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riadik2000 [5.3K]
2 years ago
10

Needddd helppp plzzzzz

Mathematics
1 answer:
Hoochie [10]2 years ago
8 0
O k s o I d o n. O t k no w
You might be interested in
✨ B R A I N L I E S T
miv72 [106K]

1

:x

2

+y

2

−6x−9y+13=0

(x−3)

2

+(y−

2

9

)

2

−9−

4

81

+13=0

(x−3)

2

+(y−

2

9

)

2

=

4

65

Here,

r

1

=

2

65

C

1

=(3,

2

9

)

Equation of another circle-

S

2

:x

2

+y

2

−2x−16y=0

(x−1)

2

+(y−8)

2

−1−64=0

(x−1)

2

+(y−8)

2

=65

Here,

r

2

=

65

C

2

=(1,8)

Distance between the centre of two circles-

C

1

C

2

=

(3−1)

2

+(8−

2

9

)

2

C

1

C

2

=

4+

4

49

=

2

65

∣r

2

−r

1

∣=

∣

∣

∣

∣

∣

∣

65

−

2

65

∣

∣

∣

∣

∣

∣

=

2

65

∵C

1

C

2

=∣r

1

−r

2

∣

Thus the two circles touches each other internally.

Since the circle touches each other internally. The point of contact P divides C

1

C

2

externally in the ratio r

1

:r

2

, i.e.,

2

65

:

65

=1:2

Therefore, coordinates of P are-

⎝

⎜

⎜

⎜

⎜

⎜

⎛

1−2

1(1)−2(3)

,

1−2

1(8)−2(

2

9

)

⎠

⎟

⎟

⎟

⎟

⎟

⎞

=(5,1)

Therefore,

Equation of common tangent is-

S

1

−S

2

=0

(5x+y−6(

2

x+5

)−9(

2

y+1

)+13)−(5x+y−2(

2

x+5

)−16(

2

y+1

))=0

2

−6x−9y−13

+x+8y+13=0

4x−7y−13=0

Hence the point of contact is (5,1) and the equation of common tangent is 4x−7y−13=0.

4 0
3 years ago
Read 2 more answers
Lin runs 5 laps in 6 minutes how many laps per minute is that.
ikadub [295]

Answer:

about 1 and a half minutes

Step-by-step explanation:

6/5

laps over minutes

4 0
3 years ago
The ground temperature at an airport is 16 °C. The temperature decreases by 5.6 °C for every increase of 1 kilometer above the g
love history [14]

0 km = 16

1km = 16 - 5,6 = 10,4

2km = 10,4 - 5,6 = 4,8

3km = 4,8 - 5,6 = -0,8

4km = -0,8 - 5,6 = -6,4

5km = -6,4 - 5,6 = -12

3 0
3 years ago
Suppose a box of Cracker Jacks contains one of 5 toy prizes: a small rubber ball, a whistle, a Captain America decoder ring, a r
lakkis [162]

Answer:

11.42 boxes

Step-by-step explanation:

For the first box bought, there is a 100% chance of getting a unique toy (since you still don't have any). E₁ = 1.

After that, there is a 4 in 5 chance of getting a unique toy from the next box, the expected number of boxes required is:

E_2 = (\frac{4}{5})^{-1} = 1.25

For the next unique toy, there is now a 3 in 5 chance of getting it:

E_3 = (\frac{3}{5})^{-1} = 1.67

Following that logic, there is a 2 in 5 chance of getting the 4th unique toy:

E_4 = (\frac{2}{5})^{-1} = 2.5

Finally, there is a 1 in 5 chance to get the last unique toy:

E_5 = (\frac{1}{5})^{-1} = 5

The expected number of boxes to obtain a full set is:

E=E_1+E_2+E_3+E_4+E_5\\E=1+1.25+1.67+2.5+5\\E=11.42\ boxes

5 0
3 years ago
You are playing a card game with friends. at one point. you double your score. in the next hand you lose 75 points. you end up w
Gnoma [55]

Answer:

i) x points; ii) 2x - 75 = -25; iii) x = 25

Step-by-step explanation:

i) Starting points

Let's say you had x points before doubling your score.

(ii) The equation

 After doubling score: 2x points

After losing 75 points: (2x - 75) points

         At end of game: -25 points

The equation is

2x - 75 = -25

iii) Solution to equation

2x - 75 = -25     Add 75 to each side

      2x =  50     Divide each side by 2

        x =  25

3 0
3 years ago
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