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Nat2105 [25]
1 year ago
12

Given f(x) = 3x+9 and g(x) = 5x-1, find f(g(x)).

Mathematics
1 answer:
irinina [24]1 year ago
5 0

Step-by-step explanation:

In this equation, given

f(x) = 3x + 9 and g(x) = 5x -1

So the question is what is the value of f if we put the value of g(x) in f(x)

So to solve the equation we need to replace the value of x in f(x) with g(x)

So it was obtained as below

f(g(x)) = 3(5x-1) + 9

= (15 x - 3) + 9

= 15 x + 6

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A 24.6 g marble sliding to the right at 62.0 cm/s overtakes and collides elastically with a 12.3 g marble moving in the same dir
Softa [21]

Answer:

Velocity of the 24.6 g marble is 31 cm/s.

Step-by-step explanation:

Given:

Marble 1:

Mass of the marble (m_1) = 12.3 gm

Velocity of m_1 before collision v_1_i = 15.5 cm/s

Velocity of m_1 after collision v_1_f = 77.5 cm/s

Marble 2:

Mass of the marble (m_2) = 24.6 gm

Velocity of m_2 before collision v_2_i = 62 cm/s

Velocity of m_2 after collision v_2_f = ?

From the law of conservation of momentum, we know that momentum before equals the momentum after :

So,

⇒ P(i)=P(f)

⇒ (m_1\times v_1_i )+(m_2\times v_2_i) =(m_1\times v_1_f)+(m_2\times v_2_f)

⇒ Plugging the values.

⇒ (12.3\times 15.5) +(24.6\times 62)=(12.3\times 77.5)+(24.6\times v_2_f)

⇒ 190.65+1525.2=953.25+24.6\times v_2_f

⇒ 1715.85=953.25+24.6\times v_2_f

⇒ 1715.85-953.25=24.6\times v_2_f ...subtracting both sides 953.25

⇒ 762.6=24.6\times v_2_f

⇒ \frac{762.6}{24.6}\ =v_2_f ...dividing both sides with 24.6

⇒ 31=v_2_f

⇒ v_2_f =31 cm/s

The velocity of the 24.6 g marble after the collision is 31 cm/s and it will move opposite to of the 12.3 g marbles that is towards left.

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