Answers
Answers:
true speed = 26.935546 knotstrue bearing = 102.265139 degreesThe values are approximate. Round them however you need to.
====================================================
Explanation:
The diagram you have drawn is correct if you're only considering one current. Specifically current #1 which has the bearing of 290 degrees moving at 25 knots.
The red angle is 290 degrees. The remaining portion that is needed to get a full 360 degrees is 360-290 = 70. This adds to the blue portion in quadrant 1, which is 90, and we get 70+90 = 160. So the blue angle is 160 degrees.
The vector for current #1 is <25*cos(160), 25*sin(160)>
This approximates to <-23.4923155, 8.5505036>
All of this is for current #1.
------------
Vector #2 is much more simple in terms that there aren't messy decimal approximations here. The direction is due north, which means that the vector is pointing straight up toward 90 degrees.
We can then say: <12*cos(90), 12*sin(90)> = <12*0, 12*1> = <0, 12>
Vector #2 is <0,12>
When you wrote <12,0>, you were on the right track, but you had the coordinates swapped in the wrong order.
----------
Then we have to account for a wind going 4 knots in the southwest direction. This is at the angle 225 degrees (we rotate 180 degrees plus another 45 to get 225). So,
vector #3 = <4*cos(225), 4*sin(225)> = <-2.8284271, -2.8284271>
This vector's coordinates are approximate
---------
To recap everything so far, vectors 1 through 3 are the following
p = <-23.4923155, 8.5505036>q = <0, 12>r = <-2.8284271, -2.8284271>I'm using variables to represent the vectors at this point, so we can then add them up to get...
s = p+q+r
s = <-23.4923155, 8.5505036> + <0,12> + <-2.8284271, -2.8284271>
s = <-23.4923155+0+(-2.8284271), 8.5505036+0+(-2.8284271)>
s = <-26.3207426, 5.7220765>
Vector s represents the sum of the three vectors p, q, and r. The two currents and the wind ultimately combine together to push the boat in the direction and along the length of vector s.
----------------------
Now that we know the coordinates of vector s, we use them to find the true speed and true bearing of the boat.
speed = sqrt(a^2 + b^2)
speed = sqrt( (-26.3207426)^2 + (5.7220765)^2 )
speed = 26.935546 knots, which is approximate
angle = arctan(b/a)
angle = arctan(5.7220765/(-26.3207426))
angle = -12.265139
Add 360 to this angle to find that we get to the coterminal angle of -12.265139+360 = 347.734861 degrees
This angle is in quadrant 4, which is the southeast quadrant. If we rotate another 360-347.734861 = 12.265139 degrees, going counterclockwise, then we'll face directly east. Then another 90 degree counterclockwise rotation has us face directly north.
In total, the true bearing is approximately 90+12.265139 = 102.265139 degrees
So we'll start aiming north, and then rotate roughly 102.265139 degrees toward the east to get to the true bearing.
Related Questions
Express $0.3\overline{2}$ as a fraction in simplest form.
Answers
Answer:
3/20
Step-by-step explanation:
[tex]\frac{0.3}{2}=\frac{0.3*10}{2*10}=\frac{3}{20}[/tex]
Find three consecutive integers such that 4 times the first decreased by the second is 12 more than twice the third
Answers
The three consecutive number are 17 , 18 and 19 respectively
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the first number be = x
Let the second number be = ( x + 1 )
Let the third number be = ( x + 2 )
Now ,
A = 4 times the first decreased by the second is 12 more than twice the third
Substituting the values in the equation , we get
4x - ( x + 1 ) = 12 + 2 ( x + 2 )
On simplifying the equation , we get
4x - x - 1 = 12 + 2x + 4
3x - 1 = 16 + 2x
Subtracting 2x on both sides of the equation , we get
x - 1 = 16
Adding 1 on both sides of the equation , we get
x = 17
Therefore , the value of x is 17
Hence , the consecutive numbers are 17 , 18 and 19
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
A painting is purchased for $350. If the value of the painting doubles every 5 years, then its value is given by the function
V(t) = 350 - 205, where t is the number of years since it was purchased and Vt) is its value in dollars) at that time. What is
the value of the painting 10 years after its purchase?
Answers
Answer:
$1400
Step-by-step explanation:
350 x 2 = 700 x 2 = $1400
In 1992, Jason bought a gallon of gas for $1.18. Yesterday, he bought a gallon of gas for $2.10. What is the percentage increase of the price of a gallon of gas
from 1992 to yesterday? If necessary, round to the nearest tenth of a percent.
Answers
Answer:
1.77 percent increase
Suppose that you are an elementary school teacher and you are evaluating the reading levels of your students. You find an individual that reads 46.4 word per minute. You do some research and determine that the reading rates for their grade level are normally distributed with a mean of 90 words per minute and a standard deviation of 24 words per minute. At what percentile is the child's reading level (round final answer to one decimal place)?
Answers
Answer:
The child's reading level is at the 3.4th percentile.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
You do some research and determine that the reading rates for their grade level are normally distributed with a mean of 90 words per minute and a standard deviation of 24 words per minute.
This means that [tex]\mu = 90, \sigma = 24[/tex]
You find an individual that reads 46.4 word per minute. At what percentile is the child's reading level?
The percentile is the p-value of Z when X = 46.4, multiplied by 100. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{46.4 - 90}{24}[/tex]
[tex]Z = -1.82[/tex]
[tex]Z = -1.82[/tex] has a p-value of 0.034.
0.034*100 = 3.4
The child's reading level is at the 3.4th percentile.
in a group of 35 students 7 have yellow socks what percentage of the students have yellow socks
Answers
Answer:
20%
Step-by-step explanation:
[tex]\frac{7}{35} =\frac{y}{100}[/tex]
35 · y = 7 · 100
35y = 700
35y ÷ 35 = 700 ÷ 35
y = 20
1. A family went to a restaurant. The total cost
of the meal was $46.50. The family had a
coupon for 30% off the total. What was the
final cost of the meal after the coupon was
used?
Answers
Answer:
32.55
Step-by-step explanation:
If you get 30% off, that means you pay (100% - 30% = 70% of the cost)
46.50 * 70%
46.50 *.70
32.55
How far will the skier travel
Answers
Answer:
2700 meters
Step-by-step explanation:
2 and a half minutes becomes 150 seconds. 150 seconds divided by 4 seconds, the amount of seconds it takes to cover 72 meters, is 37.5. 37.5 multiplied by 72, the meters covered in 4 seconds, is 2700 meters.
Which of the following numbers is one fifth of a given number if one fourth of that same number is 20
Answers
Answer:100
Step-by-step explanation:
hat is the following sum?
0 7(10√/x²y)
O
O
0 7(²√x²¹x²)
Answers
The sum of the given equation is 7[tex]\sqrt[5]{x^{2} y}[/tex].
What is fractional equation?A fractional equation is one in which one or more of its terms have the unknown as their denominator. Equations involving fractions can be resolved using the Cross-Product property.Therefore, when we reduce or simplify a fraction, we aim for maximum simplicity. In order to do this, we divide both the numerator and the denominator by the biggest integer that can be divided precisely into both numbers. In other words, we choose the greatest number that the top and bottom have in common and divide them by that.Equations using fractions require the solution of equations in which the unknown variable is a component of the fraction's numerator or denominator. To solve fractional equations, we must determine the value of the undetermined variable.Given data :
4 ([tex]\sqrt[5]{x^{2} y}[/tex].) + 3 ([tex]\sqrt[5]{x^{2} y}[/tex].)
Add similar elements
= 7[tex]\sqrt[5]{x^{2} y}[/tex].
Learn more about fractional equation refer to :
https://brainly.com/question/20323470
#SPJ1
Show your work please!!!
Answers
Answer:
Error is in line 3
Error description: Root of 4 is 2 not 4
Correct answer should be 9*√5 (12*√5 - 3*√5)
i need to show work it’s algebra 2
Answers
Answer:
a=4 because 4+2=6 on number one
If there are 26 successes in a sample with a size of 40, what is the sample
proportion?
A. 0.65
B. 0.52
C. 0.75
D. 0.26
SUBMIT
Answers
Answer:
0.65
Step-by-step explanation:
Max kicks a football up at a velocity of 25 meters per second. If the ball makes contact with his foot 0.5 meter off the ground, how long will the ball stay in the air?
Answers
Answer:
25*0.5 = 12.5
Julia's Burger Place made 3 burgers with onions and 12 burgers without onions. What is the ratio of the number of burgers without onions to the number of burgers with onions?
Answers
The ratio of number of burgers without onions to the number of burgers with onions is 4:1.
Ratio of numbers.The ratio of numbers implies the relationship between the numbers when expressed in its simplest fraction. The relationship can be written in form of a/ b or a:b.
Given in the question that Julia's Burger Place made 3 burgers with onions and 12 burgers without onions. Then the ratio required can be expressed as;
ratio of number of burgers without onions to burgers with onions = (number of burgers without onions)/ (number of burgers with onions)
= 12/ 3
= 4/ 1
The ratio of number of burgers without onions to burgers with onions = 4:1
Therefore, the ratio of the number of burgers without onions to the number of burgers with onions is 4:1.
Learn more about ratio of numbers at https://brainly.com/question/2914376
#SPJ1
Aurielle bought 13 packs of
cookies for $51.48 from the
supermarket. How many packs
of cookies can she buy for
$43.56?
Pls help
Answers
Answer:
She could buy 11 packs of cookies for $43.56.
Step-by-step explanation:
to find the answer you have to find how much 1 pack of cookies costs.
First, you divide 51.48 by 13
51.48/13 = 3.96
now that you know 1 pack of cookies cost $3.96 you can use that to find how many packs you could buy for 43.56
43.56/3.96 = 11
2. Marquan sells pretzels at Auntie Anne and earns $15 per hour,
(a) Write an expression to show the relationship between the number of hours
worked (h) and the total earnings.
(b) Use the expression to determine the amount of money he earns if he
worked for 2 hours (b) 3 hours (c) 5 hours
Yes
Answers
dollars per hour = salary
a
dollars per hours multiplied with hours worked (h) = total earnings
b
15 x 2 = 30
15 x 3 = 45
15 x 5 = 75
(h)
Kaiya Deangelo each create a number pattern
Answers
What is value of x and y if
Y=-2x+8 and Y=3x-7
Answers
Answer:
X=5 y=-2
Step-by-step explanation:
Set them equal to each other so...
-2x+8=3x-7
Simplify by balancing out the equation so
-5x=-1
So x=5
Now plug it into either y equation
-2(5)+8
-10+8
Y=-2
Hope this helps!
identify the expeession equivalent to 2x+8 by substituting x=7 and x=5.
Answers
Step-by-step explanation:
If you substitute the x in 2x+8 with 7, you get:
2(7)+8
14+8
22
If you substitute the x in 2x+8 with 5, you get:
2(5)+8
10+8
18
Hope this helps!
What is the slope of the line that is parallel to the line y = -2x + 5?
slope =
Answers
Answer:
-2
Step-by-step explanation:
Slope intercept form is
y = mx + b
Where m is the slope
Parallel lines have the same slope
----------------------------
y = -2x + 5
is in slope intercept form
the slope, m = -2
The slope of the parallel ine will be the same
m = -2
Hello there!
Parallel lines have the same slope.
So if one line has a slope of -2, then the slope of the line parallel to it is -2 as well.
Hope it helps! :)
If you have any query, please feel free to ask me! :)
~An excited gal
[tex]MagicalNature[/tex] here to help
A.
B. AB ≅ AC
C.
D. CS ≅ ST
Answers
Answer:
what are the rest of the choices, if the ones are the top ones they dont make sense.
Step-by-step explanation:
How do I solve 6,000-5,258
Answers
Answer:
742
Step-by-step explanation:
6000
-5258
742
Can someone solve this please? Thank you!
Answers
Answer:
.125
Step-by-step explanation:
1/4 times 1/2 equals .125.
Answer:
Total area of the box is 1 ft squared
Area of the shaded box is .125 ft squared
Area of the non - shaded box is .875 ft squared
Step-by-step explanation:
To find the total area, we can multiple the length * height, 1 * 1 = 1.
To find the shaded area, we can multiple the length * height, .5 * .24 = .125.
To find the total area, we can multiple the length * height of the box minus the shaded area, 1 * 1 - .125 = .875.
Sound waves can be ranked by their intensity, I, given in this formula, where r is the distance from the source of a sound with a power output of P.
[tex]P = 4xr^{2} .[/tex]
Which equation correctly rewrites the formula to solve for I?
A. [tex]I = \frac{P}{4xr^{2} }[/tex]
B. [tex]I = \frac{Pxr^{2} }{4}[/tex]
C. [tex]I = 4Pxr^{2}[/tex]
D. [tex]I = \frac{4P}{xr^{2} }[/tex]
Answers
Answer: C correctly rewrites the formula to solve I
Step-by-step explanation:
The difference between six and a number is two
Answers
Answer:
4.
Step-by-step explanation:
the difference means -.
between a number means use a variable (x) to substitute. so now you have the difference between x and 6 is to. is just means equals so you would set it up like this 6-x=2. you can make this easier by just asking yourself. what number plus 2 equals six? the answer would be 4. 4+2=6-->6-4=2.
Can someone PLEASE help I’ll give brainliest
Answers
Answer:
98°
Step-by-step explanation:
3x+89+8x+58=180
11x+147=180
11x=180-147
11x=33
x=3
< MON = 3x+89 = 3(3)+89 = 9+89= 98°
Use triangles to find the sum of the interior angle measures of the polygon.
SHOW YOUR WORK.
Answers
The sum of the interior angle measures of the polygon is 900 degrees
How to determine the sum of interior angles
From the image shown, we can see that the polygon has 7 sides.
A polygon with seven sides is called a heptagon
It is important to note that the number of triangles in a heptagon is 5.
Also, the sum of angles in a triangle is 180 degrees.
Now, the formula for calculating the sum of interior angles of a polygon is expressed as;
= (n - 2) 180
Where; n is the number of sides of the polygon
Substitute the value
= (7-2)180
Subtract the value
= 5(180)
= 900 degrees
Hence, the sum is 900 degrees
Learn more about polygons here:
https://brainly.com/question/1592456
#SPJ1
(Please help) (one question) (NO LINKS)
Answers
Answer:
0.25
Step-by-step explanation:
hope that helps!!!!!!!!!!!!!!!!!!!! :)
no links please
Evaluate 10v for v = -8.
A.
2
B.
-90
C.
80
D.
-80
Answers
Step-by-step explanation:
10(-8) substitute (-8) for V
10 • -8 = -80 Then solve by multiplying
An