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°.
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Solve for the value of x
Answer:
x=9
Step-by-step explanation:
To solve for x, you can set up a proportion between the 2 triangles we see.
The small triangle can be written as [tex]\frac{16}{20}[/tex], and the large triangle can be written as [tex]\frac{16+12}{20+2x-3} = \frac{28}{2x+17}[/tex].
Set both proportions equal to each other.
[tex]\frac{16}{20}=\frac{28}{2x+17}[/tex]
Cross multiply and solve for x.
[tex]16(2x+17)=(28)(20)[/tex]
32x+272=560
32x=288
x=9
A county has constructed a conical building to store sand. The cone has a height of 101 m and a diameter of 330 m. Find the volume of this building to the nearest hundredth. Use 3.14 for π.
Answer:
2878045.500 cubed metres
Step-by-step explanation:
volume = 1/3* pie* r*r*h
= 1/3 *3.14*165*165*101
=2878045.5 cubed metres
i hope it's helpful
Simplify (4.5)(5)(−2). (1 point)
Answer:
(4.5)(5)(−2) = (-9) × 5
= -45
Answer:
-45
Step-by-step explanation:
[tex](4.5)(5)(-2)\\\\22.5(-2)\\\\-45[/tex]
The vertices of a triangle are A(0,0),B(3,8) and C(9,0). What is the area of this triangle?
Answer:
9
Step-by-step explanation:
To find the area of a triangle where you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2. Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.
Fill in the numbers for each corresponding letter combination within the formula.
Fill in your formula like this: 0(8-10) + 3(0-0) + 9(0-8).
Subtract the numbers within the parentheses.
0 from 8 = 8, 0 from 0 = 0 and 8 from 10 = 2.
Multiply that result by the number to the left of the parentheses.
0 by 8 = 0, 3 by 0 = 0 and 9 by 2 = 18.
Add the three products together.
0 + 0 + 18 = 18
Divide the sum of the three products by 2.
18 ÷ 2 = 9
Answer:36
Step-by-step explanation:
16. Use the vertical line test to determine whether the relation is a function.
Answer:
neither of them are
Step-by-step explanation:
Round 4.789443 to the nearest whole number
Answer:
5
Step-by-step explanation:
I don't think I should have to explain this but if it's in between 4.5 and 5 it will be 5 and if it's 4.5-4 it would be 4
Evaluate the expression.
3x + 2y for x = 4.2, y = 2.7
Answer:
18
Step-by-step explanation:
4.2 • 3= 12.60
2.7 • 2= 5.4
12.6+ 5.4=
18.0
What are the coordinates of A? someone help
Answer:
(7,10)
Step-by-step explanation:
The x coordinate is the first coordinate, it is how far you go across
X = 7
The next coordinate is the y coordinate, it is how for you go up or down
y = 10
(7,10)
Simplify completely
(192x^12/3x^3)^1/3
Show all work for full credit
Answer and Explanation: The answer and explanation is in the image.
What is the product of y and 10
Answer:
10y
Step-by-step explanation:
product means to multiply so you would multiply y and 10 so the options would be
10y
y x 10
SOMEONE PLEASE HELP ME!!
Answer:
should be 3
Step-by-step explanation:
hope you get a good grade
Researching the 21st century in UAE
The perimeter of the classroom shown is 6x + 3. Find the length of the missing side.
Incorrect Work/Solution
Identify and explain the Error
x
(6x + 3) + (3x +1) + x + x
6x + 3x + x +x+3 + 1
11x + 4
3x+1
The length of the missing side is 11x + 4.
Correct Work/Solution
Share a Strategy
Answer:
Refer to link below:
Step-by-step explanation:
https://brainly.com/question/25868816?referrer=searchResults
7. A boutique is offering a 25% discount on purchase made in cash. Calculate the cash price Janelle paid for articles totaled to $465.
Answer:
$348.75
Step-by-step explanation:
$465 * 25%= 116.25
465-116.25 = $348.75
please help!! easy but i don't understand <3
in essence it's just asking on getting the equation of that line in more or less slope-intercept form, hmmm well, it's a line, so all we need is two points to get it, hmmm let's see let's use the starting point and terminal point, so we know it goes through the origin, (0,0) and also goes through (1, 0.7), let's change 0.7 to a fraction, so its 7/10, ok, let's use those two points from it.
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{\frac{7}{10}}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{\frac{7}{10}}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{0}}}\implies \cfrac{~~ \frac{7}{10}~~}{1}\implies \cfrac{7}{10}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{\cfrac{7}{10}}(x-\stackrel{x_1}{0})\implies y = \cfrac{7}{10}x[/tex]
Find the equation of the line that is parallel to x=5y-8 and pass through (6, -5) in slope intercept form
Answer:
y=1/5x-31/5 (or y=0.2x-6.2 in decimals)
Step-by-step explanation:
x=5y-8 (original equation)
x+8=5y (Addition Property of Equality)
1/5x+8/5=y (Division Property of Equality, slope of original equation is 1/5)
y-y1=m(x-x1) (point-slope formula)
y-(-5))=1/5(x-(6)) (plug in the slope that was found earlier and the point given in the question)
y+5=1/5(x-6)
y+5=1/5x-6/5 (Distributive Property of Multiplication) Note: 5 = 25/5
y=1/5x-31/5 (Subtraction Property of Equality, and there's your answer)
y=0.2x-6.2 (This is the same answer, but written with decimals)
Over a lengh of 101 inches the hight changes 5" what is the angle?
Answer:
2.83°
Step-by-step explanation:
The tangent of an angle is the ratio of rise to run.
θ = arctan(5/101) ≈ 2.83°
_____
We assume the length is referring to the horizontal distance.
If it is the distance along the path, then the angle is ...
θ = arcsin(5/101) ≈ 2.84°
A bag of mixed nuts has 18 almonds, 8 cashews, and 14 peanuts. If one nut is selected, what is the probability that a peanut is chosen?
Provide the answer as a simplified fraction.
Answer:
7/20
Step-by-step explanation:
Answer:
ok so here is answer option no1
1/8 + 1/4 = 3/8
or you could do
18 plus 14 equals 32divided into 8 equals 4
Step-by-step explanation:
if this is wrong I'm very very very really really really sorry.
Help help help help math math
Simplify the expression
3+4·10 – 8
Answer:
35
Step-by-step explanation:
one word: PEMDAS. technically they are all a bunch of words but whatever...
P: parentheses
e: exponents
m: multiply
d: divide
a: add
s: subtract
first we multiply 4*10 since that's first on the list
4*10=40
we have
3+40-8
then we add
3+40
which is 43
then we subtract 8 from it as we have 43-8
which is in the end:
35
What is the slope of the line?
1/2 2 1 -2
Answer:
the slope of the line is 2
Step-by-step explanation:
Answer:
The slope of the line is 2.
Step-by-step explanation:
The point where the line crosses the y-axis, also known as the y-intercept, is (0,1). The next clear point is (1,3).
We can use the formula for finding slope here.
[tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]
If we plug in the points, with (0,1) being the first and (1,3) being the second, we'll get this:
[tex]\frac{3-1}{1-0} --> \frac{2}{1} --> 2[/tex]
Therefore, the slope is 2.
Find an equation for the perpendicular bisector of the line segment whose endpoints
are (5, 4) and (-7,-8).
Answer:
y= -x -3
Step-by-step explanation:
A perpendicular bisector of a line cuts through the line at its midpoint perpendicularly (90°).
Let's find the slope of the line segment.
[tex]\boxed{ slope = \frac{y _{1} - y_2 }{x_1 - x_2} }[/tex]
Slope of line segment
[tex] = \frac{4 - ( - 8)}{5 - ( - 7)} [/tex]
[tex] = \frac{4 + 8}{5 + 7} [/tex]
[tex] = \frac{12}{12} [/tex]
= 1
The product of the slopes of 2 perpendicular lines is -1.
Let the slope of the perpendicular bisector be m.
m(1)= -1
m= -1
y= -x +c
To find the value of c, substitute a pair of coordinates in which the line passes through into the above equation.
Since the perpendicular bisector cuts through the midpoint of the line segment, let's find the coordinates of this midpoint.
[tex]\boxed{midpoint = ( \frac{x _{1} + x _2}{2} , \frac{y_1 + y_2}{2} )}[/tex]
Midpoint of line segment
[tex] = ( \frac{5 - 7}{2} , \frac{4 - 8}{2} )[/tex]
[tex] = ( \frac{ - 2}{2} , \frac{ - 4}{2} )[/tex]
= (-1, -2)
y= -x +c
When x= -1, y= -2,
-2= -(-1) +c
-2= 1 +c
c= -2 -1
c= -3
Thus, the equation of the perpendicular bisector is y= -x -3.
Find the mean of the data
Explanation:
Refer to the table below. I've added a third row where I multiplied each x value with its corresponding frequency value f. We can refer to this row as the xf row.
Once we know the xf values, we add them up to get 245.
We'll then divide that result over the sum of the frequency values (add everything in the second row). The sum of the frequency values is 39.
So the mean is approximately: 245/39 = 6.282051 which rounds to 6.282
Notice that this mean value is fairly close to the x value which has the highest frequency.
Jada buys 5 notebooks and 6 pens. Each notebook costs $4. Jada pays the cashier $40 and gets $8 change.
What is the cost, in dollars, of one pen? Show or explain how you got your answer.
Answer:$2
Step-by-step explanation:
5 notebooks cost $4 each
5*$4=$20
Jada pays the cashier $40 and gets $8 back
So in order to figure out how much was paid you take
$40-$8=$32
Then to figure out how much each pen cost I take
$32-$20=$12
So there was 6 pens that were bought and to get the total per each pen
$12/6=$2 each per pen
Three friends live in three different states. Monica lives in Rhode Island, Anthony lives in Ohio, and Thomas lives in Colorado.
a.) Determine the sales tax rate in each state.
Sales tax in Colorado is 2.85%, in Ohio is 5.50%, and in Rhode Island is 7%.
Colorado: 3.50 = 1003.60 = X3.60 x 100 / 3.50 = X360 / 3.5 = X102.85 = X2.85% = Sales taxOhio: Y = 1.055X10 x 1.055 = Y10.55 = Y10 = 10010.55 = X10.55 x 100 / 10 = X1055 / 10 = X105.5 = X5.5% = Sales taxRhode Island: 10 = 10010.70 = X10.70 x 100 / 10 = X1070 / 100 = X107 = X7% = Sales taxTherefore, sales tax in Colorado is 2.85%, in Ohio is 5.50%, and in Rhode Island is 7%.
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Melanie was training for a race. The line plot below shows the number of miles Melanie ran last week.
4. What does ¾ + ¼ = ?
Answer in simplest form.
Line f is parallel to line g.which statements about line f and g is true
Answer:
Step-by-step explanation:
They have different y intercepts.
They have the same slope.
Here are 2 examples
y = 3x + 5
y = 3x + 19
The slopes are both three. The y intercepts are 5 for the top equation and 19 for the bottom equation.
They are both lines. That means their domain is -infinity <x < + infinity
Their range is - infinity <y < + infinity.
We are excluding examples like x = 3 and x = 5 and y = 1 and y = 3.
It is true that they both are parallel in both cases, but the discussion for each pair is a little different.
1 5/8 ÷ (−1 3/5) Please help
What is the value of x and y?
Answer:
x = 90y = 43Step-by-step explanation:
The angle bisector in this isosceles triangle is also its altitude. It meets the base segment at right angles.
x° = 90°
__
The acute angles in a right triangle are complementary.
y° = 90° -47°
y° = 43°
Together, Mike and Bill have $50 more than Joe has. Mike has $26 more than Bill. The three boys have a total $506. How much money does each boy have.
i wish i had that much money
Answer:
Step-by-step explanation:
1. 84
2. 96
Answer: Divisible by 2, 3, 6
3. 896
4. 942
Answer: Divisible by 2, 3, 6
5. 22,335
6. 39,075
Answer: Divisible by 3, 5
Find Prime Factorizations and Least Common Multiples In the following exercises, find the
prime factorization.
7. 86
8. 78
Answer: 2 3 13 ⋅ ⋅
9. 455
10. 400
Answer: 222255 ⋅⋅⋅⋅⋅
11. 432
12. 627
Answer: 3 11 19 ⋅ ⋅
In the following exercises, find the least common multiple of each pair of numbers using the
prime factors method.
13. 8, 12
hope that help mark me brinliylist
