HOMEWORK HELP!!! ASAPP!!!
An airplane is flying on a compass heading (bearing) of 300° at 345 mph. A wind is
blowing with the bearing 280° at 20 mph.
(a) Find the component form of the velocity of the airplane,
(b) Find the actual ground speed and direction of the plane.
(Simplify your answer. Round to the nearest tenth as needed.)
Answers
Answer:
(a) north: 172.5 mph; west: 298.8 mph
(b) 363.9 mph at 298.9°
Step-by-step explanation:
The components of velocity are found using the formula for polar to rectangular coordinate conversion. The actual ground speed will be the result of adding the velocity vectors of the airplane and wind.
__
(a)The usual formula for converting polar coordinates (r; θ) to rectangular coordinates (x, y) is ...
(x, y) = r(cos(θ), sin(θ))
When this formula is used with bearing angles, the resulting components are (north, east).
The airplane velocity components are ...
north: 345·cos(300°) = 172.5 . . . . mph
east: 345·sin(300°) ≈ -298.8 . . . . mph (or 298.8 mph to the west)
__
(b)The sum of the two velocity vectors is found by a calculator to be ...
345∠300° +20∠280° = 363.9∠298.9°
If you wanted to calculate this by hand, you would find the components of the wind speed, add them to the components of the plane speed, and convert the rectangular components back to polar coordinates. The usual way that is done is using the formula ...
r = √(x² +y²)
θ = arctan(y/x) . . . . paying attention to quadrant
If you use x=northerly component, y=easterly component, then the resulting angle is the bearing angle.
_____
Additional comment
Some calculators are able to convert directly between (x, y) coordinates and (r; θ) coordinates. The calculator shown in the attachment converts (r; θ) coordinates to/from complex numbers. For the purpose here, the real part of the number is the northerly component, and the imaginary part is the easterly component.
The conversion to a complex number is x +iy = r(cos(θ) +i·sin(θ)), sometimes abbreviated r·cis(θ). The notation used here is even more compact: r∠θ. Conveniently, the calculator we used is able to employ this notation.
Related Questions
whats the volume formula?
Answers
find the product of smallest natural number and the smallest whole number
Answers
1x0=0
i hope that’s right
A jogger on the beach at Cape Hatteras covered 8 miles at a constant speed. Given that distance run varies directly as time, what is the constant of variation in miles per hour if it took the jogger 45 minutes to cover the 8 miles?
Answers
The velocity of the jogger will be 0.18 miles per minute.
What is velocity?Velocity is defined as the ratio of the distance moved by the object in a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.
Given that:-
It took the jogger 45 minutes to cover the 8 milesThe velocity will be calculated as:-
V = Distance ÷ Time
V = 8 ÷ 45
V = 0.18 miles per minute
Therefore the velocity of the jogger will be 0.18 miles per minute.
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PLEASE HELP ME!!! Fist person to answer gets brainly
Answers
Step-by-step explanation:
I only know the answer for the second task
Answer:
a) No
b) No
c) Yes
d) No
Step-by-Step Explanation:
We can use the Pythagoras Theorem to check whether it is a right triangle.
Hypotenuse^2 = 1st Side^2 + 2nd Side^2
a) 7, 12, 14
Therefore,
=> 14^2 = 7^2 + 12^2
=> 196 = 193
RHS is not equal to LHS.
Therefore, its not a Right Triangle.
b) 6, 14, 19
Therefore,
=> 19^2 = 6^2 + 14^2
=> 361 = 232
RHS is not equal to LHS.
Therefore, its not a Right Triangle.
c) 12, 35, 37
Therefore,
=> 37^2 = 12^2 + 35^2
=> 1369 = 1369
RHS is equal to LHS.
Therefore, it is a Right Triangle.
d) 4, 8, 9
Therefore,
=> 9^2 = 4^2 + 8^2
=> 81 = 80
RHS is not equal to LHS.
Therefore, its not a Right Triangle.
2nd Image:-
Answer: 352 ft^3
Step-by-Step Explanation:
r = 4 ft
h = 7 ft
Volume = πr^2h
Therefore,
= πr^2h
= π * r^2 * h
= 3.14 * 4^2 * 7
= 3.14 * 16 * 7
= 351.68
Volume = 351.68 ft^3
Rounded off = 352 ft^3
If you appreciate the effort that I put into making this answer, please mark it as Brainliest. Thank you.
If two samples are drawn randomly from the same population and sample A has n=350 and sample B has n=500, which sample will have a larger standard error of the mean?
Group of answer choices
Sample B
Sample A
The standard errors will be the same
Answers
Reason:
The standard error of the mean has the formula [tex]\frac{\sigma}{\sqrt{n}}[/tex] where [tex]\sigma[/tex] (greek letter sigma) is the standard deviation and n is the sample size.
As n gets bigger, the standard error [tex]\frac{\sigma}{\sqrt{n}}[/tex] gets smaller, and vice versa. This assumes sigma is fixed. A larger sample indicates the error goes down to narrow in better on the population mean.
Based on what I mentioned, this tells us that sample A has the larger standard error since n = 350 is smaller than n = 500 for sample B.
Question Nine 8 coins are tossed what is the probability of getting at least one Head showing on any of the coins?
Answers
The probability of at least one of the coins showing heads is 4
is 3 divisible by 811
Answers
ans = 0.00369913687
hope it helps...!!!!
Any one able to help me out with this one?
Answers
Answer:
54 yards²
Step-by-step explanation:
First, we can find the area of the figure as a whole.
6 x 11 = 66
Now we have to find the area of the smaller rectangle
3 x 4 = 12
Finally, we subtract the whole and the smaller rectangle
66 - 12 = 54
Which expression is equivalent to the expression shown?
7
71 7²
2
16
7
1'
712
Answers
7¹⁴÷7²
= 7¹⁴-²
=7¹²
hope this helps:)
At a football game, 35% of people attending were supporting the home team, while 65% were supporting the visiting team. If 455 people attending the game supported the home team, what was the total number of people attending the game?
Answers
Answer:
1300 ppl
Step-by-step explanation:
35% = .35 in decimal
.35 x =455
x = 455/.35 = 1300 ppl
150 inches equals how many feet and inches?
Answers
Answer:
12 feet and 6inches ..................
Answer:
12 feet and 6 inches
Step-by-step explanation:
762/164,391
Need full work
Answers
Answer:
254/54797
Step-by-step explanation:
image attached
11. Write an equation of the line with x-intercept (-7,0) and y-intercept (0,5).
Answers
Answer:
5x-7y+35=0.
Step-by-step explanation:
1) according to the condition it is possible to make up the required equation:
[tex]\frac{x}{-7} =\frac{y}{5} =1;[/tex]
note, the numbers -7 and 5 are from the given coordinates;
2) if to re-write the equation into common form, then
5x-7y+35=0.
Jaxon is flying a kite, holding his hands a distance of 3.25 feet above
the ground and letting all the kite's string play out. He measures the
angle of elevation from his hand to the kite to be 24°. If the string from
the kite to his hand is 105 feet long, how many feet is the kite above the
ground? Round your answer to the nearest tenth of a foot if necessary.
Answers
Using the slope concept, it is found that the kite is 46.50 feet above the ground.
What is a slope?The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.
In this problem:
The angle is of 24º.The vertical change is of 3.5 + x.The horizontal change is of 105.Hence:
tan(24º) = (3.5 + x)/105.
3.5 + x = 105tan(24º)
x = 105tan(24º) - 3.5
x = 43.25 ft.
Hence, the height of the kite is:
43.25 ft + 3.25 ft = 46.50 feet.
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Answer:
Step-by-step explanation:
�
105
105
x
sin
24
1
=
1
sin 24
=
�
105
105
x
105
sin
24
=
105 sin 24=
�
x
Cross multiply.
�
=
42.707347...
x=42.707347...
Type into calculator.
Add 3.25, the distance from the ground to his hand:
Add 3.25, the distance from the ground to his hand:
42.707347...
+
3.25
=
42.707347...+3.25=
45.957347...
45.957347...
≈
≈
46
46
Round to the nearest tenth.
The kite is 46 feet above the ground.
The kite is 46 feet above the ground.
Steve hade 17 pencils in his backpack. this represents 5 more than 6/7 the number of pencils that Clyde has in his backpack
Answers
Answer:
Clyde has 14 pencils in his backpack
Step-by-step explanation:
Let x be the number of pencils that Clyde has in his backpack.
We can translate this statement “Steve hade 17 pencils in his backpack. this represents 5 more than 6/7 the number of pencils that Clyde has in his backpack” mathematically like this :
[tex]17=5+\frac{6}{7} x \\\\ \Longleftrightarrow 17-5=\frac{6}{7} x \\\\ \Longleftrightarrow 12=\frac{6}{7} x \\ \\\Longleftrightarrow x=\frac{12\times 7}{6} =14[/tex]
Let he has n pencils
So
[tex]\\ \rm\hookrightarrow \dfrac{6n}{7}+5=17[/tex]
[tex]\\ \rm\hookrightarrow \dfrac{6n}{7}=12[/tex]
[tex]\\ \rm\hookrightarrow 6n=84[/tex]
[tex]\\ \rm\hookrightarrow n=14[/tex]
Let y = 2(x – 5)2 – 6.
Part A: Is the given relation a function? Is it one-to-one? Explain completely. If it is not one-to-one, determine a possible restriction on the domain such that the relation is one-to-one.
Part B: Determine y–1. Show all necessary calculations.
Part C: Prove algebraically that y and y–1 are inverse functions.
I WILL GIVE BRAINLIEST PLS HELPPPP!!!!
Answers
The given equation represents a function and inverse of the function exist if x ≥ 6.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a function:
y = 2(x – 5)² – 6
Part A:
Using vertical line test, we can find the whether the graph is a function or not.
After drawing a graph for the given curve, and drawing a vertical line.
The vertical line touches only one point for the one input.
The given equation represents a function.
Part B:
Replace x → y and y → x
x = 2(y – 5)² – 6
2(y – 5)² = x + 6
[tex]\rm y^-^1 = \sqrt{\dfrac{x+6}{2}} +5[/tex]
Plug x = 1 in the y:
y = 26
Plug [tex]\rm y ^-^1[/tex] = 1 in inverse of a function:
x = 26
Thus, the given equation represents a function and inverse of the function exist if x ≥ 6.
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The GCF of 12 and 28 is _____.
Answers
Answer:
The GCF of 12 and 28 is 4
hope it helpsss
Answer: is 4 thats the answer
Step-by-step explanation: i have none im not good at explaining math welp have a good day
The area of triangle ABC is 50 square units. What is the length of CD?
Answers
The CEO of Jisko requests our help in preparing year-end financial reports. The CEO explains that they are having difficulty classifying accounts. The Tableau dashboard shows December 31 year-end data from the company’s accounting system.
Prepare the current assets section of its December 31 year-end balance sheet.
Answers
A current asset is an asset that can reasonably be expected to be sold, consumed, or exhausted through the normal operations of a business within the current fiscal year
What is current asset?Your information is incomplete. Therefore, an overview of the current asset will be given. Current assets are those that you can convert into cash within one year, such as short-term investments and accounts receivable.
Current assets include cash, cash equivalents, accounts receivable, stock inventory, marketable securities, pre-paid liabilities, and other liquid assets.
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Aiden earned $334.40 at his job when he worked for 16 hours. How much money did he earn each hour?
Answers
Answer : 20.9
Answer:
$20.90
Step-by-step explanation:
If we want to find Aiden's hourly rate, and we know how long he worked, and how much money he made, then we can simply divide his profit by how long he worked. This will give us the precise amount of money he made per hour.
So,
$334.40 / 16 hours = 20.9
This means Aiden earned approximately $20.90 per hour.
Hope this helped!
what is the reference angle for a 240 degree angle?
Answers
What is the volume of the figure composed of two congruent triangular prisms if a = 5 units, b = 3 units, and c = 6 units?
A.
60 cubic units
B.
45 cubic units
C.
90 cubic units
D.
180 cubic units
Answers
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 15 more than the second.
Answers
Answer:
Angle #1 is 45 degrees
Angle #2 is 60 degrees
Angle #3 is 75 degrees
Step-by-step explanation:
x- angle #1
y- angle #2
(180-x-y)- angle #3
3x=180-x
4x=180
x=45
180-x-y=y+15
y=60
180-60-45=
180-105= 75
hey can anyone help find the missing measurement pls
Answers
Answer:
? ≈ 6.5 yd
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here A = 13.3 and h = 4.1 , then
[tex]\frac{1}{2}[/tex] × 4.1b = 13.3 ( multiply both sides by 2 to clear the fraction )
4.1b = 26.6 ( divide both sides by 4.1 )
b = ? ≈ 6.5 yd ( to the nearest tenth )
List all the possible rational roots x^3 + x^2 -3x+12
Answers
Answer: See below
Step-by-step explanation:
[tex]$$Find the possible rational roots using the rational root theorem:$$x^{3}+x^{2}-3 x+12=0$$Select the coefficient of the leading term and the constant term:$1 x^{3}+x^{2}-3 x+12=0$\\Find the positive divisors of 12 and 1: \\\\Divisors of $12: 1,2,3,4,6,12$\\Divisors of $1: 1$\\Divide each of the divisors of 12 by 1 :\\$\frac{1}{1}, \frac{2}{1}, \frac{3}{1}, \frac{4}{1}, \frac{6}{1}, \frac{12}{1}$2, \pm 3, \pm 4, \pm 6, \pm 12$$[/tex]
[tex]$$Because both positive and negative values are valid candidates, the possible rational roots of $x^{3}+x^{2}-3 x+12=0$ are:$$\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 12[/tex]
What is the product of 709 and 68?
Answers
Answer:
[tex]709*68=48212[/tex]
ans = 48212
how many solutions does the following equation have? explain
5x- 3x + 5 = 8x +5
Answers
Answer:
Plug into desmos, the exact equation, and put in what point comes out.
Step-by-step explanation:
Answer:
Once fully solved, x is equal to 0, so it means that there is only one solution
Step-by-step explanation:
When you combine like terms (without adding variables to either side), the equation is equal to:
2x + 5 = 8x + 5
Then, the next step is:
5 = 8x + 5 - 2x
Finally, the last one is:
0 = 6x, which is x = 0.
a shape is shown on the centimetre grid below work out the area of the shape after it has been enlarged by scale factor 2 state the units of your answer
Answers
Answer:
20 cm²
Step-by-step explanation:
If the given shape has been enlarged by scale factor 2, then each of the side lengths will be increased from 1 cm to 2 cm, as 1 × 2 = 2
Area of the given shape is 5 cm².
As we are working with area, we cannot simply multiply the area of the given shape by the scale factor. Area is measured in square units, therefore we need to multiply the area of the given shape by the square of the scale factor.
⇒ area of the enlarged shape = area of given shape × sf²
= 5 cm² × 2²
= 5 cm² × 4
= 20 cm²
(see attached image for proof)
<~~• ¥ Pls HELP me!! ¥ • ~~>
Pls help me figure out the 3 boxes left pls help me
Answers
Step-by-step explanation:
divide equation by 2
subtract 6
-x
Tracey bought a diamond ring appraised at $1200 at an antique store. If diamonds have appreciated in value at an annual rate of 12%, what was the value of the ring 10 years ago? (Round your answer to the nearest dollar.)
Answers
Answer:
1600 / 1.1^10 = $616.87
Step-by-step explanation:
Im not so sure, but here
the value of the diamond ring 10 years ago was approximately $419.47
To find the value of the diamond ring 10 years ago, we need to calculate its original value before the annual appreciation.
Let's assume the original value of the ring 10 years ago was "x" dollars.
After 10 years, with an annual appreciation rate of 12%, the value of the ring became $1200.
The formula to calculate the future value (FV) of an investment with compound interest is:
FV = PV * (1 + r)ⁿ
where:
FV = future value
PV = present value (original value)
r = annual interest rate (as a decimal)
n = number of years
In this case, we have:
FV = $1200 (present value after 10 years)
r = 12% (0.12 as a decimal)
n = 10 years
Now, we can rearrange the formula to find the original value (PV):
PV = FV / (1 + r)ⁿ
PV = $1200 / (1 + 0.12)¹⁰
PV = $1200 / 2.85610019
PV ≈ $419.47
So, the value of the diamond ring 10 years ago was approximately $419 (rounded to the nearest dollar).
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