7. An aircraft flies 400 km from a point O on a bearing of 025°
and then 700 km on a bearing of 080° to arrive at B.
a) How far north of O is B?
b) How far east of O is B?
Answer:
484 km north858 km eastStep-by-step explanation:
You want the distances north and east of the origin that a plane ends up after flying 400 km at a bearing of 25°, then 700 km at 80°.
Coordinate transformationFor some distance r and bearing angle θ, the (north, east) coordinates will be ...
(north, east) = (r·cos(θ), r·sin(θ))
ApplicationFor the trip at hand, the final coordinates of the plane are ...
a)Distance north = (400 km)cos(25°) +(700 km)cos(80°)
= 362.52 km +121.55 km = 484.07 km
B is about 484 km north of O.
b)Distance east = (400 km)sin(25°) +(700 km)sin(80°)
= 169.05 km +689.37 km = 858.41 km
B is about 858 km east of O.
__
Additional comment
Rectangular coordinates of a point at distance r from the origin and an angle θ measured CCW from the +x axis are given by ...
(x, y) = (r·cos(θ), r·sin(θ))
You may notice the similarity to the coordinates described above. That is why we can use a calculator the way we have in the attachment. The imaginary part of the complex number represents the distance east.
Seventy-seven million people were born between 1946 and 1964. The us census classifies this group of individuals as baby boomers. It is said that today and
Write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.
E (-8,9)
F(-4,9)
G(-4,2)
D(2,-8)
The coordinates of the vertices E (-8,9), F(-4,9), G(-4,2), and D(2,-8) when rotated 90° counterclockwise around the origin of the new coordinates will be E'( - 9, - 8 ), F'( - 9, - 4 ), G'( - 2, - 4 ), and D'( 8, 2 ).
A point A( x, y ) becomes A' when a point is rotated 90 degrees counterclockwise about the origin ( - y, x ). To put it another way, flip x and y, and make y negative.
Therefore, when point E( - 8, 9 ) is rotated 90° counterclockwise around the origin will be:
E'( - 9, - 8 )
When point F( - 4, 9 ) is rotated 90° counterclockwise around the origin the new point will be:
F'( - 9, - 4 )
When point G( - 4, 2 ) is rotated 90° counterclockwise around the origin the new point will be:
G'( - 2, - 4 )
When point D( 2, - 8 ) is rotated 90° counterclockwise around the origin the new point will be:
D'( 8, 2 )
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(6x²y − 7) − (3xy² + x²y² − 2)
Answer:
-x^2y^2+6x^2y-3xy^2-5
Step-by-step explanation:
It kind of depends on what you are planning to do with the following expression. However, if you are looking to simplify the expression, the solution is:
[tex]6x^2y-3xy^2+x^2y^2-9[/tex]
Hope this helps! If not, feel free to comment below and I will see what else I can do to help. If it did help, lmk! Thanks and good luck!
A light bulb manufacturer did an inventory count
on the last day of the corporate financial year
It showed they had 2000 bulbs in the warehouse
Each bulb had been purchased at a delivered
cast of £2 with a average delivery cost of f0:30
per bulb and light bulbs have selling price of
£2.20 what is the value of the inventory.
The value of the inventory will be 4000
Bulbs in the warehouse: 2000 bulbs
Cost of each bulb to the manufacturer: 2
Average delivery cost = 0.30
The selling price of the bulb = 2.20
Value of inventory: The monetary value assigned to the items in inventory at the end of an accounting period is known as inventory valuation. The inventory is valued based on the expenses incurred to get it and prepare it for sale.
The biggest current business assets are inventories. You can assess your cost of goods sold (COGS) and, ultimately, your profitability, thanks to inventory valuation.
The value of the inventory is calculated on the cost price, therefore the value of the inventory will be:
= Cost of each bulb*Number of bulbs
= 2000*2
= 4000
So, the value of the inventory will be 4000
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Question 4 true or false?
Answer:
True.Step-by-step explanation:
Solve equation:
1/5 / 2 = 1/10= 0.2 / 2 = 0.1=0.1 = 1/100.1 = 0.1 = 1/10This is true.Answer: true
0.1=[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
[tex]\frac{1}{5}/2[/tex]
Express [tex]\frac{1}{5}/2[/tex]
as a single fraction.
[tex]\frac{1}{5*2}[/tex]
Multiply 5 and 2 to get 10.
[tex]\frac{1}{10}[/tex]
FACTOR
[tex]\frac{1}{2.5}[/tex] =0.1
4(xy)² – 2x + 5y for x = 6 and y
=2
Answer:
574
Step-by-step explanation:
3. Write the number: three hundred
seven thousand, fifty-nine and six
tenths
S
V = 4 + at, solve for a.
Answer: a=(V-4)/t
Step-by-step explanation:
V = 4 + at
V-4=at
a=(V-4)/t
How much cardboard will Jayden need to make the box?
OA 60 ft²
OB. 96 ft²
OC. 128 ft²
OD. 144 ft²
Jayden needs (C) 128 ft² cardboard to make a box.
What are parallelograms?A parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides in Euclidean geometry. A parallelogram's opposite or facing sides are of equal length, and its opposite angles are of equal measure. The congruence of opposite sides and angles is a direct result of the Euclidean parallel postulate, and neither condition can be proven without resorting to the Euclidean parallel postulate or one of its equivalent formulations.The net is made up of six parallelograms, each representing one of the box's faces.
Four rectangular faces with dimensions of 6 ft × 4 ftThe other two faces are square in shape, with side lengths of 4 feet.The area represented by the net can be used to estimate how much cardboard Jayden will need to make the box.
The calculations are as follows:
Rectangular faces: length × height = 6 ft × 4 ft = 24 ft²Square faces: side length² = (4 ft)² = 16 ft²So, our rectangles and two squares:
4 × 24 ft² + 2 × 16 ft² = 96 ft² + 32 ft² = 128 ft².Therefore, Jayden needs (C) 128 ft² cardboard to make a box.
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PLEASE HELP!!!What is the effect on the graph of
f(x)=∣x∣when the function is changed to g(x)=∣3x∣+1?
A.
The graph is compressed vertically and shifted to the right 1 unit.
B.
The graph is stretched vertically and shifted to the left 1 unit.
C.
The graph is stretched horizontally and shifted up 1 unit.
D.
The graph is compressed horizontally and shifted up 1 unit.
Answer:
24
23fc
23
45jh4
66
35g
35
56
34
84x7 complete the equation
Answer:
The answer to your question is 588
Answer:
588
Hope this helps
solve 3cosx = 2+cosx
x= 0.
Step-by-step explanation:1. Write the expression.[tex]3cosx = 2+cosx[/tex]
2. Divide both sides by 3.[tex]\frac{3cosx}{3} = \frac{2+cosx}{3} \\\\\frac{3cosx}{3} = \frac{2}{3} +\frac{cosx}{3} \\ \\cosx=\frac{2}{3} +\frac{cosx}{3}[/tex]
3. Subtract [tex]\frac{cosx}{3}[/tex] from both sides.[tex]\frac{3cosx}{3} = \frac{2+cosx}{3} \\\\\frac{3cosx}{3} = \frac{2}{3} +\frac{cosx}{3} \\ \\cosx-\frac{cosx}{3}=\frac{2}{3} +\frac{cosx}{3}-\frac{cosx}{3}\\ \\\\cosx-\frac{cosx}{3}=\frac{2}{3}[/tex]
4. Simplify the fraction subtraction.[tex]\frac{3cosx}{3} -\frac{cosx}{3}=\frac{2}{3}\\ \\\frac{3cosx-cosx}{3}=\frac{2}{3}[/tex]
5. Multiply both sides by 3.[tex]3*\frac{3cosx-cosx}{3}=\frac{2}{3}*3\\ \\3cosx-cosx=\frac{6}{3}\\ \\3cosx-cosx=2[/tex]
6. Solve the subtraction.[tex]2cosx=2[/tex]
7. Divide both sides by 2.[tex]\frac{2cosx}{2} =\frac{2}{2} \\ \\cosx=1[/tex]
8. Take [tex]cos^{-1}[/tex] from both sides.[tex]cos^{-1}(cosx) =cos^{-1}(1)\\ \\x=cos^{-1}(1)\\ \\x=0.[/tex]
Hey y’all, 10 pm now :( got one more question and then I’ll be gone so pls help
Answer:
x=27 or x= -8
Step-by-step explanation:
rearrange the terms
convert the expression
simplify the expression
rewrite the equation
solve the equation
formulate new equations
I can't show the full steps since there's no image
Answer:
this is answers
scan and see
what is42089 divided by 8
Answer:
5261
Step-by-step explanation:
your welcome
If x varies directly as y and when x = 5, y = 20. Find the relationship between x and y.
the relationship between x and y when x varies directly is 4 x = y.
We know that when x varies directly with y, then:
x = k y
Now, we have x = 5 and y = 20
Substituting the values in the expression, we get that:
5 = 20 k
k = 5 / 20
k = 1 / 4
So, we get the relation as:
x = 1 / 4 y
4 x = y
Therefore, the relationship between x and y when x varies directly is 4 x = y.
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After a person gets a 2% raise in salary, the new salary is $11874. What was the original salary?
Answer:
Original salary was $11641.17Step-by-step explanation:
Let the initial salary be x.
Set equation and solve for x:
x + 2% of x = 11874x + x*2/100 = 11874x + 0.02x = 118741.02x = 11874x = 11874/1.02x = 11641.17 (rounded to the nearest cent)
Answer:
The original salary is $11641.18.
Step-by-step explanation:
The equation will be,
→ x + (x × 2)/100 = 11874
Now the original salary will be,
→ x + (x × 2)/100 = 11874
→ x + 0.02x = 11874
→ 1.02x = 11874
→ x = 11874/1.02
→ x = 11641.1764706
→ [ x = 11641.18 ]
Hence, original salary is $11641.18.
Does 7*10 to fifth power equal 7*100,000?
Find three consecutive even integers such that the square of the third is 52 more than the square of the second.
The Three consecutive numbers will be 24.5, 25.5, 26.5
We have to take three consecutive numbers. Let the first number be 'x' and the consecutive two numbers be (x + 1), and (x + 2).
It is given that the square of the third number is greater than the square of the second number by 52. We need to create an equation that represents this situation. So, we get :
=> (x + 2)² = (x + 1)² + 52
=> x² + 4x + 4 = x² + 2x + 1 + 52
=> x = 49/2 => x = 24.5
We get value of x = 24.5. Putting this value of x in consecutive numbers we get the first, second, and third numbers as 24.5, 25.5, and 26.5 respectively.
Hence, we get the three consecutive numbers: 24.5, 25.5, and 26.5
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Whitney buys two submarine sandwiches for an after-school party. One sandwich is 45 inches long and the other sandwich is 20 inches long. Whitney wants to cut servings of the same length from both sandwiches, without having any sandwich left over. What is the greatest length serving that Whitney can cut?
Answer:
5 inches
Step-by-step explanation:
Whitney wants the greatest length that is an even divisor of both 45 inches and 20 inches.
Greatest common factorThe length Whitney is looking for is called the "greatest common divisor" (GCD) or "greatest common factor" (GCF) of the two numbers 45 and 20. There are a couple of different ways this can be found.
FactoringThe prime factors of the two numbers are ...
45 = 3×3×5
20 = 2×2×5
The only factor common to the two products is 5. It is the greatest common factor.
Whitney can cut lengths of 5 inches.
Euclid's algorithmAnother way to find the GCD is to use Euclid's algorithm. That has you ...
Divide the larger number by the smaller and keep the remainder.If the remainder is not zero, replace the larger number with it and repeat.If the remainder is zero, the smaller number is the GCD.Using this algorithm, we have ...
45/20 = 2 r 5
20/5 = 4 r 0 . . . . . The GCD is 5
Whitney can cut lengths of 5 inches.
mayas penny bank is 1/2 full. after she adds 120 pennies,it is 2/3 full. How,many pennis can mayas bank hold?
Answer:
720
Step-by-step explanation:
We are looking for the difference between 2/3 and 1/2, which we know to be 120. To subtract fractions of different denominators, we need to find the common denominator (this can be found by finding the LCM of both denominators)
120 = 2/3 - 1/2 = 4/6 - 3/6
1/6 = 120
We can multiply 120 by 6 to find the value of the full bank.
1/1 = 720
Your cell phone plan costs $24.99 per month plus $0.19 for each text message you send or receive. You have at most $34 to spend on your cell phone bill. What is the maximum number of text
messages that you can send or receive next month?
The maximum number of text messages is
Answer:
33
messages
Step-by-step explanation:
Find the a) down payment, and b) amount of the mortgage loan. 2. Alvira and Barry Gomez purchased a home priced at $280,000. They put down 40%.
The down payment is $112,000.
And, Amount of the mortgage loan is $168,000.
Here,
Alvira and Barry Gomez purchased a home priced at $280,000.
They put down 40%.
We have to find down payment.
And, Amount of the mortgage loan.
What is Down payment?
A sum of money that a buyer pays in the early stages of purchasing an expensive good or service is called down payment.
Now,
Alvira and Barry Gomez purchased a home priced at $280,000.
They put down 40%.
Hence, The down payment = $280,000 x 40%
= $280,000 x 40 / 100
= $112,000
And, Amount of the mortgage loan = Total amount - Down payment
= $280,000 - $112,000
= $168,000
Therefore, The down payment is $112,000.
And, Amount of the mortgage loan is $168,000.
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5- b = 2t Solve for t or f I give extra points
Answer:
[tex]t = - \frac{1}{2} b + \frac{5}{2} [/tex]
Graph the compound inequality 6x+2y<12 or x-6y>6
The graph of the compound inequalities with intersection points
(2.21, -0.63) is given below.
Please see the graph attached.
What is compound inequality?A compound inequality has two inequality statements joined either by the "or" or “and.”
We have,
6x+2y<12 or x-6y>6
We can graph each inequality.
And we also need to see the intersection between the inequalities.
Let,
6x + 2y = 12____(1)
x - 6y = 6_______(2)
From (1)
x = (12 - 2y ) / 6 put in (2)
(12 - 2y) / 6 - 6y = 6
2 - 1/3y - 6y = 6
2 - 6 = (1/3)y + 6y
-4 = 19y / 3
y = -12 / 19
y = - 0.63 put in (1)
6x + 2 x (-0.63) = 12
6x = 12 + 1.26
x = 13.26 / 6
x = 2.21
The point of intersection on the graph is (2.21, -0.63).
Thus the graph of the compound inequalities with intersection points (2.21, -0.63) is given below.
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help is appreciated!!!! NEED HELP ASAP.
Answer: wouldn't that be 10 feet and 8 feet?
Step-by-step explanation:
because they both are the same size on both sides
and i have no clue if that helped
Answer:
Area of two rooms is 357 square feet
Length of the baseboards = 89.5 ft
Step-by-step explanation:
Area and perimeter of rectangular room:Area of the room = length * width
Area of the two rooms = area of bigger room + area of smaller room
= 19 * 15 + 8 * 9
= 285 + 72
= 357 square feet
To find the length of the baseboard, we need to subtract the width of the opening (5 feet) and width of the entry (2 1/2 feet) from the perimeter of the bigger room and subtract the width of the opening (5 feet) from the perimeter of the smaller room.
Bigger room:
length = 19 ft
Width = 15 ft
Width of the entry = 2 1/2 ft = 2.5 ft
Width of the opening between two rooms = 5 ft
Perimeter of bigger room = 2l + 2w - 5 - 2.5
= 2*19 + 2*15 - 7.5
= 38 + 30 - 7.5
= 60.5 ft
Smaller room:
length = 8ft
Width = 9 ft
Width of the opening = 5 ft
Perimeter of the smaller room = 2*8 + 2*9 - 5
= 16 + 18 - 5
= 29 ft
Length of the base board = 60.5 + 29
= 89.5 ft
express 7.065 as a mixed number
Answer: [tex]7 \frac{13}{200}[/tex]
Step-by-step explanation:
7.065=
[tex]7 \frac{65}{1000}[/tex]= ==> GCF of 65 and 1000 is 5
[tex]7 \frac{65/5}{1000/5}[/tex]=[tex]7 \frac{13}{200}[/tex]
A theater charges $8 for main-floor seats and $4 for balcony seats. If all seats are sold, the ticket income is $5200. At one show, 25% of the main-floor seats and 50% of the balcony seats were
income was $1800 How many seats are on the main floor and how many are in the balcony?
By solving a system of equations we can see that there are 400 main-floor seats and 500 balcony seats.
How many seats are on the main floor and how many are in the balcony?Let's define the two variables:
x = number of seats on the main-floor.y = number of balcony seats.We know that if all the seats are sold, then the total income is $5,200, we can write the equation:
x*$8 + y*$4 = $5,200
And if 25% of the main-floor and 50% of the balcony seats are sold, then we get an income of $1800, then we can write:
0.25*x*$8 + 0.5*y*$4 = $1,800
x*$2 + y*$2 = $1,800
So we have a system of equations:
x*$8 + y*$4 = $5,200
x*$2 + y*$2 = $1,800
If we subtract twice the second equation for the first one we get:
(x*$8 + y*$4) - (x*$2 + y*$2) = $5,200 - 2*$1,800
x*$4 = $1,600
x = $1,600/$4 = 400
So there are 400 seats on the main-floor.
Using the first equation we can find:
x*$8 + y*$4 = $5,200
400*$8 + y*$4 = $5,200
$3,200 + y*$4 = $5,200
y*$4 = $5,200 - $3,200 = $2,000
y = $2,000/$4 = 500
So there are 500 balcony seats.
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what is the perimeter of a regular, triangular yield sign with aside length of 15 in
45 inches s the perimeter of a regular, triangular yield sign with aside length of 15 in
What is perimeter?The perimeter of a shape is the sum of the lengths of all its edges. For example, a triangle has three edges, so its perimeter is equal to the sum of those three lengths.
The perimeter of a square can be easily calculated if one side and all other sides are given as being the same length; for example, a square with sides measuring 5 inches long has a perimeter of 20 inches because 5 x 4 = 20. By multiplying the sum of the length and width by two, one can determine a rectangle's perimeter.
We will use the simple perimeter formula as yield sign is equilateral triangle
So, 15 × 3 = 45 inches
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Can you help make a 10 help you add 7+4+5 explain
Answer:
16
Step-by-step explanation: