Answer:
The distance between the two jets is approximately 2.947 kilometers.
Step-by-step explanation:
From the statement we know the location of each jet in polar coordinates, which are defined by the following notation:
[tex]\vec r = (r, \theta)[/tex] (1)
Where:
[tex]r[/tex] - Distance of the jet from the origin, measured in kilometers.
[tex]\theta[/tex] - Angle of the jet with respect to the east direction, measured in sexagesimal degrees.
To transform polar coordinates into rectangular coordinates, we use the following expressions:
[tex]x = r\cdot \cos \theta[/tex] (2)
[tex]y = r\cdot \sin \theta[/tex] (3)
And lastly, we determine the distance between the two jets ([tex]d[/tex]), measured in kilometers, by the Pythagorean Theorem:
[tex]d = \sqrt{(r_{2}\cdot \cos \theta_{2}-r_{1}\cdot \cos \theta_{1})^{2}+(r_{2}\cdot \sin \theta_{2}-r_{1}\cdot \sin \theta_{1})^{2}}[/tex] (4)
If we know that [tex]r_{2} = 4\,km[/tex], [tex]\theta_{2} = 150^{\circ}[/tex], [tex]r_{1} = 2\,km[/tex] and [tex]\theta_{1} = 195^{\circ}[/tex], the distance between the two jets is:
[tex]d = \sqrt{[(4\,km)\cdot \cos 150^{\circ} -(2\,km)\cdot \cos 195^{\circ}]^{2}+[(4\,km)\cdot \sin 150^{\circ} -(2\,km)\cdot \sin 195^{\circ}]^{2}}[/tex]
[tex]d \approx 2.947\,km[/tex]
The distance between the two jets is approximately 2.947 kilometers.
what is the value of -2 1/6 - 1 1/4 + 1 3/4
Answer:
Step-by-step explanation:
-2 1/6-1 1/4 +1 3/4
[tex]=-\frac{13}{6} -\frac{5}{4} +\frac{7}{4} \\(L.C.M. ~of ~6,4,4=12)\\=\frac{-26-15+21}{12} \\=-\frac{20}{12}\\=-\frac{5}{3} \\=-1 \frac{2}{3}[/tex]
in 2010 an item cost $200. The price increase by 1.5% each year. How much wil it cost in 2030?
Round
your
answer to the nearest cent.
Step-by-step explanation:
Let P be price after t year . From the formula of compounding
P = 9 (1.015)^t
Taking log to the base e on both sides
ln P = ln 9 + t ln 1.015
= (2.197 + .0149t )
P = e^{(2.197+.0149t)}
Please help me, I am bad at math so please help
A gum tree reached a height of 150 ft in 15 years. Cathy and Darla write different equations to find the yearly average growth g of the tree. Cathy writes 15g = 150. Darla writes 150/15 = g. Do these equations have the same solution? Explain.
Answer:
Yes, they have the same answer because because 150/15 = 10 and in the equation 15g = 150, you have to solve it by dividing 150 by 15 which gets 10. Therefor, they are the same.
Step-by-step explanation:
Answer: They have the same solution.
Step-by-step explanation: 15g=150 has an answer of 10 ft. (divide 150 by 15 to get g alone.) 150/15=g has an answer of 10 as well. (Simplify to find g.)
Which statement is true about the equation (see picture)
A. It has no solution.
B. It has one solution.
C. It has two solutions.
D. It has infinitely many solutions.
Answer:
D would be your answer
Step-by-step explanation:
Simplify :)
A teacher wants to split 2 erasers between 5 students equally. How many erasers will each student get?
Answer:
If the teacher wants to split an eraser into 5 pieces she/he could but they would be small pieces. if she/he splits them, each student would get one small piece and since there are two erasers, then each student would get 2 small pieces of an eraser.
Step-by-step explanation:
Mario is tracking the progress of his plant's growth. After 4 days the plant was 5 cm high. 13 days later the plant was 18.5 cm tall.
What is the rate of growth of the plant?
How tall was the plant when Mario planted it?
How tall will the plant be after 20 days?
Answer:
sjdhdjdbdkendbdidjdnd
Ill mark brainliest to the correct answer
Answer:
I think 1/5 would be the answer
Step-by-step explanation:
I hope this helps
Ben gets 5 more presents than his naughty little sister Gwen this holiday season. If together they receive 21 presents, how many
presents does each kid receive?
9514 1404 393
Answer:
Ben: 13Gwen: 8Step-by-step explanation:
The given relations give rise to two equations:
b = g + 5
b + g = 21
Using the first to substitute for b in the second, we have ...
(g +5) +g = 21
2g = 16 . . . . . . . subtract 5
g = 8 . . . . . . . . . divide by 2
b = 8 +5 = 13
Ben got 13 presents; Gwen got 8.
For the diagram below let m∠1 = (7x + 5)°, m∠2 = (9x − 8)°, and m∠3 = (11x − 15)°. A triangle with exterior angles 1, 2, 3. Complete the work shown to find the m∠3. Set the sum of the exterior angles to 360° and solve for x. 7x + 5 + 9x − 8 + 11x − 15 = 360 27x − 18 = 360 27x = 378 x = 14 Substitute the value of x into the expression that represents mAngle3. mAngle3 = 11(14) – 15 mAngle3 = °
Answer:
139
Step-by-step explanation:
Answer:
I put 139 and got it right!
Step-by-step explanation:
hope this helps :)
A truck driver has to make a delivery at a location that is 230.2 miles away. She drives an average of 55 miles each hour for 3.25 hours. If the truck driver continues at the same speed, will she make it to the location in the next hour?
and how many does she or he have to go
Answer:
The driver will make it to the location in the next hour
Step-by-step explanation:
First, find how many miles they traveled in 3.25 hours, by multiplying 55 by 3.25:
55(3.25)
= 178.75
Then, add 55 to this to see if the driver will make it in the next hour:
178.75 + 55
= 233.75
Since this is greater than 230.2, this means they will make it to the location.
So, the driver will make it to the location in the next hour.
Answer:
Yes
Step-by-step explanation:
Since the truck driver is going at an average speed of 55 miles per hour and has already driven for 3.25 hours that means she has already covered a distance of ...
55 * 3.25 = 178.75 miles
If she continues at the same speed and travels for one more hour that means that she would cover another 55 miles which would put her at a total distance of ...
178.75 + 55 = 233.75 miles
Therefore, the answer would be Yes she would arrive at her location. ;)
Use the graph to solve the system of linear equations.
x - y = 4
4x + y = 1
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The value of x and y is 1 and -3.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4y = 6 is an equation.
2x = 4 is an equation.
4x - 6x + 6x = 6 is an equation.
We have,
x - y = 4 _____(1)
4x + y = 1 _____(2)
From (1) we get,
x = 4 + y ____(3)
Putting (3) in (2) we get,
4x + y = 1
4 (4 + y) + y = 1
16 + 4y + y = 1
16 + 5y = 1
Subtract 16 on both sides.
5y = 1 - 16
5y = -15
Divide both sides by 5.
y = -3
Now,
Putting y = -3 in (3) we get,
x = 4 + y
x = 4 - 3
x = 1
Thus,
The value of x and y is 1 and -3.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ2
Consider this equation: 9x - 7 - 3x + 9 = x + 7 + 5x + 9. How many solutions does this equation have?
Step-by-step explanation:
9x - 7 - 3x + 9 = x + 7 + 5x + 9
6x + 2 = 6x + 16
2 = 16
Since 2 = 16 is false, there exist no real solutions for x.
Final Answer: No Solution. The equation would have 0 solutions.
Steps/Explanations:
Hey there! The answer is No Solution because -7 = 7. If 7 = 7, then it would be true and have one solution, which is not the case here.
Step 1: You should cancel [tex]9[/tex] on both sides.
[tex]9x - 7 - 3x = x + 7 + 5x[/tex]
Step 2: Simplify [tex]9x - 7 - 3x[/tex] to [tex]6x - 7[/tex].
[tex]6x - 7 = x + 7 + 5x[/tex]
Step 3: Simplify [tex]x + 7 + 5x[/tex] to [tex]6x + 7[/tex].
[tex]6x - 7 = 6x + 7[/tex]
Step 4: You'll need to cancel [tex]6x[/tex] on both sides.
[tex]- 7 = 7[/tex]
Step 5: Since [tex]-7 = 7[/tex] is false, there would be no solution.
No Solution
~I hope I helped you :)~
what is the cost of the item that would make these discount equivalent?
Discount:
30% off $22.50 off
Answer:
$15.75
Step-by-step explanation:
Turn the percentage into a decimal.
30% = 0.3
Multiply.
22.5 * 0.3 = 6.75
Subtract.
22.5 - 6.75 = 15.75
Best of Luck!
can someone help me on this one
The bank agrees to give you a loan of $7,000 with 1% simple interest over 2 years. How much will your monthly payments be?
Answer:
25550 is The Answer i think
I need help with this question plsss
Answer: maybe its 6
Step-by-step explanation:
i think its 6 because it has +3 so maybe adding 3+3
Use the diagram of a prism to answer the question. 4 cm, 2 cm, 3 cm. What is the total surface area of the prism?
Answer:
52cm3
Step-by-step explanation:
Solve: (3/4) divided by 6 (2/3)
Answer:
0.1875
Step-by-step explanation:
3/4/6(2/3)
3/4/12/3
3/4/4
0.75/4
=0.1875
Trent saved up $500 for summer vacation. If he spends $25 a week for eight weeks, how much money does he have left? Explain? (Can somebody help plz- )
Answer:300
Step-by-step explanation:
25*8 =200
500-200=300
Answer:
$300
Step-by-step explanation:
25 a week for 8 weeks is a total of 25*8 or 200 so he spent $200
500 - 200 is 300 so he has $300 left
nyatakan faktor faktor perdana bagi 40
Answer:
wot is this monstrosity
Help plz I really need it
Answer:
translation then reflection
Step-by-step explanation:
Mr. Johnson currently has a square garden. He wants to redesign his garden and make it into a rectangle with a length that is 5 feet shorter than three times its width. He decides the perimeter should be 70. PLEASEEEEE ITS URGENT
Answer:
Width of the rectangle = 10 feet
Length of the rectangle = 25 feet
Step-by-step explanation:
Perimeter of a rectangle = 2(length + width)
Let
Width of the rectangle = x feet
Length of the rectangle = 3x - 5 feet
Perimeter of the rectangle = 70 feet
Perimeter of a rectangle = 2(length + width)
70 = 2{x + (3x - 5)}
70 = 2{x + 3x - 5}
70 = 2(4x - 5)
70 = 8x - 10
70 + 10 = 8x
80 = 8x
Divide both sides by 8
x = 80 / 8
= 10
Width of the rectangle = 10 feet
Length of the rectangle = 3(10) - 5
= 30 - 5
= 25 feet
5 more than the product of 23 and a number n
Answer:
23n +5
Step-by-step explanation:
break down the expression into parts
5 more is +5
product is multiplication of 23 and n so 23n
then put it together
please give thanks :)
Use the pencil,plot the point (3 1/2, 2 3/4)
Answer:
The diagram of the plotting point [tex]\left(3\frac{1}{2},\:2\frac{3}{4}\right)=\left(3.5,\:2.75\right)[/tex] is attached below.
Step-by-step explanation:
Given the points
[tex]\left(3\frac{1}{2},\:2\frac{3}{4}\right)[/tex]
as
[tex]3\frac{1}{2}=\frac{7}{2}=3.5[/tex]
[tex]2\frac{3}{4}=\frac{11}{4}=2.75[/tex]
so the point can be visualized as:
[tex]\left(3\frac{1}{2},\:2\frac{3}{4}\right)=\left(3.5,\:2.75\right)[/tex]
Now, we can check the point x = 3.5, and determine the corresponding value y = 2.75 and plot the point at the location (x, y) = (3.5, 2.75)
The diagram of the plotting point [tex]\left(3\frac{1}{2},\:2\frac{3}{4}\right)=\left(3.5,\:2.75\right)[/tex] is attached below.
Temperature at 8AM was -8°. The temperature at 8 PM is 3º.
What is the change in temperature from 8 AM to 8 PM?
Answer:
11
Step-by-step explanation:
pls help needed asap
George is buying peaches and kiwis. He buys p peaches at $4.29 each and k kiwis at $2 each. What expression would you write to show the total cost of the peaches and kiwis?
Answer:
Step-by-step explanation:
the total cost, c will be
c= p(4.29)+k(2)
if the length of two sides of a triangle are 7 and 10 the length of the third side may be
A. 1
B.3
C.2
D.4
explain
Answer:
D. 4
Step-by-step explanation:
Let's look at all the options first. All of the options are below 7 and 10, hence we can deduce that it is not the hypotenuse. Looking at 7 and 10, we see that 10 is the larger number, and hence we know that 10 is the hypotenuse.
Hence, as the other two sides added up in a triangle must be larger than the hypotenuse, the only available option is 4, since 4 + 7 = 11 > 10.
Hope this helped!
Find the slope between the
following points:
(-3,3), and (5, 10)
Answer:
7/8
Step-by-step explanation:
I got it right
Answer:
7/8
Step-by-step explanation:
cuz
what are the common multiple of 4 and 6 between 1 and 42
Answer: 300
Step-by-step explanation: