Answer:
a) 323 kph with a directional bearing of S 22° E
Step-by-step explanation:
to find the ground speed:
just do the pythagorean theorem.
c²=300²+120²
c²=104400
c=323
to find the directional bearing:
use the law of sines!
sin(90)/323 = sin(θ)/120
(*explanation: since the plane is heading due south and the wind is from due west, it makes a 90 degree angle; and the side opposite of the 90 degree angle is 323. set it equal to sin theta over 120; theta is the angle u r trying to find, and the side opposite of it is 120)
cross multiply:
120sin90=323sin(θ)
divide 323 on both sides:
sin(θ)=0.3715
use inverse sin to find out degree measure:
sin⁻¹(0.3715)=21.8
rounds up to 22.
The ground speed and direction of the plane is 323 kph with a directional bearing of S 22° E. Therefore, option A is the correct answer.
To find the ground speed of the plane, we need to know what a vector is
What is a vector?
A vector is a variable that has both magnitude and direction.
Since the airplane is headed due south with an airspeed of 300 kph, its vector is V = (-300 kph)j.
Also, the wind is blowing from the west at 120 kph. Its vector is v = (-120 kph)i
Now, the ground speed of the plane V' is the resultant vector of the airspeed and wind speed.
What is a resultant vector?A resultant vector is the sum of two or more vectors.
So, V' = v + V
V' = (-120 kph)i + (-300 kph)j
So, its magnitude V' = √(x² + y²) where
x = -120 kph and
y = -300 kph.
So, V' = √[(-120 kph)² + (-300 kph)²]
= √[14400 kph² + 90000 kph²]
= √(104400 kph²)
= 323.11 kph
≅ 323 kph
The direction of the plane
Its direction, Ф = tan⁻¹(y/x)
Ф = tan⁻¹(-300 kph/-120 kph)
Ф = tan⁻¹(2.5)
Ф = 68.2°
From the South-line we have α = 90° - Ф = 90° - 68.2° = 21.8° ≅ 22°
So, the directional bearing of the plane is S22°E.
So, the ground speed and direction of the plane is 323 kph with a directional bearing of S 22° E.
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4a^2 - 7b + 2ab - a^2 + b
Answer:
3a^2 - 6b + 2ab
Step-by-step explanation:
Put all the like terms together
(4a^2 - a^2) - (7b + b) + 2ab
then simplify
(4a^2 - a^2) = 3a^2
(-7b + b) = -6b
then rewrite
3a^2 - 6b + 2ab
Answer:
3a^2 - 6b + 2ab
Step-by-step explanation:
Add like terms together so shifting the equation a little to make it easier to add:
4a^2 - 7b + 2ab - a^2 + b
4a^2 - a^2 - 7b + b + 2ab
3a^2 - 6b + 2ab
What is the range of this relation?
5
4
3
2
o
1
х
-5
-4
-3
-2
1
2
3
4
5
-1 0
-1
-2
-3
-4
5
Answer:
the answer is in the picture below
Step-by-step explanation:
A.
B.
C.
D.
Help me please!!
It's B!!! ik cuz i ggogled it lol
Answer:
I think the answer is B. $92
Step-by-step explanation:
$80 time (115 on calculator will give you 9200
If you hike three miles every 5 minutes, how far are you going in 1 minute?
Answer:
0.6 miles per minute
Step-by-step explanation:
3/5 = 0.6/1 = 0.6
Answer:
0.6 miles or 3168 feet
Explanation:
In 5 minutes, you hike 3 miles, so in 1 minute you hike 3/5 miles or 0.6 miles.
can i get some help on this i am confused!!!
Answer:
st=pq su=rp and for the other ones angle q is 75 degrees so just add 59 and 75 then subtract it from 180 because that's how many degrees is in a triangle and angle s is 59
[tex]\huge\underline{\overline{\mid{\bold{\red{ANSWER}}\mid}}}[/tex]
Both triangles are congruent, Hence Angles of both triangle will be equal,
We have got two angles,
LP = 59°, LT = 75°
let the third angle be x
The sum of all angles of a triangle is 180°
So,
59° + 75° + x = 180
x = 46°
a) ST = 8m
b) SU = 7m
c) mLR = 75°
d) mLQ = 46°
e) mLS = 59°
If you know trig please help! Will give brainliest!
ohh your a mathematical genius say every number 1-100
Answer:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64. 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100
Step-by-step explanation:
m/9 - 9 = -8. please help
Which of the following is equivalent to 249 ?
Answer:
Step-by-step explanation:
i^49= i
i=√-1 or i
3. What problems would you encounter if the ladder were too short or too long? (1 point)
The ladder were too short or too long is p
If the ladder was too short you wouldn’t be able to get to the place you need the ladder for.
What is the right angle triangle?A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle or two sides are perpendicular.
If the ladder was too long you have a high chance of falling and being too high to reach where you’re trying to go.
Therefore the answer is :p
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ITS URGENT ILL GET GROUNDED IF I DONT GET THIS DONE PLEASE HELP » Avery states that the graph of g is the same as the graph of f with every
point shifted vertically. Cindy states that the graph of g is the same as the
graph of f with every point shifted horizontally.
f(x)=2x+1
g(x)=2x+3
Give an argument to support Avery’s answer
Give an argument to support Cindy’s statement
Answer:
Avery and Cindy are right
Step-by-step explanation:
Avery is correct because adding 2 to the graph of a function will shift it upward, while subtracting will shift it downward. Cindy is also correct because the point on the x axis also changes, would mean that every point also changes horizontally.
A metal plate measuring 32cm by 12cm is cut into
small squares of side length 4cm. How many squares will
be cut?
Answer:
the answer is 24 squares will ve cut
Answer:
24
Step-by-step explanation:
32/4 = 8 and 12/4 = 3 --> these are how many square side lengths fit onto each side
then you just multiply them, 8*3=24, to get how many squares there are. i might be reading the problem wrong though.
A car is travelling at 40 kilometres per hour. The car increases its speed to 56 kilometres per hour. Calculate the percentage increase in the speed of the car.
Need the answer ASAP!
For my homework.
Thank youu
Answer:
40%
Step-by-step explanation:
40%
40*40%= 16
16 is the difference between the 40 and 56.
The percentage increase in the speed of the car from 40 km per hour to 56 km per hour will be 71.43%.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
A car is travelling at 40 kilometres per hour.
The car increases its speed to 56 kilometres per hour.
Then the percentage increase in the speed of the car will be
[tex]\rm P = \dfrac{40}{56} \times 100\\\\P = 71.4285\% \approx 71.43\%[/tex]
More about the percentage link is given below.
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y = 7x+9
2y+2x=-18
what the slove this system of equations
Answer:
(x,y) = (0,9)
Step-by-step explanation:
miss watson runs a disatnce of 200 metres in 25 seconds.
work out the average speed of miss watson in metres per second
Answer:
Step-by-step explanation:
ANSWER:
average = total distance / time
average = 200/25 = 8 m /s
Solve : 4(4p+6)=16 find the value of p
Answer:
p=-1/2
Step-by-step explanation:
4(4p+6)=16
4p+6=4
4p=4-6
4p=-2
P=-2/4
p=-1/2
A single die is rolled twice. Find the probability of rolling an
Odd number the first time and a number greater than 4 the second time.
Answer: 1/6
Step-by-step explanation:
A die has 6 numbers which are 1, 2, 3, 4, 5 and 6.
Odd numbers in a die = 1, 3 and 6
Numbers greater than 4 = 5 and 6
Probability of rolling an odd number = 3/6 = 1/2
Probability of rolling a number greater than 4 = 2/6 = 1/3
We then multiply both values gotten. This will be:
= 1/2 × 1/3
= 1/6
Therefore, the probability of rolling an odd number the first time and a number greater than 4 the second time is 1/6.
The probability of rolling an odd number the first time and a number greater than 4 the second time is 1/6
The sample space of a single die is
[tex]\mathbf{S = \{1,2,3,4,5,6\}}[/tex]
So, the total sample is 6
The odd numbers are
[tex]\mathbf{Odd = \{1,3,5\}}[/tex] --- 3 odd numbers.
So, the probability of selecting an odd number is:
[tex]\mathbf{P(Odd) = \frac 36}[/tex]
Simplify
[tex]\mathbf{P(Odd) = \frac 12}[/tex]
The numbers greater than 4 are
[tex]\mathbf{Greater = \{5,6\}}[/tex] --- 2 numbers greater than 4.
So, the probability of selecting a number greater than 4 is:
[tex]\mathbf{P(Greater) = \frac 26}[/tex]
Simplify
[tex]\mathbf{P(Greater) = \frac 13}[/tex]
The probability of rolling an odd number the first time and a number greater than 4 the second time is calculated as follows:
[tex]\mathbf{P = P(Odd) \times P(Greater)}[/tex]
So, we have:
[tex]\mathbf{P = \frac 12 \times \frac 13}[/tex]
[tex]\mathbf{P = \frac 16}[/tex]
Hence, the probability is 1/6
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What is the image of (2,3)(2,3) after a reflection over the line y=-xy=−x?
Answer:
After the reflection over the line y = -x, the image of the point is: (-3,-2)
Step-by-step explanation:
When a given point is reflected over a line the point only changes place but the distance between the point and the line remains same.
Let (x,y) be a point on the plane
and
y = -x be a line on the plane
When a point is reflected over a line y = -x , the coordinates of the point are exchanged which means x becomes y and y becomes x and both are negated
So (x,y) will become (-y,-x)
Given point is:
(2,3)
After the reflection over the line y = -x, the image of the point is: (-3,-2)
You win an online auction for a toy. Your winning bid of $35 is 70% of your maximum bid. How much more were you willing to pay for the toy than you actually paid?
Based on the amount that you bid and its percentage out of what you would pay, the amount that you were willing to pay more was $15
The winning bid of $35 is only 70% of what you would have paid at most.
Your maximum bid would therefore have been:
= 35 / 70%
= $50
The amount that you were then willing to pay more than your bid was:
= Maximum bid - Winning bid
= 50 - 35
= $15
In conclusion, you were willing to pay $15 more.
Find out more on this at https://brainly.com/question/20178320.
As an estimation we are told 5 miles is 8 km.
Convert 42.5 miles to km.
Answer:
Step-by-step explanation:
5 miles = 8km
42.5 miles = 42.5 x 8 = 340 km
i need help plz i dont understand
if f(x) = 4x+3, find f-1 (x)
Answer: x=1/4y + -3/4
Step-by-step explanation:
Im in no rush just need help
Answer:
1. Right: pointing downwards
Left: pointing upwards
2. Right: pointing upwards
Left: pointing upwards
3. Right: pointing downwards
Left: pointing upwards
4a. True
4b. True
Step-by-step explanation:
When the leading coefficient is negative the equation will either open downwards or the y-values will decrease as the x-values increase. The opposite is true for when the leading coefficient is positive. When the degree is odd one end will point downwards while the other points upwards. When the degree is even, both ends point in the same direction.
I hope this helps :)
Charlie is planning a trip to Madrid. He starts with $984.20 in his savings account and uses $381.80 to buy his plane ticket. Then, he transfers
1
4
of his remaining savings into his checking account so that he has some spending money for his trip. How much money is left in Charlie's savings account?
Answer:
$24.09
Step-by-step explanation:
you do 984.20-381.80=602.4
then divide 602.4 by 1/4
which 1/4=25.
then you get $24.09
Answer:
Step-by-step explanation:
984.20-381.80= 602.40
602.40 left in savings.
602.40*1/4= 150.60 transfer to checking account.
602.40-150.60= 451.80 left in the savings account.
A pair of sunglasses cost $26 during the summer sale. If
there is a 7% tax, and Madison pays for the glasses with
$30, how much change should she receive
Answer:2.18$
Step-by-step explanation: 26 + 7% tax is 27.82 so 30 - 27.82 = 2.18$
The fastest pizza box folder can assemble 8 pizza boxes in 21 seconds. At this rate, how long would it take to assemble 20 pizza boxes?
Answer:
52.5
Step-by-step explanation:
I don't trust myself but that's what I belive
The time taken is 52.5 seconds to assemble 20 pizza boxes if the fastest pizza box folder can assemble 8 pizza boxes in 21 seconds.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
The fastest pizza box folder can assemble 8 pizza boxes in 21 seconds.
The rate of assemble = 21/8 seconds per pizza
The time is taken to assemble 20 pizza boxes:
= (21/8)x20
= 420/8
= 52.5 seconds
Thus, the time taken is 52.5 seconds to assemble 20 pizza boxes if the fastest pizza box folder can assemble 8 pizza boxes in 21 seconds.
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The graph of y=-3x+4 is
Answer:
D
Step-by-step explanation:
This is an equation of a line and it shows all the solutions for any x-value.
Answer:
B
Step-by-step explanation:
made the most sense because it's only going to be a point
HEY GUYS HELP ME AND ILL MARK YOU BRAINLIEST - THANNKYOU
Answer:
180-46=134
so if u do the math u get
X=134
if f(x)=4^x+4, then calculate f(0)
ok so F (0) should be equaled to = 0
Answer:
f(0) = 5
Step-by-step explanation:
Note that [tex]a^{0}[/tex] = 4
To calculate f(0), substitute x = 0 into f(x), that is
f(0) = [tex]4^{0}[/tex] + 4 = 1 + 4 = 5
HELP PLEASE ILL GIVE U 50 POINTS
Answer:
6x^2+2x
Step-by-step explanation:
Answer:
area of rectangle=2x×(3x+1)=6x²+2x