Answer:
The rate of change of the distance between the airplanes is approximately 316.760 kilometers.
Step-by-step explanation:
The distance between both airplanes (r), in kilometers, can be determined by the Pythagorean Theorem, that is:
[tex]r^{2} = x^{2}+y^{2}[/tex] (1)
Where:
[tex]x[/tex] - Distance of the westbound airplane from airport, in kilometers.
[tex]y[/tex] - Distance of the southbound airplane from airport, in kilometers.
By Differential Calculus, we derive an expression for the rate of change of the distance between the airplanes ([tex]\dot r[/tex]), in kilometers per hour:
[tex]2\cdot r\cdot \dot r = 2\cdot x \cdot \dot x + 2\cdot y \cdot \dot y[/tex]
[tex]\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}[/tex] (2)
Where:
[tex]\dot x[/tex] - Rate of change of the distance of the westbound airplane, in kilometers per hour.
[tex]\dot y[/tex] - Rate of change of the distance of the southbound airplane, in kilometers per hour.
If we know that [tex]x = 17\,km[/tex], [tex]y = 28\,km[/tex], [tex]\dot x = -164\,\frac{km}{h}[/tex] and [tex]\dot y = -271\,\frac{km}{h}[/tex], then the rate of change of the distance between the airplanes is:
[tex]\dot r = \frac{x\cdot \dot x + y\cdot \dot y}{\sqrt{x^{2}+y^{2}}}[/tex]
[tex]\dot r \approx -316.760\,km[/tex]
The rate of change of the distance between the airplanes is approximately 316.760 kilometers.
Nola made the model to show multiplying a fraction by a fraction. Which multiplication sentence does the model show?
Answer:
The answer is "[tex]\frac{2}{3}[/tex]"
Step-by-step explanation:
In this question the graph file is missing which is defined in the attachment section please find it.
Let the 18 square boxes are available, 12 of those are in color.
If published in part, it will be
[tex]\to \frac{12}{18}= \frac{4}{6}=\frac{2}{3}[/tex]
There are two colors out of 3 square boxes.
Find the slope of the line that passes through each pair of points
A(4, 5) and B(–3, 5)
S(3, –6) and T(3, –9)
Answer:
A and B: slope = 0
S and T: slope = undefined
Step-by-step explanation:
To find the slope of the line that passes between a pair of points, use the slope formula, [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. Substitute the x and y values of two points into that formula and simplify.
1) Let's try this with the first problem. Substitute the x and y values of (4,5) and (-3,5) into the formula, then solve:
[tex]m = \frac{(5)-(5)}{(-3)-(4)}\\m = \frac{5-5}{-3-4} \\m = \frac{0}{-7} \\m = 0[/tex]
So, the slope of the line between A and B is 0.
2) Do the same with the second problem, substituting the x and y values of (3,-6) and (3,-9):
[tex]m = \frac{(-9)-(-6)}{(3)-(3)} \\m = \frac{-9+6}{3-3} \\m = \frac{-3}{0} \\[/tex]
However, we can't divide by zero. So, the slope between points S and T must be undefined.
help me plz..
the pair of line represented by equation 9x²+12xy+(k+1)y²=0 coincide, find the value of k
Answer:
k=3 is your answer
Step-by-step explanation:
given equation :
9x²+12xy+(k+1)y²=0
comparing above equation with
ax²+2hxy+by²
we get
a=9
h=12/2=6
b=k+1
since lines are coincident
ø=0
Tan0=±[2√(h²-ab)]/(a+b)
we get
h²=ab
6²=9(k+1)
36/9=k+1
4=k+1
k=4-1=3
The value of k will be;
⇒ k = 3
What is Equation of line?The equation of line passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;
y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The pair of equation is,
⇒ 9x² + 12xy + (k + 1)y² = 0
Now,
We know that;
The condition of coincide of pair of line ax² + 2hxy + by² = 0 is,
⇒ h² = ab
So, For the equation of the pair of line 9x² + 12xy + (k + 1)y² = 0, we have;
⇒ 2h = 12
⇒ h = 6
⇒ a = 9
⇒ b = (k + 1)
Substitute all the values in given condition for coincide , we get;
⇒ h² = ab
⇒ 6² = 9 (k + 1)
⇒ 36/9 = k + 1
⇒ 4 = k + 1
⇒ k = 4 - 1
⇒ k = 3
Thus, The value of k = 3
Learn more about the equation of line visit:
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Abdul rented a truck for one day. There was a base fee of $19.99, and there was an additional charge of 76 cents for each mile driven. Abdul had to pay
$181.87 when he returned the truck. For how many miles did he drive the truck?
miles
х
?
Answer:
The truck drove 213 miles.
Step-by-step explanation:
181.87-19.99= 161.88
161.88÷0.76= 213
!!!!!!Please help me. I will give brainiest and like!!!!!!!
The graph shows the amount
of money you are saving for
a computer.
What is the slope
Interpret the slope of the line in the context of the problem.
You meet two talking sea turtles. The sum of their ages is 388. The male turtle is 42 years older than the female. How old is the male
Answer:
the answer is b on plato
Step-by-step explanation
:
The age of the male sea turtle will be 215 years old.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
You meet two talking sea turtles. The sum of their ages is 388. The male turtle is 42 years older than the female.
Let x be the age of a male and y be the age of a female. Then the equations will be
x + y = 388 ...1
x = y + 42 ...2
From equations 1 and 2, then we have
y + 42 + y = 388
2y = 346
y = 173 years old
Then the value of x will be
x = 173 + 42
x = 215 years old
The age of the male sea turtle will be 215 years old.
More about the solution of the equation link is given below.
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What is m∠1? Help me, please
Answer:
119
Step-by-step explanation:
By using exterior angle theorem, we know that 31+angle 1 =150. therefore angle 1=119. Exterior angle theorem is where an angle exterior of an angle in the triangle addus up to 180 degreees, we also know the angles in a triangle sum to 180 degrees. Both sides have a common angle. If we subract it from the equation, we get what is said above.
Sarah's Surfboards charges a fee of $60 to rent a
surfboard and then $10.50 each hour
Sally's Surfboards doesn't charge a fee but they
cost $15.50 per hour
At how many hours will the cost be the same to rent
a surfboard for each shop?
A) 6 hours
B) 9 hours
C) 12 hours
D) 15 hours
Answer:C 12hours
Step-by-step explanation:
please answer this for me
Answer:
70
Step-by-step explanation:
you add 95 and 15 and get 110 then you do 180-110 getting 70
A car used 16 gallons of gasoline and traveled a total distance of 460 miles. The car's fuel efficiency is 30 miles per gallon on the highway and 25 miles per gallon in the city. How many gallons of gasoline were used on the highway.
Answer:
12 gallons
Step-by-step explanation:
Total gallons = 16 gallons
Total distance = 460 miles
Fuel efficiency in the highway = 30 miles per gallon
Fuel efficiency in the city = 25 miles per gallon
Let
h = gallons of gasoline were used on the highway.
460 = 30h + 25(16 - h)
460 = 30h + 400 - 25h
460 - 400 = 30h - 25h
60 = 5h
h = 60/5
h = 12 gallons
12 gallons of gasoline were used on the highway.
ILL GIVE BRAINLY THING PROMISE
look at attachment
Answer:
f(x) = (x - 6)^2 -2
vertex lies at (6, -2)
Step-by-step explanation:
Carter has 13 peppermints. Nina has p fewer peppermints than Carter. Write an expression that shows how many peppermints Nina has.
Type an asterisk ( * ) if you want to use a multiplication sign and a slash ( / ) if you want to use a division sign.
Which shows all of the solutions of the equation? h e l p
which type of triangle has side lengths of 5 in, 6 in, and 7 in? A) acute B) equilateral C) obtuse D) right
Step-by-step explanation:
we know this is not equilateral and right because not equal in size and two side square is not equal to hypotenuse the ans is a or b
Jerry's Ice Cream Hut had Chocolate or Vanilla shakes. On the 4th of July they sold 1,440 shakes total with the ratio of chocolate to vanilla being 6:9. How many chocolate shakes did they sell? Be sure to add a picture of your work showing your tape diagram. Answer using a complete sentence.
Answer: 576
Step-by-step explanation:
The road mileage between City M and several
selected cities is shown in the table. If we consider
this as a function that pairs each city with a distance
is the function a one-to-one function?
Answer:
No, it's not a one to one function
Step-by-step explanation:
In one to one function, the function is either increasing or decreasing. Also, in this type of function, the same values can not be assigned to two different domain elements.
In this case, distance from city C and City E are both 1195 miles from city M.
Thus defaults the law of one to one function.
Therefore it's not one to one function.
In the triangle shown below TB, EC and are MEDIANS; TB = 6x - 15 and DB = 5 5. Solve for x
Answer:
I am not sure on this one, sorry :(
Step-by-step explanation:
Just go down the row and say yes no yes no in order!you don't have to type the whole thing out
Answer:
1) yes
2) no
3) yes
4)no
5)no
Step-by-step explanation:
Where is -7 located? plot -7 on the number line
please help me!
Answer:
Go two back away from -5
Step-by-step explanation:
I don't know how to explain this but like start at -5 and then go back two?
Or start at -10 and go forward 3
hope it helps :)
please help me!!!!!!
Answer:
(2)
Step-by-step explanation:
mean: (13+15+17+17+17+20+27)/7=18
median: 17
mode: 17
Decrease £16855.21 by 13.5%
Answer:
£14579.76
Step-by-step explanation:
First do 16855.21 * .135 = 2275.45335 now do 16855.21 - 2275.45335 to get 14579.75665 round this to get 14579.76
Find the value of x in the isosceles triangle shown below
Step-by-step explanation:
x is the hypothnes so u can done by trigonometric formula
c2=a2+b2
×2=6square +8square
x2=36+64
x=square root of 100
x=10(sorry my phone hasn't square)
Answer:
x = 10
Step-by-step explanation:
One can assume that the line drawn down the middle splits the triangle into two congruent portions, thus it is an angle bisector, altitude, and median. This forms two congruent right triangles. Therefore, one can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states the following,
[tex]a^2 + b^2 = c^2[/tex]
Where (a) and (b) are the legs or the sies next to the right angle, and (c) is the hypotenuse or the side opposite the right angle.
Substitute in the given values and solve, remember that a median splits the base in half,
[tex](8)^2+(6)^2=c^2\\\\64 + 36 = c^2\\\\100 = c^2\\\\10 = c[/tex]
Select all the expressions that are greater than 1.
A. 5 divided by 9/10
B. 3/5 divided by 6
C. 4/5 divided by 3/7
D. 2 3/5 divided by 1 3/5
E. 12/5 divided by 13/5
PLEASE HELP THANK YOU
Select the following expressions. I will just list the letter choice:
A, C, D
Sophia and Tyler are running around a 400-meter track. They start running from the speed of 4 m/s. How long will it take Sophia to lap Tyler?
Answer:
100 minutes
Step-by-step explanation:
Given data
Total distaance= 400meters
Speed= 4m/s
We know that the expression for speed is
Speed= distance/time
substitute to find time
4= 400/time
time= 400/4
time= 100 minutes
How much more interest would you get in
3 years from 16% compounded quarterly
compared to 16% simple interest on a
$5900 deposit?
Answer:
944
Step-by-step explanation:
calculate the average rate of change in grams per day from dat 1 to day 7
Answer:
8
Step-by-step explanation:
1 2/5
rename the mixed number as an improper faction
a. 3/5
b, 12/5
c, 2/6
d, 7/5
Answer:
the answer is b
Step-by-step explanation:
i don't know I just do lol
plsss help!!!! any extra links will be reported!
Answer:
Outlier: Value that is extremely to the right or the left due to an external cause
For math: 1 is the outlier
Answer:
I am not 100% but I believe they are 1 and 6 if there are 2 answer options
Step-by-step explanation:
The least measurement is the sequence is 128. The greatest measurement is 172. Find the number of sides in this polygon given the sum of the measures is equal to 180 (n-2) degrees
Answer:
the number of sides is 12
Step-by-step explanation:
The computation of the number of sides in the polygon is shown below:
As we know that
S_n = n ÷ 2 (a_1 + a_n)
= n ÷ 2 × (128 + 172)
= 150 n
Now given that the sum of the measures = 180 (n - 2)
So,
Sn = 180 (n - 2)
150n = 180n - 360
30n = 360
n = 12
Hence, the number of sides is 12
What’s the area of the polygon?
Answer:
[tex]108 in^{2}[/tex]
Step-by-step explanation:
Separate it into 2 parts:
The first would be that the length and width of the smaller rectangle would be, 7 in. and 6 in.
7 x 6 = 42 in^2
The second would be that the length and width of the larger rectangle would be, 11 in. and 6 in.
11 x 6 = 66 in^2
Total:
66 + 42 = 108 in^2
Answer:
108 [tex]in ^2[/tex]
Step-by-step explanation:
This polygon consists of two rectangles, one in the top-right hand corner and another in the bottom. To divide these two rectangles, imagine a line extended from the central horizontal line in the polygon. As I work the problem, remember that the formula for the area of a rectangle is [tex]A=l * h[/tex], where A is the area of the rectangle, l the length of the rectangle (one of the sides), and h is the height of the rectangle (the length of a side perpendicular to l).
Starting with the top-right rectangle:
We already know one of the sides of the rectangle is 4 in, so let's imagine this to be h, because it is the height of the rectangle. Finding l is more complicated. We know the length of the larger rectangle is 12 in (more on that later) and the 6 in length is the part of the length that is not a part of the top-right rectangle. This, since the vertical line all the way to the right is straight, the length is the difference between these two lengths, or:
[tex]l=12-6=6[/tex] in
Now that we know l and h, we can evaluate the area of the first rectangle, which is
[tex]A= 6 *4= 24[/tex] in^2
Now for the bottom rectangle:
We know both l and h for this rectangle, which are 12 in and 7 in respectively. Using the area formula for a rectangle above:
[tex]A=12*7=84[/tex] in^2
Since the polygon contains both rectangles, its area is the sum of the areas of the two rectangles. Thus,
[tex]A=24+84=108[/tex] in^2
QED