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Debora [2.8K]
3 years ago
12

Click on the number until you find the right quotient. 36m5n5 ÷ (12m3)

Mathematics
1 answer:
Len [333]3 years ago
5 0

<em>So</em><em> </em><em>the</em><em> </em><em>answer</em><em> </em><em>is</em><em> </em><em>3</em><em>m</em><em>^</em><em>2</em><em>n</em><em>^</em><em>5</em>

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✨ 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
2 years ago
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I need help simplifying a math problem. It is (x^2 * x^-3)^4
Mashutka [201]
(x^2 \times x^{-3})^4 \\ \\ (x^{2-3})^4 \ / \ product \ rule \\ \\ (x^{-1})^4 \ / \ simplify \\ \\ x^{-4} \ / \ simplify \\ \\ \frac{1}{x^4} \ / \ negative \ power \ rule \\ \\ Answer: \frac{1}{x^4}
4 0
3 years ago
Given: h(x)=-4x and g(x) = 3x +1<br> Find:<br> (nog)
pashok25 [27]

Answer:

Step-by-step explanation:

h(g(x))

g(x)= 3x + 1

h(3x + 1) = 4(3x + 1) = 12x + 4

4 0
3 years ago
A computer repairman makes $25 per hour. Which equation models the situation?
Leona [35]

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4 0
2 years ago
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Multiply.<br> Write your answer in simplest form.<br> Help me plz
damaskus [11]
(-5/3)•(-6/1)=(30/3)
(30/3) simplified is (10/1)
3 0
3 years ago
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