A ship leaves port at noon and has a bearing of S29oW. The ship sails at 20 knots. How many nautical miles south and how many nautical miles west will the ship have traveled by 6:00 PM
Answers
Answer:
Approximately [tex]58.2\; \text{nautical miles}[/tex] (assuming that the bearing is [tex]{\rm S$29^{\circ}$W}[/tex].)
Step-by-step explanation:
Let [tex]v[/tex] denote the speed of the ship, and let [tex]t[/tex] denote the duration of the trip. The magnitude of the displacement of this ship would be [tex]v\, t[/tex].
Refer to the diagram attached. The direction [tex]{\rm S$29^{\circ}$W}[/tex] means [tex]29^{\circ}[/tex] west of south. Thus, start with the south direction and turn towards west (clockwise) by [tex]29^{\circ}[/tex] to find the direction of the displacement of the ship.
The hypothenuse of the right triangle in this diagram represents the displacement of the ship, with a length of [tex]v\, t[/tex]. The dashed horizontal line segment represents the distance that the ship has travelled to the west (which this question is asking for.) The angle opposite to that line segment is exactly [tex]29^{\circ}[/tex].
Since the hypotenuse is of length [tex]v\, t[/tex], the dashed line segment opposite to the [tex]\theta = 29^{\circ}[/tex] vertex would have a length of:
[tex]\begin{aligned}& \text{opposite (to $\theta$)} \\ =\; & \text{hypotenuse} \times \frac{\text{opposite (to $\theta$)}}{\text{hypotenuse}} \\ =\; & \text{hypotenuse} \times \sin (\theta) \\ =\; & v\, t \, \sin(\theta) \\ =\; & v\, t\, \sin(29^{\circ})\end{aligned}[/tex].
Substitute in [tex]\begin{aligned} v &= 20\; \frac{\text{nautical mile}}{\text{hour}}\end{aligned}[/tex] and [tex]t = 6\; \text{hour}[/tex]:
[tex]\begin{aligned} & v\, t\, \sin(29^{\circ}) \\ =\; & 20\; \frac{\text{nautical mile}}{\text{hour}} \times 6\; \text{hour} \times \sin(29^{\circ}) \\ \approx\; & 58.2\; \text{nautical mile}\end{aligned}[/tex].
Related Questions
what is the answer to this equation using the quadratic formula? 3x^2+2x+4x=0
Answers
Answer: No real number solutions
The complex number solutions are [tex]x = \frac{-1+ i\sqrt{11}}{3} \ \text{ or } \ x = \frac{-1- i\sqrt{11}}{3}\\\\[/tex]
where [tex]i = \sqrt{-1}[/tex]
=======================================================
Explanation:
The given equation 3x^2+2x+4 = 0 is in the form ax^2 + bx + c = 0
We have
a = 3b = 2c = 4Let's compute the discriminant.
d = b^2 - 4ac
d = (2)^2-4(3)(4)
d = -44
The result is negative, so there are no real number solutions.
----------------
If you wanted to find the complex valued solutions, then we apply the quadratic formula.
Plug in a = 3, b = 2, c = 4
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(2)\pm\sqrt{(2)^2-4(3)(4)}}{2(3)}\\\\x = \frac{-2\pm\sqrt{-44}}{6}\\\\x = \frac{-2\pm\sqrt{-1*4*11}}{6}\\\\x = \frac{-2\pm\sqrt{-1}*\sqrt{4}*\sqrt{11}}{6}\\\\[/tex]
[tex]x = \frac{-2\pm i*2*\sqrt{11}}{6}\\\\x = \frac{-2\pm2i\sqrt{11}}{6}\\\\x = \frac{2(-1\pm i\sqrt{11})}{6}\\\\x = \frac{-1\pm i\sqrt{11}}{3}\\\\x = \frac{-1+ i\sqrt{11}}{3} \ \text{ or } \ x = \frac{-1- i\sqrt{11}}{3}\\\\[/tex]
Notice in step 3 we have -44 under the square root. The negative value in the square root leads directly to the imaginary number [tex]i = \sqrt{-1}[/tex]
Though the term "imaginary" is a bit unfair and misleading because numbers like -22 are just as imaginary and made up by humans. It just depends on context in which imaginary numbers are useful (eg: with physics or engineering).
Order from least to greatest.
Answers
(17.7) x (11.4)
Show the work that helped you solve it please
Answers
if 11 is subratecet from 4 times a number the result is 89 find the number
Answers
Answer:
25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
4x-11=89
4x=89+11
4x=100
x= 25
I hope this will help
Find the distance between the lines with equations -4x + 7y + 9 = 0 and y = 4/7x - 9
a.6.7
b.6.73
c.6.71
d.6.72
Answers
The distance between the lines with equations -4x + 7y + 9 = 0 and y = 4/7x - 9 is 7.71 units.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
The distance between the two straight parallel lines can be found by finding the difference between the y-intercept of the two lines. Therefore, for the two of the given equation, the value of the y-intercept can be written as,
Y-intercept of -4x + 7y + 9 = 0
-4x + 7y + 9 = 0
7y = 4x - 9
y = (4x - 9)/7
y = 4x/7 - 9/7
y-intercept = -9/7
Y-intercept of y = 4/7x - 9
y = 4/7x - 9
y-intercept = -9
Now, the difference distance between the two lines will be,
Distance = Difference between the y-intercept
= -9 - (-9/7)
= -9 + 1.2857
= 7.71
Hence, the distance between the lines with equations -4x + 7y + 9 = 0 and y = 4/7x - 9 is 7.71 units.
Learn more about Equation of Line:
https://brainly.com/question/21511618
#SPJ2
Which of the following is equal to -11?
0-6-(-5)
0-5+-6
0-5+6
Answers
EXPLANATION:
∠ R and∠ S are complementary. If m ∠ R = 12x - 3 and m ∠ S = 7x - 2, find m ∠ R.
m ∠ R = (blank)degrees
Answers
Step-by-step explanation:
Sum of two complementary angle is 90°so. <R+<S =90°12x-3+7x-2=90°19x-5=90°19x=95°X= 5<R= 60-3=57°5/12 x 2/5???
CAN SOMEONE PLEASE ANSWER
20 Point Reward!!!!
Answers
Answer:
1/6
Multiply 5/12 x 2/5 then cross cancel 12 and 2 and get 6 then cross cancel 5 and 5 to get 1.
Final answer:
1/6
write the equation in slope-intercept form.
Answers
Answer:
y = 2x - 3Step-by-step explanation:
Given line:
y = - 1/2x - 1We need to find a line that is perpendicular to the given line and passes through the pint (6, 9)
We know perpendicular lines have opposite-reciprocal slopes.
The slope of the line is:
(-1) / (- 1/2) = 1 *2 = 2Use point-slope form to find the line:
y - 9 = 2(x - 6)Convert the equation into slope-intercept form:
y - 9 = 2x - 12y = 2x - 12 + 9y = 2x - 3The sides of a triangle are represented by (3s - 1), (2s + 5), and (s + 4).
1.)Find the expression for the perimeter of the triangle.
2.) What will be the perimeter if s = 7?
Answers
Answer:
1) 6s + 8
2) 50
Step-by-step explanation:
1)
To find the perimeter, add the lengths of the sides.
perimeter = 3s - 1 + 2s + 5 + s + 4
perimeter = 6s + 8
2)
Replace s with 7 in the perimeter expression.
perimeter = 6(7) + 8
perimeter = 42 + 8
perimeter = 50
Answer: 6s+8
Step-by-step explanation:
just did the assignment
A train travels at a rate of (4x + 5) miles per hour. How many miles can it travel at that rate in
(x - 1) hours? Express your answer as a polynomial.
Answers
(4x+5) miles..........1 hour
x miles .........(x-1) hour
(4x+5) * (x-1) = 1 * x
in (x - 1)h = x / (4x+5) miles
recursive formula for 0.15, 0.17, 0.19, 0.21, 0.23
Answers
Answer:
An = a1 + (n-1) d
Step-by-step explanation:
A G.P. Bulk bills at $41.20 per consultation, and sees a new patient every 15 minutes for 3 hours. A new employee calculates the number of patients and then calculates the Medicare bill as follows: Number of patients: 3 ÷ 0.15 = 20 Medicare bill: 20 × $41.20 = $ 824
Answers
Given that,
A G.P. Bulk bills at $41.20 per consultation, and sees a new patient every 15 minutes for 3 hours.
Solution,
3 hours means 180 minutes
It means that he sees a new patient every 15 minutes for 180 minutes.
No of patients = [tex]\dfrac{180}{15}=12[/tex]
Fees for per consultation is $41.20. Total bill will be :
Bill = $41.20×12
= $494.4
He has not converted 3 hours to minutes. It is the error made by the new employee. He get wrong Medicare bill for the patients.
How many is this
2( 9 - 7r ) + 8r
Answers
solving steps:
2( 9 - 7r ) + 8r
2(9) - 2(7r) + 8r
18 - 14r + 8r
18 - 6r
Answer:
18 - 6r
Step-by-step explanation:
2(9 - 7r) + 8r
Expand the brackets:
⇒ 2 · 9 - 2 · 7r + 8r
⇒ 18 - 14r + 8r
Combine like terms:
⇒ 18 - 6r
Which shows the correct placement of the decimal point in the product?
52.1
× 3.4
1771.4
177.14
17.714
1.7714
i will crown to correct answer pls and ty
Answers
Answer:
b.177.14
Step-by-step explanation:
because 52.1x 3.4 = 177.14
Please help!!!!!! Hurry i only have 10 mins ill give brainy
Which operation should be used to solve LaTeX: \frac{x}{3} = 15x3=15 ?
Group of answer choices
+ 3
÷ 3
x 3
– 3
Answers
What is the measure of the indicated angle?
Answers
Answer:
Interior measure of triangle always equal up to 180°.
65+90+? = 180
155+? = 180
? = 180-155
? = 25
hellpppppppppppppppp 43points
Answers
Answer:
a) 4x
b) 2 + 4y
Step-by-step explanation:
a) 7x - 6x + 3x
To do this, we just need to collect the terms together. They are all coefficients of x, so all we need to do is add the number together.
7 - 6 + 3 = 4
7x - 6x + 3x = 4x
b) 2(1 + 2y)
Here we need to expand the brackets. 2 is shown to be multiplied by 1 +2y:
2(1 + 2y)
= 2*1 + 2*2y
= 2 + 4y
I hope this helps :)
2
Think: A student attempted to solve the equation below by Pair/Share: Do you agree or
completing the square.
disagree with the steps taken so
far? Explain.
x²- 2x-1=2
+1+1
because ...
x ²-2x=3
XP-2x +1 = 3+1
*²-2x + 1 = 4
(X+1}=4
b = 2
half:-1
Square: 1
Answers
Answer:
Step-by-step explanation:
Here is how to solve it using factoring:
x^2 - 2x - 1 = 2
x^2 - 2x - 3 = 0
(x + 1)(x - 3) = 0
x = -1, 3.
Answer:
your process is not correct
(x^2-2x+1 = 3+1)
you were wrong here
Step-by-step explanation:
I am not good in english so it is hard for me to explain...
A rectangle has a length of x and a width that is 8 units shorter than twice the length.
a. Draw a picture to represent the box.
b. Write a simplified polynomial to represent the area of the rectangle.
c. What would the area be if = 10 ?
Answers
Step-by-step explanation:
length = x
width = 2x-8
b.) to get the area you need to multiply the length and the width.
l×w= area
x(2x-8)
2x^2-8x
c.) 2x^2-8x = 10
subtract 10 both sides
2x^2-8x-10 = 0
2(x^2-4x-5) = 0
2(x-5)(x+1) = 0
x = 5
the area would be 10.
What is the simplified version of [tex]\frac{x^5x^6}{y^6}[/tex]
Answers
In the diagram, AC is a diameter of the circle with center O. If m_ACB = 50°, what is m_BAC?
Answers
Answer: Your answer 40°
Step-by-step explanation:
Hope this helped!
PLEASE MARK ME AS BRAINLIEST!!!
Need Help! 50 points!!
Answers
Answer:
see below
Step-by-step explanation:
eq.1 2a - b + 2c = -8
eq.2 5b - 3c = 21
eq.3 -7a -10c = -2
3 equations, 3 unknown.
first step is to eliminate b using eq1 and eq2
2a - b + 2c = -8 (5)
5b - 3c = 21
10a - 5b + 10c = -40
5b - 3c = 21
10a + 7c = -21 ------------eq. A
lets solve a using eq. A
10a + 7c = -21
a = (-7c - 21) / 10
now substitute a into eq.3
-7a -10c = -2
-7(-7c - 21) -10c = -2 distribute
10
4.9c + 14.7 - 10c = -2 add similar terms
-5.1c = -2 - 14.7 simplify
c = -16.7 / -5.1
c ≈ 3
solve b using eq. 2 and substitute c.
5b - 3c = 21
5b = 21 + 3c
5b = 21 + 3(3.2)
b = 30.825 / 5
b ≈ 6
solve a using eq. A
10a + 7c = -21
10a + 7(3.2) = -21
10a = -21 - 22.4
a = -43.4 / 10
a ≈ -4
therefore, the statement (-4, 6, 3) is correct.Answer:
a
Step-by-step explanation:
Find the common difference of the
arithmetic sequence -6, -13, -20, ...
Answers
Answer:
-7
Step-by-step explanation:
what is the equation of a line that is parallel to x + 3y =12 and goes through (6,-3) in slope intercept form
Answers
Answer: -1/3 x -1
Step-by-step explanation:
By doing some stuff, you get the slope of the first line as -1/3. Set up -1/3 x +b and you plug in the coordinates. That makes b= -1. Hope it helps :)
(1, 0) is an ordered pair of the function f(x) = 1 + x. True False
Answers
edjfrjenfmdkefehnjfn3mfrjfnrjnfmrmfkrnfj
it is false
What do you call the point where a perpendicular bisector crosses another line?
Answers
Answer:
If AB crosses at a right angle, it is called the "perpendicular bisector" of PQ. If it crosses at any other angle it is simply called a bisector. Drag the points A or B and see both types. For obvious reasons, the point F is called the midpoint of the line PQ. See also Angle bisector.
use the net to find the surface area of the prism.(not drawn to scale)
ANSWERS:
268 m
402.62 m
725.32 m
853 m
Answers
Answer:
402.62
I used a surface area for a right triangular prism calculator
Beth is making fruit salad. She adds 4 grapes for every 2 strawberries. If she uses 12 strawberries, how many grapes will she use?
Answers
Answer:
24
Step-by-step explanation:
12/2=6
6*4=24
Answer:
Beth will use 24 grapes.
Step-by-step explanation:
Not going to lie I forgot how i got my answer but ik its good.
abc is isosceles triangle above is ac=20 and bc=3x-7 what is x
Answers
Answer:
x = 9
Step-by-step explanation:
Isosceles means that the two sides equal each other
As such, to find the value of x we must equal the two expressions together and isolate the variable
20 = 3x - 7
add 7 to both sides
27 = 3x
divide both sides by 3
9 = x
Answer:
The variable x equals 9.
Step-by-step explanation:
3x - 7 = 20
3x = 27
X = 9