1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kipiarov [429]
3 years ago
5

Danny flies a drone in a circular path around an object that is 210 feet west and 220 feet south of his position. The drone's pa

th takes it over a point that is 160 feet east and 160 feet south of him. Find an equation for the drone's path. (Assume Danny is located at the origin, with the horizontal axis running east-west and the vertical axis running north-south)
Mathematics
1 answer:
Readme [11.4K]3 years ago
4 0

Answer:

The answer is below

Step-by-step explanation:

A circle is the locus of a points such that its distance from a fixed point is always constant.

Since the drone moves in a circular path, therefore the path of the drone forms a circle. The equation of a circle is given by:

(x - h)² + (y - k)² = r²;  where (h, k) is the center of the circle and r is the radius of the circle.

Danny is located at the origin. Since the drone flies in a circular path around an object that is 210 feet west and 220 feet south of his position. Hence the center of the circular path is (-210, -220).

Also, the drone's path takes it over a point that is 160 feet east and 160 feet south of him i.e. (160, -160). Therefore the radius of the circle is the distance between point (-210, -220) and point  (160, -160)

radius=\sqrt{(160-(-210))^2+(-160-(-220))^2}=\sqrt{140500}

Using (x - h)² + (y - k)² = r²:

[x - (-210)]² + [y - (-220)]² = (√140500)²

(x + 210)² + (y + 220)² = 140500

x² + 420x + 44100 + y² + 440y + 48400 = 140500

x² + y² + 420x + 440y - 48000 = 0

You might be interested in
2.) What value for c will make the expression a perfect square trinomial?
andre [41]

Answer : \frac{49}{4}

Given expression is x^2 - 7x + c

To make perfect square trinominal we use completing the square method

In completing the square method we add and subtract the half of square of coefficient of middle term

Here coefficient of middle term is -7

Half of -7 is \frac{-7}{2}

Square of \frac{-7}{2} is (\frac{-7}{2})^2 = \frac{49}{4}

So the expression becomes x^2 - 7x +  [tex] \frac{49}{4} that gives perfect square trinomial

Hence , the value of 'c' is \frac{49}{4}


6 0
3 years ago
Read 2 more answers
One pound of candies costs $3.50. How much will we have to pay for 3 lb?
Romashka-Z-Leto [24]

Answer: 10.50 dollars


Step-by-step explanation:

3.50 x 3 = 10.50

8 0
3 years ago
How do you find the area of a circle with the circumference?
Naya [18.7K]
Circumference = 2*pi*radius

find the radius using this formula.
 
then use this formula => area of circle = pi*radius*radius 

put the value of the radius that you get with the first formula to find the area

hope it helps you

6 0
3 years ago
Amanda went to the store to purchase ink pens. She found three kinds of pens. The first cost $4 each; the price of the second ki
KonstantinChe [14]

Answer:

Amanda buy first kind of pen = 3

Amanda buy second kind of pen = 2

Amanda buy third kind of pen = 15

Step-by-step explanation:

Given - Amanda went to the store to purchase ink pens. She found three    

            kinds of pens. The first cost $4 each; the price of the second kind

            was 4 for $1; and the cost for the third kind was 2 for $1. She bought

            20 pens and she bought at least one of each kind. (It is possible to

            buy only 1 of the pens that are "4 for $1" or "2 for $1".) The cost was

            $20.

To find - When she got back to her office, Amanda decided to turn this into

              a math problem for me. She asked: how many of each kind did I

              buy?

Proof -

Let Amanda buy first kind of pen = x

                      second kind of pen = y

                           third kind of pen = z

As given,

She bought total pen = 20

⇒x + y + z = 20          ...............(1)

Now,

As given,

cost for first kind pen = $4 for 1 pen

As she bought x pens of first kind , so

Cost of x pens of first kind = $4x

Now,

The price of the second kind was 4 for $1

⇒Cost of second kind = $\frac{1}{4} for 1 pen

As she bought y pens of send kind , so

Cost of y pens of second kind = $\frac{1}{4}y

Now,

The price of the third kind was 2 for $1

⇒Cost of third kind = $\frac{1}{2} for 1 pen

As she bought z pens of send kind , so

Cost of z pens of third kind = $\frac{1}{2}z

Now,

As given, The cost was $20

⇒4x + \frac{1}{4}y + \frac{1}{2}z = 20

⇒16x + y + 2z = 80             .....................(2)

∴ we get 2 equations

x + y + z = 20                   .....................(1)

16x + y + 2z = 80             .....................(2)

Now,

Subtract equation (1) from equation (2) , we get

16x + y + 2z  - ( x+ y + z )= 80 - 20

⇒16x + y + 2z - x - y - z = 60

⇒15x + z = 60

⇒z = 60 - 15x

Now,

Put the value of z in equation (1) , we get

x + y + 60 - 15 x = 20

⇒ y - 14x = 20 - 60

⇒y - 14x = -40

⇒14x - y = 40

⇒y = 14x - 40

Now,

we get

z = 60 - 15x

y = 14x - 40

As given

she bought at least one of each kind

it means x > 1, y > 1, z > 1

Now,

If x = 1, then y = 14 - 40 = -26

Not possible

If x = 2 , then y = 14(2) - 40 = -12

Not possible

If x = 3, then y = 14(3) - 40 = 2 and z = 60 - 15(3) = 15

Possible.

If x = 4,  then y = 14(4) - 40 = 16 and z = 60 - 15(4) = 0

Not Possible.

If x = 5, then y = 14(5) - 40 = 30 and z = 60 - 15(5) = -15

Not Possible.

∴ we get

x = 3, y = 2, z = 15

Amanda buy first kind of pen = x = 3

Amanda buy second kind of pen = y = 2

Amanda buy third kind of pen = z = 15

7 0
3 years ago
Which set of side lengths forms a right triangle?
pochemuha

Awnser:

9,12,18

Step-by-step explanation:

you have to add the smallest numbers together and it has to be greater that the greatest number.

9+12= 21

21>18

4 0
3 years ago
Other questions:
  • Mateo made the model below to represent the number of miles he swims in the
    10·1 answer
  • Gustion1
    7·1 answer
  • The difference of a number q and 8
    10·2 answers
  • Recall that if we have m vectors u1, U2, ..., um in R", then we can form the matrix A whose columns are u1, ... , Um. Let B be t
    11·1 answer
  • What is an equivalent expression for 4y plus y
    11·1 answer
  • Some large boxes of small oranges contained 344 oranges each.how many oranges were in 4 boxes?
    7·2 answers
  • Two bike riders left each other and started to ride in opposite directions. Two hours later they were 54 miles apart. If one of
    15·1 answer
  • 5lb 7oz -11oz need help quick​
    7·1 answer
  • What are the x-intercepts?​
    12·2 answers
  • I need helppppp asappp!!
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!