaystyle \theta = arccos \left(\frac{x}{13}\right)[/tex]
[tex]\displaystyle \frac{d}{dx} \theta = \frac{d\left(arccos \left(\frac{x}{13}\right)\right)}{dx} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}}[/tex]
Using chain rule of differentiation, we have;
[tex]\displaystyle \frac{d\theta}{dt} = \mathbf{ \frac{d\theta}{dx} \times \frac{dx}{dt}}[/tex]
Therefore;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-x^2} }{x^2-169}\times \frac{dx}{dt} = \mathbf{\frac{\sqrt{169-x^2} }{x^2-169}\times 2}[/tex]
When x = 12, we get;
[tex]\displaystyle \frac{d\theta}{dt} =\frac{\sqrt{169-12^2} }{12^2-169}\times 2 = -\frac{2}{5} = -0.4[/tex]
The rate of change of the angle, θ, with time at the instant when x = 12 is -0.4 rad/s
Learn more about rate of change here:
https://brainly.com/question/24686935
Identify an equation in point-slope form for the line parallel to y = -
2/3x+8 that passes through (4, -5).
A. y-4=(x+5)
B. y+5=2/3 (x-4)
C. y+5 = 3/2(x-4)
D. y-5=-2/3(x + 4)
f(x) = x2. What is g(x)?
Answer:
the answer is A. g(x) = -x^2 - 4
Step-by-step explanation:
hope this helps! :)
In an economics class, 4 students earned an A, 6 earned a B, 5 earned a C, 5 earned a D, and 3 earned an F. If a single student is picked at random, what is the probability that they earned an B or C?
Provide your answer as a simplified fraction.
Answer:
11/23
Step-by-step explanation:
B = 6
C = 5
6+5=11
11/23
Please help me! Im a little bit stumped!
Answer:
2x+34=4x+20
14=2x
x=7
Step-by-step explanation:
So the answer is 7
Answer:
some bedmas laws you have to use
first do the 4(x+5) since its distubutive
you get 2x + 34 = 4x + 20 normally i like to keep x positive so i dont have to divide by -1 at the end so subtract 5 to the other side qnd subtract 2x to the other side and you get
2x= 14
x = 7 is the answer
What is the distribution property and combining like terms for -8(b+3)
Answer:
-8b-24
Step-by-step explanation:
Just ask.
Hope this helps! :)
Answer:
-8b-24
Step-by-step explanation:
you would just distribute that -8 to what's inside the ( ).
Ryan works at the donut shop where he makes $10.25 per hour He also works part time at the school bookstore where he makes $8.75 an hour if he worked 20 total hours last week and made $196 how many hours he did work at the bookstore?
Answer:
aprometly 19 I think
Step-by-step explanation:
cause don't you have yo divide 196 ÷ 10.25
arithmetic sequence, help with #18 plz
Answer:
15th term is 29/4
Use Arithmetic equation
a1 = 1/4
d= common difference = 2/4
a15 = a1 + (n-1) d
a15 = 1/4 + (15 - 1) 2/4
a15 = 1/4 + 14 (2/4)
a15 = 1/4 + 7
a15 = 29/4 or 7 1/4
What will be the average of the first five
consecutive numbers starting from 11
Answer:
13
Step-by-step explanation:
The average of any 5 consecutive numbers is the 3rd one (the middle one of the group). The third consecutive number starting from 11 is 13.
The average of {11, 12, 13, 14, 15} is 13.
A nature preserve worker calculates there are 6,000 deer in Sharon Woods Park. She also estimates that 75 more deer die than are born each year.
a. Write a linear function to estimate how many deer will be in the park in x years.
b. Use the linear function to predict how many deer will be in the park in 3 years.
c. In how many years will there be 5,325 deer left in Sharon Woods Park?
The linear equation used to represent this situation is y = -75x + 6000
A linear equation is in the form:
y = mx + b;
where y, x are variable, m is the slope of the line and b is the y intercept.
Let y represent the amount of deer present in x years. There are 6000 deer presently, hence a = 6000. Also 75 more deer die than are born each year. Hence m = -75.
The linear equation is given by:
y = -75x + 6000
In 3 years:
y = -75(3) + 6000
y = 5775
For there to be 5325 deer:
5325 = -75x + 6000
x = 9 years
Find out more at: https://brainly.com/question/21105092
Does (–1, 2) make the equation y = x + 9 true?
Answer:
(-1, 2) does not make the equation y=x+9 true.
Step-by-step explanation:
y=x+9
(-1, 2)=(x, y)
2=(-1)+9,
-1+9=8,
2 does not equal to 8.
Answer: No.
13. This shows a part of a multiplication table. Find the missing numbers. Explain how you found the numbers.
35 40
42 ?
? ?
The missing numbers in the multiplication table are 49, 48 and 56 respectively
Given:
35
42
?
35 = 7 × 5
42 = 7 × 6
? = 7 × 7 = 49
40
?
?
40 = 8 × 5
? = 8 × 6 = 48
? = 8 × 7 = 56
Multiplication table is a mathematical table showing the products of each of integers such as 7 and 5, 1 and 10, 13 and 12 etcTherefore, the missing numbers in the multiplication table are 49, 48 and 56 respectively
Learn more about multiplication:
https://brainly.com/question/10873737
4) Change the recurring decimal 0.18 to a fraction. (2marks)
You must show all your working.
Answer:
18/100 or 9/50
Step-by-step explanation:
First, put 0.18 over 100 because there are 2 digits in the decimal, so you convert it to 18/100. Then, simplify it, and because the GCF is 2, divide the numerator and denominator. The final fraction ins 9/50.
How do you solve this
Answer:
x > 3
Step-by-step explanation:
And then, I believe you just need to solve that answer. But I'm not sure tho
In the typing World 120 words in 3 minutes is average how many words could they type in 2 hours
Answer:
7,200 words
Step-by-step explanation:
Answer: 4,800
I multiplied 120 by 20 because 60 divided by 3 is 20. Then I multiplied my answer by 2 because the question is asking how many words could they type in 2 hours
on what interval (s) are f(x) = x3 2x²+x+6 decreasing?
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
please help will brain list if correct no links please
Answer:
C
Step-by-step explanation:
the angle opposite of it is 30
discuss the criteria of a good test
At Pizza Pi, 68% of the pizzas made last week had extra cheese. If 17 pizzas had extra cheese, how many pizzas in all were made last week?
Answer: 50
Step-by-step explanation:
Answer:
50%
Step-by-step explanation:
what is the slope of -y=-x+6
Answer:
m = 1b = -6Step-by-step explanation:
We know that:
-y = -x + 6y = mx + bFirst, we need to change the 'y' sign.
=> -y = -x + 6=> y = x - 6Now, let's compare both of the equations to find slope.
=> (y = x - 6) = (y = mx + b)We can see that the slope is 1 and the y-intercept is -6.
Conclusion:
Therefore:
m = 1b = -6Hoped this helped.
What is nx25=5x60 and how did you get the answer?
Hey there!
n * 25 = 5 * 60
25n = 5 * 60
25n = 300
DIVIDE 25 to BOTH SIDES
25n/25 = 300/25
CANCEL out: 25/25 because it gives you 1
KEEP: 300/25 because it helps solve for the n-value
NEW EQUATION: n = 300/25
SIMPLIFY IT!
n = 12
Therefore, your answer is: n = 12
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
single simplified fraction
X/3+X/5
is it true that George Washington LOVED political parties?
Answer:
No, It's false.
Step-by-step explanation:
In the long history of the United States, only one president, George Washington, did not represent a political party.
due in 1 hour please help
Answer:
1 2 3 4 = 123.23
Step-by-step explanation:
Fid the value of the expression
Answer:
2
Step-by-step explanation:
The question askes what is k divided by m (k/m) when k is equal to 8 and m is equal to 4. So, plug the values into the original questions 8÷4. This means that the number 8 is being split into 4 groups. When 8 is divided into 4 groups each group is left with 2. Therefore, the answer is 2.
Another way to solve this is to make a fraction. 8÷4 is the same as 8/4. If you simplify that fraction you also get 2.
20.4 is what percent of 17?
Answer:
120%
20.4 is 120% of 17.
Step-by-step explanation:
20.4/17 = 1.2
1.2 x 100 = 120%
Hope this helped. Have a good one!