an airplane heads west at 400 miles per hour in a 50-mile-per-hour northwest wind. find a vector that models the resulting direction and speed of the airplane. find the groundspeed and bearing of the airplane in the wind.
Answers
the resulting groundspeed of the airplane in the wind is approximately 410.8 mph, and the bearing (direction relative to north) is approximately 126.4 degrees.
To model the resulting direction and speed of the airplane, we can consider the airplane's velocity vector and the wind's velocity vector separately, and then add them together to find the resultant vector.
Let's break down the velocities:
1. Airplane's velocity vector: The airplane is heading west at 400 miles per hour. Since there is no wind, the airplane's velocity vector is solely in the west direction, given by (-400, 0) mph.
2. Wind's velocity vector: The wind is blowing from the northwest at 50 miles per hour. We can decompose this vector into its horizontal (west) and vertical (north) components. The northwest direction can be represented as a vector with equal magnitudes in the west and north directions. Therefore, the wind's velocity vector can be represented as (-50√2, 50√2) mph.
To find the resultant vector, we add the airplane's velocity vector and the wind's velocity vector:
Resultant vector = Airplane's velocity vector + Wind's velocity vector
Resultant vector = (-400, 0) + (-50√2, 50√2)
Resultant vector = (-400 - 50√2, 50√2)
The resulting vector represents the direction and speed of the airplane in the wind.
To find the groundspeed (speed relative to the ground) and the bearing (direction relative to north) of the airplane, we can calculate the magnitude and angle of the resultant vector.
Magnitude of the resultant vector (groundspeed) = √((-400 - 50√2)^2 + (50√2)^2)
Angle of the resultant vector (bearing) = arctan((50√2) / (-400 - 50√2))
Calculating these values, we find:
Groundspeed ≈ 410.8 mph
Bearing ≈ 126.4 degrees
Therefore, the resulting groundspeed of the airplane in the wind is approximately 410.8 mph, and the bearing (direction relative to north) is approximately 126.4 degrees.
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Related Questions
Help me with these problems please. Worth 50 points
Answers
1. The parentheses used here to make the statements true is multiplication.
2. 35/12
3. 1541/40 m² and 437/10 ft²
4. 73/10 and 61/12
5. -4, -3 and -2 are the first 3 integer solutions.
Define mensuration?In the field of mathematics known as measurement, length, volume, shape, surface area, and other properties are measured for 2D and 3D objects.
In other terms, it is the method of measuring based on mathematical formulas and algebraic equations.
9 - 3 × 7 + 21 ÷ 3 = 49
5 - 3 × 3² + 2 = 20.
Now,
7/8 ÷ 3/10
= 7/8 × 10/3
= 70/24
= 35/12
Area of triangle = 1/2 × b × h
= 1/2 × 23/2 × 67/10
= 1541/40 m²
Now area of parallelogram = b × h
= 19/4 × 46/5
= 437/10 ft²
Next we have,
1/2 + 34/5 = 73/10
47/6 - 11/4 = 61/12
The first 3 integer solutions are: -4, -3 and -2.
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769 ÷ 30 in standard algorithm
plz i need asap
Answers
Answer:
it equal 25 and the remainder is 19. :)
Answer:
Step-by-step explanation:
exact form
769/30
decimal form
25.63
mixed number formed
25 19/30
studies have shown that bats can consume an average of 10 mosquitoes per minute. what is the probability that a bat does not consume any mosquitoes in a 30-second interval?
Answers
The probability that a bat does not consume any mosquitoes in a 30-second interval is 0.0067379 or 0.67%.
In this case, the average rate of mosquitoes consumed by a bat is 10 per minute.
To find the rate for a 30-second interval, calculate the rate for 1 minute and then adjust it for the 30-second interval:
Average rate for 1 minute = 10 mosquitoes
Rate for 30 seconds = \(\dfrac{10 \,mosquitoes}{1 \,minute} \times \dfrac{1}{2}\)
= 5 mosquitoes
The Poisson distribution probability mass function is given by:
\(\[ P(X = k) = \dfrac{e^{-\lambda} \cdot \lambda^k}{k!} \]\)
Where:
\(\(\lambda\)\) is the average rate of events.
In this case, to find the probability that k = 0.
So, let's plug in the values:
\(\(\lambda = 5\)\)
\(\(k = 0\)\), back to the formula as
\(\[ P(X = 0) = \dfrac{e^{-5} \cdot 5^0}{0!} \]\)
Calculating the probability as
\(\[ P(X = 0) = e^{-5}\)
\(= 0.0067379\)
Therefore, the probability is 0.0067379 or 0.67%.
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I need help with this
Answers
Using a trigonometric relation we will see that:
1) DE = 33.86
2) R = 20.6°.
How to work with right triangles?1) We want to get DE which is the adjacent cathetus to the given angle.
Then we can use the trigonometric relation:
tan(a) = (opposite cathetus)/(adjacent cathetus).
Here we have:
a = 21°
opposite cathetus = 13
adjacent cathetus = DE.
Replacing that we get:
DE = 13/tan(21°) = 33.86
2) Now we want to get an angle.
This time we have:
Adjacent cathetus = 24opposite cathetus = 9Using the same trigonometric relation we get:
tan(R) = 9/24
Using the inverse tangent function:
R = Atan(9/24) = 20.6°.
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please help me solve this and ad how you did it as well thank you
Answers
Answer:14.42
How to get it:Use Pythagorean Theorem to solve this problem. Since a squared plus b squared =c squared and we have an and c we can work backwards. Start by squaring 17 (17x17) which would be 289. Then do 9 squared (9x9) to get 81. Subtract 289-81 to get 208, square root this for your answer 14.4222 round to 14.42. You can check this by doing 14.4222 squared plus 9 squared then square root it and you should get approximately, but not exactly 17.
The staff of Mr. Wayne Wertz, VP of Operations at Portland Peoples Bank, prepared a frequency histogram of waiting time for walk-in customers. Approximately how many walk-in customers waited at least 6 minutes? (Note the position of the labels on the x-axis — the first column is the number of customers who waited 1 minute and the last column is the number of customers who waited 10 minutes)
Answers
The number of people who waited at least 6 minutes is given as follows:
50 people.
What is shown by the histogram?The height of each bin of the histogram represents the number of observations of the data-set in the desired interval.
The desired outcomes for this problem are given as follows:
Between 6 and 7 minutes: 20 people.Between 7 and 8 minutes: 15 people.Between 8 and 9 minutes: 10 people.Between 9 and 10 minutes: 5 people.Hence the number of people who waited at least 6 minutes is given as follows:
20 + 15 + 10 + 5 = 50 people.
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Evaluate: -2[-4+3(2-32+4⋅2-3)-3]
Answers
Answer:
68
Step-by-step explanation:
-2[-4+ 3(2 - 32 + 4 · 2 -3) - 3] Start in the center and work your way out.
-2[-4 + 3(2 - 32 + 8 -3) - 3]
-2[-4 + 3(-30 + 8 - 3) -3]
-2[-4 + 3(-22 -3) -3]
-2[-4 + 3(-25)-3]
-2[-4 -27 -3}
-2[-31 - 3]
-2(-34)
68
HELP ASAP.!!!!!!! Jahlil is saving money at a constant rate to buy a new TV. After saving for $3$ months, Jahlil has $\$330$ . After saving for $5$ months, Jahlil has $\$510$ . Construct a function that models the relationship between the amount of money Jahlil has saved and the number of months he has saved for. Show or explain how you constructed the function. Respond in the space provided.
Answers
Answer:
y=90x+60
Step-by-step explanation:
x=months
y=dollars
Find dollars/month by finding the slope.
(3, 330), (5, 510)
-> (510-330)/(5-3) -> 90
Since its a constant rate, the function will be in the form, y=mx+b, and since we found the slope we can plug m=90.
y=90x+b
To find be, we simply substitute one of the points.
330=90(3)+b
b=60
Thus, plugging it in,
y=90x+60
another sequence is defined by a term to term sequence where k and r are constants
SEE IMAGE BELOW
Answers
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
\(U(n + 1) = kU(n) + r\)
_________________________________
\(n = 1\)
\(U(1 + 1) = kU(1) + r\)
\(U(2) = k \times U(1) + r\)
\(188 = k \times (37) + r\)
\(37k + r = 188 \: \: \: (( \alpha ))\)_________________________________
\(n = 2\)
\(U(2 + 1) = kU(2) + r\)
\(U(3) = k \times U(2) + r\)
\(943 = k \times (188) + r\)
\(188k + r = 943 \: \: \: (( \beta ))\)
_________________________________
\(188k + r = 943 \: \: \: (( \beta ))\)
\(37k + r = 188 \: \: \: \: \: (( \alpha ))\)
\((( \beta )) - (( \alpha )) = \)
\(188k - 37k + r - r = 943 - 188 \\ \)
\(151k = 755\)
Divide sides by 151
\( \frac{151k}{151} = \frac{755}{151} \\ \)
\(k = 5\)
Put the value of k in one of the equations to find the r :
\(37k + r = 188\)
\(37 \times (5) + r = 188\)
\(185 + r = 188\)
\(r + 185 = 188\)
Subtract sides 185
\(r + 185 - 185 = 188 - 185\)
\(r = 3\)
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How do you find the slope of a perpendicular line with an equation and point?
Answers
First, by solving for y, convert the equation of the given line into slope-intercept form y=mx+c .You obtain the slope of the equation as m. Since the slopes of perpendicular lines are negative reciprocal, the slope of the line we're looking is the negative reciprocal of the perpendicular equation.
By entering the supplied point into the formula y = mx + b and solving for b, we arrive at the value of b. Consequently, the line's equation is formed.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
A line's slope often indicates the steepness and direction of the line.
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m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
How to slove 5.4 ÷ 6 using modules to divide
Answers
Answer:
0.9
Step-by-step explanation:
5.4 divided by 6 = 0.9
Calculate 70/cos 20° round to 1 decimal place.
Answers
The answer of this 70/cos 20° round to 1 decimal place is 74.5
To solve the equation 70/cos 20° , firstly we need to find out the value of the cos 20°.
From the simple calculator we can find the value of cos 20° which is 0.9397.
Now we use this value to solve the above equation.
70/cos 20°;
70/0.9397;
74.491.
written that we have to round of the value to first decimal place, so the answer will become 74.5
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Nicole babysits on the weekends. She charges a flat fee of $10 and then $5 per hour. If she made $40 on Friday night, how many hours did she babysit?
Choose the equation to represent this situation.
Group of answer choices
Answers
pls help im failing i need help ASAP
Answers
The answer is choice 1 because when you divide 2 numbers with the same base and different exponents you subtract the second exponent from the first.
p^-m / p^-n = p^(-m - (-n))
CHOICE 1
Hope this helps
Given points A(-1,4) and B(x,7), determine the value(s) of x if AB=5cm
Answers
The value of x is either 3 or -5 based on the distance formula.
What is a co-ordinate system?
In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.
Main body:
according to question
Given points A(-1,4) and B(x,7)
Also AB = 5 cm
Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)
here by using points ,
5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)
taking square on both side ,'
25 = \((x+1)^{2} +3^{2}\)
25-9 = (x+1)²
16 = (x+1)²
taking square root on both sides,
x+1= ±4
x = 4-1 = 3 or x = -4-1 = -5
Hence value of x is either 3 or -5.
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please someone help me with this its due in 2 hours
Answers
Answer:
Step-by-step explanation:
I don't know what you want to find but
CB ^2 = AC^2 + AB^2 -2AC.AB.Cos(BAC) Cosine Rule
CB^2 = 9 +64 - 2.3.8.Cos(40)
CB ~ 6
Write True or False.
b. The graphical technique used to describe the relationship between two interval (i.e. quantitative) variables is the scatter diagram.
c. When possible, the best way to establish that an observed association is the result of a cause- and-effect relation is by means of the correlation coefficient.
d. Using the regression equation to make predictions for values of the predictor variable outside the range of the observed values of the predictor variable is called extrapolation.
e. All normal distributions are defined by the mean and standard deviation.
f. The length, X, of a fish from a particular mountain lake in Idaho is normally distributed with μ = 8.7 inches and σ = 1.2 inches. X is a discrete variable.
g. Two t-curves have degrees of freedom 10 and 22 respectively. The one with 10 degrees of freedom more closesly resembles the standard normal curve.
h. The correlation between the daily sales of air conditioners and the daily sales of electric fans in July found to be 0.92. A least squares regression line that predicts daily sales of air conditioners (y) from daily sales of electric fans (x) is fitted to the data. An increase in the daily sales of electric fans causes an increase in the daily sales of air conditioners in July
Answers
the answer is probably g
Here is a triangle ABC.
A
30°
Work out the value of sin ABC
Give your answer in the form
6.5 cm
n
C
10.7 cm
m where m and n are integers.
B
/+21.
Answers
Triangle ABC, we are given the measure of angle A as 30 degrees, the length of side AC as 10.7 cm, and the length of side BC as 6.5 cm.
To work out the value of sin(ABC), we can use the trigonometric ratio of the sine function.
The sine function relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle.
In the given information, we don't have a right triangle or the length of the side opposite angle ABC.
Without this information, it is not possible to calculate the value of sin(ABC) accurately.
If you have any other information regarding the triangle, such as the length of side AB or the measure of angle B or C, please provide it so that I can assist you further in calculating sin(ABC).
We may utilise the sine function's trigonometric ratio to get the value of sin(ABC).
The sine function connects the ratio of the hypotenuse length of a right triangle to the length of the side opposite an angle.
A right triangle or the length of the side opposite angle ABC are absent from the provided information.
The value of sin(ABC) cannot be reliably calculated without these information.
Please share any more information you may have about the triangle, such as the length of side AB or the size of angles B or C, so I can help you with the calculation of sin(ABC).
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If 24 muffins cost 46$ how much does 1 muffin cost
Answers
Answer:
1,916666666666667$Step-by-step explanation:
If 24 muffins cost 46$ how much does 1 muffin cost?
46 : 24 =
1,916666666666667$
(the total cost is 46$ or 48? are you sure?)
Hey there!
It costs about $46 for 24 muffins, so in order to find out the total cost for 1 muffin you have to DIVIDE 46 from 24 or 24 from 46.
So, lets first divide 46 from 24
46 / 24
= 46 ÷ 24
= 46 ÷ 2 / 24 ÷ 2
= 23 / 12
= 1.916667
≈ 1.92
Therefore, your answer is: $1.92
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
derive the decision boundaries in the above case. • derive the conditional mle estimator of θ.
Answers
The form of the likelihood function to proceed with deriving the conditional MLE estimator of θ.
what is decision boundaries.?
Decision boundaries refer to the dividing lines or regions that separate different classes or categories in a classification problem. They are determined based on the features or attributes of the data and the classification algorithm being used. The decision boundary serves as a threshold or criterion for assigning new or unseen data points to specific classes based on their feature values.
To derive the decision boundaries in the given case, more specific information or context is needed. Decision boundaries are determined based on the specific classification or grouping criteria and the underlying data distribution. Please provide additional details or specifications regarding the problem or classification task.
Regarding the conditional maximum likelihood estimator (MLE) of θ, more information is required to proceed with the derivation. The MLE involves finding the parameter value that maximizes the likelihood function based on the observed data and any relevant assumptions or models. Please provide the specific context, assumptions, and the form of the likelihood function to proceed with deriving the conditional MLE estimator of θ.
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A. Is there a GCF?
B. Is the polynomial a special case? If so, name the special polynomial.
2y^2 − 128x^2
Answers
The given polynomial is a special case of the difference of two squares.
A. For the given polynomial, there is a GCF (Greatest Common Factor).
128x2 + 2y2 can be translated into:
\(2(y^2 - 64x^2)\)
GCF in this case is 2.
B. The polynomial in question is a particular instance of the difference between two squares.
128x2 + 2y2 can be translated into:
\(2(y^2 - (8x)^2)\)
which is the squares' difference:
(√y²)² - (√(8x)²)²
Since the difference of two squares is a specific case of the given polynomial, it follows.
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Pls help I’ll mark you brainlist!
Answers
Answer:
2
Step-by-step explanation:
1<2
2<13
:D
Answer:
its just "B"
Step-by-step explanation:
uhhhhh yea :)))
Help please and thank you.
Answers
Answer:
b
Step-by-step explanation:
pls answer this ( both parts)
Answers
Answer:
Yes, It is
Step-by-step explanation:
0.005
Divide the numerator by the denominator, to find the answer
but I don’t know if you’re looking for a bigger decimal
Find the required annual interest rate, to the nearest tenth of a percent, for $955 to grow to $1514 if interest is compounded monthly for 3 years.
A. 30.9%
B. 10.3%
C. 1.3%
D. 15.5%
Answers
Answer:
D
Step-by-step explanation:
\(A=P(1+\dfrac{r}{n})^{nt}\)
where A is the final amount of money, P is the initial amount of money input, r is the interest rate, n is the amount of times compounded per year, and t is the time in years.
\(1514=955(1+\dfrac{r}{12})^{(12)(3)}\)
\(1.585=(1+\dfrac{r}{12})^{36}\)
\(1.0128762=1+\dfrac{r}{12} \\\\\\0.0128762=\dfrac{r}{12} \\\\\\r\approx 0.155=15.5\%\)
Hope this helps!
Help please with graphing and the solution !
Answers
The weight of gift is 5 pound extra with medium size of box.
What is the weight of items?In science and engineering, the weight of an object is the force acting on the object due to gravity.
Let the weight is W
The first company charged “$15 to ship a medium box, plus an additional $1 per pound”.
So, that the amount of certain weight is F = $15 + $1*W
The second company charged “$10 to ship a medium box, plus an additional $2per pound”.
So, that the amount of certain weight is S = $10 + $2*W
The two shipping methods will cost the same amount
so that, F = S
$15 + $1*W = $10 + $2*W
$5 = $1*W
W = 5 pound.
So that the weight of gift is 5 pound extra with medium size of box.
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what is the probability that when a pair of dice are rolled, either (at least) one dice shows a 5, or that the dice sum to 8?
Answers
Observing the cases provided with the formula of probability and implementing it with OR rule , The answer is 0.22.
What do you mean by probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
What is sample space?All potential results make up the sample space of a random experiment. A subset of the sample space is an event connected to a random experiment. Any outcome's probability is a value between 0 and 1. The sum of all the outcomes' probabilities is one.
Probability that dice rolled shows a 5 once = 1/36
Probability that dice rolled shows a 5 twice = 2/36
Probability that the sum is 8 = 5/36
Total probability = 1/36 + 2/36 + 5/36 = 0.22
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A rectangular prism has a volume of 360 in3. If the height measures 6in. which base measurements could the prism have?
Answers
Answer:
Both sides that are parallel ( 6 inches I believe ) would be 12 in total for both sides. Then the top and bottom would be 3 inches ( I believe ) which would be 6. I think you need to do 6 times 12 until you get 360 and then see how many times you multiplied it and that is your answer. But I am not FULLY sure. Hope this helps somehow!
Step-by-step explanation:
You pick a card at random. 4 5 6 7 What is P(not odd)? Write your answer as a percentage.
Answers
Answer:
50%
Step-by-step explanation:
There are 4 cards. 4 and 6 are not odd, which is 2 cards.
P(not odd) = number of cards that are not odd/ total number of cards
= 2/4 = 1/2 = .5 = 50%
(1 point) the shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 8 years and a standard deviation of 0.3 years. what value of shelf life do 16% of the battery shelf lives fall below? round your answer to one decimal place.
Answers
8.27 is the normally distributed value of the shelf life which falls under 16% of the battery shelf life.
Because the shelf life of a battery manufactured by one big business is known to be regularly distributed, we would use the normal distribution formula, which is stated as
z = (x - µ) ÷ σ
Where
x = shelf life of a battery in years.
µ = mean shell life
σ = standard deviation
Based on the facts provided,
µ = 8 years
σ = 0.3 years
The z score corresponds to a p-value of 16% in the normal distribution table,
(16 ÷ 100 = 0.16) is - 0.9.
Therefore,
- 0.9 = (x - 9) ÷ 0.3
0.3 × (- 0.9) = x - 8
0.27 = x - 8
x = 0.27 + 8
x = 8.27
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