addison and kelsey are running on a path modeled by x^2+y^2-10x-18y-378=0, where the distance is in meters. what is the maximum distance between the runners at any given time

Answers

Answer 1

The maximum distance is the diameter of the circle, which is of 44 units.

The equation of a circle of radius r and center [tex](x_0,y_0)[/tex] is given by:

[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]

The diameter is twice the radius, and is the maximum distance between two points inside a circle.

In this problem, the circular path is modeled by:

[tex]x^2 + y^2 - 10x - 18y - 378 = 0[/tex]

We complete the squares to place it in the standard format, thus:

[tex]x^2 - 10x + y^2 - 18y = 378[/tex]

[tex](x - 5)^2 + (y - 9)^2 = 378 + 25 + 81[/tex]

[tex](x - 5)^2 + (y - 9)^2 = 484[/tex]

Thus, the radius is:

[tex]r^2 = 484 \rightarrow r = \sqrt{484} = 22[/tex]

Then, the diameter is:

[tex]d = 2r = 2(22) = 44[/tex]

The maximum distance is the diameter of the circle, which is of 44 units.

A similar problem is given at https://brainly.com/question/24992361


Related Questions

convert 0.0425 as a fraction in its simplest form​

Answers

Answer:

17/400

Step-by-step explanation:

.0425 = 425/10,000

this can be simplified to be 17/400

Tell whether the shaded figure is a reflection of the nonshaded figure

Answers

Answer:

1. isn't a reflection

2. is a reflection

3. is a reflection

answer pleaseeee!!! question below

Answers

C because it makes sense

Need answer right now!!

Answers

Answer:

20

Step-by-step explanation:

All you do is find an exponent that adds up to 24

YOU GOT A FISH TANK FOR YOUR BIRTHDAY. BEFORE YOU HEAD OFF TO THE PET STORE TO BUY SOME FISH TO FILL YOUR TANK, YOU WANT TO CALCULATE THE TANK'S VOLUME. THE FISH TANK IS A RECTANGULAR PRISM WITH A HEIGHT OF 8 CM, A WIDTH OF 7CM, AND A LENGTH OF 15 CM. WHAT IS THE VOLUME OF THE FISH TANK?

Answers

Answer:

Volume of the fish tank = 840 cm³

Step-by-step explanation:

Given:

Length of rectangular prism tank = 15 cm

Height of rectangular prism tank = 8 cm

Width of rectangular prism tank = 7 cm

Volume of the rectangular prism tank = Length × Width × Height

V = 15 × 7 × 8

V = 840 cm³

Volume of the fish tank = 840 cm³

y = x + 5
y = -2x - 4
what are the y and x values please ​

Answers

Answer:

x=-3, and y=2

Step-by-step explanation:

Since both equations are equal to y, set them equal to each other and solve for x, that way you can solve for y:

x+5=-2x-4

3x+5=-4

3x=-9

x=-3

Plugging in x=-3 into one of the original equations:

y = x + 5

y = -3 + 5

y = 2

Therefore, x=-3 and y=2. You can also write as the ordered pair (-3,2) since that's where the two equations would intercept on a graph.

Help I’ll give Brainly est

Answers

Answer:

26 sq units.......

Last week at the grocery store the price of apples was $1.60. What will the price for 5 1/2 pounds of apples?

Answers

Answer: I think the answer is $8.80

Answer:$8.80

Step-by-step explanation: You would take the 1.60 times 5 to get the number 8. Then you would take 1.60 again and times it by 0.5 to get 0.8 or 0.80. And then you would add the 0.8 and the 8 together to get your total of $8.80.

the CN Tower of Toronto, Canada is 553 M tall. how tall is the tower in cm

Answers

Answer:

The answer is 55,300.

Step-by-step explanation:

There are 100 centimeters in one meter so you can multiply by 100 to get the answer. I hope this helps! Have a great rest of your day!

Why is it important to measure angles accurately​

Answers

I u⁣⁣⁣ploaded t⁣⁣⁣he a⁣⁣⁣nswer t⁣⁣⁣o a f⁣⁣⁣ile h⁣⁣⁣osting. H⁣⁣⁣ere's l⁣⁣⁣ink:

bit.[tex]^{}[/tex]ly/3a8Nt8n

In the field of astronomy, the ability to measure angles accurately and precisely enables us to calculate the position and relative movement of the stars and galaxies in relation to each other, to determine how far distant they are from us, and even to estimate their relative size.

Will mark brainliest! Please explain, because I don't understand how to do it.

Answers

Answer:

Step-by-step explanation: The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

How many times can u Subtract 10 form a 100?

Answers

Answer:

10 times

Step-by-step explanation:

can i get brainly

If we go through it logically, it is only 1 time.

Step-by-step explanation:

Hope this helps

If 2n=6, what is n?

A. 12
B. 3
C.8
D.4

Answers

divide both sides by 2, 2/2 cancels out and 6/2 is 3, so you are left with n=3!
B. Is the answer because 6 divided by 2 is 3

2. Which expression is equivalent to (7r - 10)5
e) (5 ⦁ 7r) - (5 ⦁ 10)
f) (5 ⦁ 10) - (5 ⦁ 7r)
g) (5 ⦁ 7r) + (5 ⦁ 10)
h) 5 ⦁ 17r

Answers

E. (5 * 7r) - (5 * 10)

A large farm tractor costs $98,424, If a farmer makes 36 equal payments, how much Is each payment?

Answers

Answer:

Step-by-step explanation:

2,734 is your answer.

Help me pleaseeeeeeeeeeeeeee

Answers

Answer:   A) 729Step-by-step explanation:

The number of trees are multiplied by 3 each week.

                 Weeks)   1     2     3     4       5         6          7Number of Trees)   1     3     9     27     81     243      729 I hope that helped]Sincerely, 4018669

One card is drawn at random from a deck of cards. What is the probability that the card will be a red ace?

Answers

Answer:

Since a normal deck of cards holds 52 cards, and there are two red aces, ace of diamonds and ace of hearts. So 2/52 probability that you will draw a red ace, to simplify it is a 3.84% chance of drawing a red ace.

What is the approximate circumstances of the circle shown below?
A. 122.4 cm
B. 30.6 cm
C. 56.8 cm
D. 61.2 cm

Answers

Answer:

the answer to this is D) 61.2

Si por 3 kilogramos de manzana se pagan $20. ¿Cuánto hay que pagar por 15 kilogramos?

Answers

PLEASE ANSWER BOTH AS FAST AS POSSIBLE PLEASE HELP HELP ILL MARK BRAINLEST!!!!!

Answer:

$100

Step-by-step explanation:

15÷3=5

20•5=100

Hope this helps

Find the mean absolute deviation
21,25,30,14,26,22

please help me !!

Answers

Answer:

The answer is 4.

Step-by-step explanation:

To find the mean absolute deviation of the data you provided, you need to find the mean first. You add all the points together to get 138. Then you divide that number by how many points there are which there are 6 points so you divide 138 by 6 to get 23. Then you calculate how far away each data point is from the mean using positive distances. These are called absolute deviations. Once you add up all the numbers to get 24, you divided them by how many points there are which is 6 again. You should get 4 in the end.

Hope that helps. =)

2 groups of 17 plz help and 4 groups of 18

Answers

Answer:

8.5 & 4.5

Step-by-step explanation:

2 groups of 17 is 17 ÷ 2 because your dividing 17 people into 2 groups, same thing with 4 groups of 18.

So, 17 ÷ 2 = 8.5 & 18 ÷ 4 = 4.5

Students in the gardeing club are planting a flower garden. They have a total of $200 to spend. They spent $80 on the much. how many packs of bulds can they buy if eachpack cost $30

Answers

Answer:

they can by 4

Step-by-step explanation:

which is greater 4/8 or 2/4 ? i am stuck and this answer is on a test im doing

Answers

Answer:

they are both equal the are both half's

Step-by-step explanation:

2 is a half of 4 and 4 is a half of 8 so they both basically 1/2

can i have brainly

Answer:

They are equal!

Step-by-step explanation:

If you simplify 4/8 you would get 1/2, because 4 is half of 8. And if you look at 2/4 that simplifies to 1/2, because 2 is half of 4. I Hope This Helps :)

HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
3. Use the information about the m<2 and m determine the missing information.
m22 = 97°
m26 = 83°
m
2
5
m2 3 =
m2 5 =
3
4
7
8
m210 =
m2 7 =
9
10
13
14
m2 9 =
m216 =
$
11
12
15/16

Answers

Answer:

m<3 = 97

m<10 = 97

m<9 = 83

m<5 = 97

m<7 = 83

m<16 = 97

Step-by-step explanation:

m<3 = m<2 because of vertical angles

m<10 = m<2 because of corresponding angles

m<9 + 97 = 180

m<9 = 83

m<5 + 83 = 180

m<5 = 97

m<7 = m<6 because of vertical angles

m<16 = m<5 because of alternate exterior angles.

The figure below shows a tile shaped like an isosceles triangle with a base of 14 centimeters and a height of 24 centimeters.

image 11a048f9b50a43d4a9382edb59367f11

What is the perimeter of the tile?

A.
168 cm

B.
66 cm

C.
38 cm

D.
64 cm

Answers

Answer:

it's c

Step-by-step explanation:

because 24 + 38 = 38

Can some one help me on 11- 12

Answers

PLEASE ANSWER BOTH AS FAST AS POSSIBLE PLEASE HELP HELP ILL MARK BRAINLEST!!!!! PLEASE ANSWER BOTH AS FAST AS POSSIBLE PLEASE HELP HELP ILL MARK BRAINLEST!!!!! PLEASE ANSWER BOTH AS FAST AS POSSIBLE PLEASE HELP HELP ILL MARK BRAINLEST!!!!! PLEASE ANSWER BOTH AS FAST AS POSSIBLE PLEASE HELP HELP ILL MARK BRAINLEST!!!!! PLEASE ANSWER BOTH AS FAST AS POSSIBLE PLEASE HELP HELP ILL MARK BRAINLEST!!!!!

Answer:

11. 6 feet  12. 140 inches cubed

Step-by-step explanation:

To get the cylinder use the formula  [tex]h=\frac{V}{\pi r^{2} }[/tex].

To get the volume on the laptop use the formula volume=length x width x height.

What is the perimeter of a triangle with sides the following lengths: 3a + 2c,5c + 9 and 5a - 6. Simplify the expression.

Answers

Answer:

8a+7c-3

Step-by-step explanation:

PLS HELP!!

In the following diagram, L || M. (i think that's an L, i dont know)

Solve for each of the variables w, x, y, and z. For each solution, explain, in complete sentences which special angles allowed you to create an equation in order to find a solution.

Answers

Answer:

Un sistema de ecuaciones es un conjunto de ecuaciones con las mismas incógnitas. Un

sistema de ecuaciones lineales es un sistema de ecuaciones en el que cada ecuación es lineal. Una solución de un sistema es una asignación de valores para las incógnitas que hace

verdadera cada una de las ecuaciones. Resolver un sistema signifi ca hallar todas las soluciones del sistema.

Step-by-step explanation:

HELP!!!PLS!!!NOW!!!FAST!!!ASAP!!!

Answers

Answer:

lol what

Step-by-step explanation:

Answer:

:)

Step-by-step explanation:

The polynomial is (x-2) is a factor of the polynomial 4x^2-6x-4

A. True
B. False

Answers

True, (x-2) is a factor of the polynomial 4x^2-6x-4. Option A is correct.

What exactly is a polynomial?

A polynomial is an algebraic statement made up of variables and coefficients.

Variables are sometimes known as unknowns. We can use arithmetic operations like addition, subtraction, and so on. However, the variable is not divisible.

Given equation;

[tex]\rm 4x^2-6x-4[/tex]

The factors of the given equation:

2(2x+1)(x−2)

True, (x-2) is a factor of the polynomial 4x^2-6x-4.

Hence option A is correct.

To learn more about polynomials, refer to:

https://brainly.com/question/17822016

#SPJ1

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