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kipiarov [429]
2 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]2 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

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Given a table of values of a quadratic function, which of the following do you absolutely need in order to find its equation? *
nadya68 [22]

Answer:

The general form of a quadratic function is --> y = ax2 + bx + c

Since (0, -2) exists for the function, we can plug in those values:

-2 = a(0)2 + b(0) + c

-2 = 0 + 0 + c

-2 = c

So now our function so far is --> y = ax2 + bx - 2

We have two pairs of coordinates left: (-1, -8) and (3, -8).

First, plug in the first pair and simplify as much as you can:

-8 = a(-1)2 + b(-1) - 2

-8 = a - b - 2 ( add 2 to both sides )

-6 = a - b (stop here because we can't go further)

Second, plug in the second pair and simplify as much as you can:

-8 = a(3)2 + b(3) - 2

-8 = 9a + 3b - 2 ( add 2 to both sides )

-6 = 9a + 3b (stop here because we can't go further)

Now we have these two equations left:

a - b = -6

9a + 3b = -6

Now we solve for a and b using systems of equations, using one of three ways:

substitution

elimination

graphing (not my favorite, but it is doable)

Using substitution:

a - b = -6 can be rewritten as a = b - 6

plug into the second equation and solve for b

9(b - 6) + 3b = -6 (distribute the 9)

9b - 54 + 3b = -6 (combine all of the b's)

12b - 54 = -6 (add 54 to both sides)

12b = 48 (divide by 12 on both sides to isolate b)

b = 4

plug b into one of the original two equations

a - 4 = -6 (add 4 to both sides)

a = -2

The quadratic equation for this table is y = -2x2 + 4b - 2

6 0
2 years ago
Find the are of the SHADED region.
Mazyrski [523]
First find the area of the parallelogram


Area of parallelogram = b x h
= 12 x 7
= 84

Then find area of kite

Area of kite = (xy)/2
= (7 x 12)/2
= 84/2
= 42

Now we are gonna subtract the area of the kite from the area of the parallelogram.

84 - 42 = 42

Therefore the area of the shaded region is 42.
7 0
2 years ago
What is the value of y in the equation 4y – 2(1 – y) = –44?
Sergio039 [100]

Answer:

-7

Step-by-step explanation:

To find y, follow these steps:

4y - 2 (1 - y) = -44

First, distribute the -2 into the parenthesis:

4y - 2 + 2y = -44

The reason the 2y is positive is due to the fact that negative and negative cancel each other out and form a positive.

Now, combine like terms:

6y - 2 = -44

To get y, you need to isolate it from the constants. In order to do so, do the inverse relationship for the constant -2. To do this, add 2 to -44:

6y = -42

Now, divide six on both sides. You divide because six is currently being multiplied with y. Keep in mind that the 42 is still negative!

y = -7

Hope this helps!

4 0
3 years ago
Read 2 more answers
at a farm the ratio of cows to horses was 9:2 if there were 72 cows at the farm how many horses were there
dem82 [27]
72 divides by 9 is 8 so 2 times 8 is sixteen so that would be the answer
8 0
2 years ago
PLEASE HELP I DONT GET IT
irga5000 [103]
I think it's b but i'm not sure!
5 0
3 years ago
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