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3 years ago

Identify the equation of the circle J with center K(-7,3) and radius 6.

Mathematics

2 answers:

andreyandreev [35.5K]3 years ago

8 0

Answer:

equation of the circle J with center K(-7,3) and radius 6 is=

x^2+y^2+14x-6y+22=0

Step by step explanation:

Equation of circle with given centre (h,k) and radius r is

(x-h)^2+(y-k)^2=r^2

Given centre are K(-7,3) and radius 6.

So equation of Circle=

(x- -7)^2+(y-3)^2=6^2

x^2+14x+49+y^2-6y+9=36

x^2+y^2+14x-6y+22=0 answer

Troyanec [42]3 years ago

5 0

Answer:

(x + 7)² + ( y − 3)² = 36

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is (x − h)² + (y − k)² = r².

Define h, k and r using the given values. So, h= −7, k = 3, and r = 6.

Substitute the values into the equation of a circle.

(x − (−7))² + (y −3)²= 62

Simplify.

(x + 7)² + (y − 3)²= 36

Therefore, the equation of the circle J with center K (−7, 3) and radius 6 is (x + 7)² + (y − 3)²= 36.

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mb- The graph shows the relationship between time and the number of soda bottles a machine can make. Use the points (2,100) and

Evgesh-ka [11]

Answer:

1200

Step-by-step explanation:

We can gather from what's given that y=20xy represents the total number of bottles produced in the given time in seconds, which is x. When x=1, y=20, This means that each second the machine can make 20 soda bottles. Each minute is 60 seconds, so when x=60, y=20*60 =1200 soda bottles.

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2 years ago

16) Graph g(x) = x + 3 + 2

krek1111 [17]

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1 year ago

A castle has to be guarded 24 hours a day. Five knights are ordered to split each day's guard duty equally. How long will each k

Harman [31]

Answer:

Each knight will guard <u>288 minutes</u> in one day.

Step-by-step explanation:

Given:

A castle has to be guarded 24 hours a day. Five knights are ordered to split each day's guard duty equally.

Now, to find the minutes will each night spend on guard duty in one day.

As, in 1 hour there are 60 minutes.

Thus, in 24 hour there are 60 × 24 = 1440 minutes.

Total minutes for guarding = 1440 minutes.

So, there are knights ordered for guarding are = 5.

And each day's guard duty equally.

Now, to get the minutes will each night spend on guard duty in one day we divide the total minutes for guarding by number of knights that is 5:

$1440\div5$

$=288\ minutes.$

Therefore, each knight will guard 288 minutes in one day.

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3 years ago

Use the law of cosines to solve for the measure of the largest angle in triangle ABC.

marta [7]

AB is the longest side, so ∠C is the largest angle.
use law of cosine: 16²=9²+12²-2*9*12cosC
216cosC=81+144-256=-31
cosC=-0.14352
C≈98

6 0

3 years ago

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If line segment BC is considered the base of triangle ABC, what is the corresponding height of the triangle?

Leni [432]

Answer:

1.6 units

Step-by-step explanation:

Coordinates of A : (-1,1)

Coordinates of B : (3,2)

Coordinates of C :( -1,-1)

Now to find the length of the sides of the triangle we will use distance formula :

$d =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

To find length of AB

A = $(x_1,y_1)=(-1,1)$

B= $(x_2,y_2)=(3,2)$

Now substitute the values in the formula:

$d =\sqrt{(3-(-1))^2+(2-1)^2}$

$d =\sqrt{(4)^2+(1)^2}$

$d =\sqrt{16+1}$

$d =\sqrt{17}$

$d =4.12$

Now to find length of BC

B= $(x_1,y_1)=(3,2)$

C = $(x_2,y_2)=(-1,-1)$

Now substitute the values in the formula:

$d =\sqrt{(-1-3)^2+(-1-2)^2}$

$d =\sqrt{(-4)^2+(-3)^2}$

$d =\sqrt{16+9}$

$d =\sqrt{25}$

$d =5$

Now to find length of AC

A = $(x_1,y_1)=(-1,1)$

C = $(x_2,y_2)=(-1,-1)$

Now substitute the values in the formula:

$d =\sqrt{(-1-(-1))^2+(-1-1)^2}$

$d =\sqrt{(0)^2+(-2)^2}$

$d =\sqrt{4}$

$d =2$

Thus the sides of triangle are of length 4.12, 5 and 2

Now to find area of triangle we will use heron's formula :

To calculate the area of given triangle we will use the heron's formula :

$Area = \sqrt{s(s-a)(s-b)(s-c)}$

Where $s = \frac{a+b+c}{2}$

a,b,c are the side lengths of triangle

a = 4.12

b=5

c=2

Substitute the values

Now substitute the values :

$s = \frac{4.12+5+2}{2}$

$s =5.56$

$Area = \sqrt{5.56(5.56-4.12)(5.56-5)(5.56-2)}$

$Area = 3.99$

Now to find the height of altitude corresponding to side BC

So, formula of area of triangle $=\frac{1}{2} \times Base \times Height$

Since Area = 3.99 square units

So, $3.99 =\frac{1}{2} \times BC \times Height$

So, $3.99 =\frac{1}{2} \times 5\times Height$

$3.99 =2.5 \times Height$

$\frac{3.99}{2.5}=Height$

$1.596=Height$

Thus the altitude corresponding to the BC is of length 1.596 unit ≈ 1.6 units

Thus Option D is correct.

7 0

2 years ago

Read 2 more answers