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torisob [31]
3 years ago
7

Two gears in a machine are aligned by a mark drawn from the center of one gear to the center of the other. If the first gear has

24 teeth, and the second gear has 40 teeth, how many revolutions of the first gear are needed until the marks line up again?
Mathematics
1 answer:
Aleksandr [31]3 years ago
8 0

Answer:

5

Step-by-step explanation:

for the first gear

revolutions/teeth

1 / 24

2 / 48

3 / 72

4 / 96

5 / 120

6 / 144

for the second gear

revolutions/teeth

1 / 40

2 / 80

3 / 120

4 / 160

<em>the two marks will meet after 120 teeth, 5 revolutions of the first gear and 3 revolutions of the second.</em>

the way to get that amount of teeth is

24 = 2 \times 2 \times 2 \times 3 =  {2}^{3}  \times 3

40 = 2 \times 2 \times 2 \times 5 =   {2}^{3}  \times 5

the Least Common Multiple equals the product of all factors, but those factors who are repeted for both numbers should be only once.

{2}^{3} \times 5 \times 3 = 120

120 teeth are 5 revolutions for gear1 and 3 por gear2

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Can someone plz help me Thank you in advance:)
yulyashka [42]

Answer : The specific heat of the metal is, 2178.67J/kg^oC

Explanation :

In this problem we assumed that heat given by the hot body is equal to the heat taken by the cold body.

q_1=-q_2

m_1\times c_1\times (T_f-T_1)=-m_2\times c_2\times (T_f-T_2)

where,

c_1 = specific heat of metal = ?

c_2 = specific heat of ice = 2000J/kg^oC

m_1 = mass of metal = 1.00 kg

m_2 = mass of ice = 1.00 kg

T_f = final temperature of mixture = -8.88^oC

T_1 = initial temperature of metal = 5.00^oC

T_2 = initial temperature of ice = -24.0^oC

Now put all the given values in the above formula, we get:

(1.00kg)\times c_1\times (-8.88-5.00)^oC=-[(1.00kg)\times 2000J/kg^oC\times (-8.88-(-24.0))^oC]

c_1=2178.67J/kg^oC

Therefore, the specific heat of the metal is, 2178.67J/kg^oC

4 0
3 years ago
Consider the inequality -20.2 &gt; 0y. Which of the following must be true? Check all that apply. You cannot divide by zero. The
Katarina [22]

Answer:

You can not divide by zero.

The inequality is equivalent to - 20.2 > 0 which is false.

Step-by-step explanation:

We can not divide both sides by zero, because if we divide both sides by zero, then the inequality becomes

- \frac{20.2}{0} > y

⇒ - ∞ > y, which is not possible.

Again, the given inequality is - 20.2 > 0 × y.

We have to multiply y with zero and a product of zero with any term is also zero.

Hence, the inequality becomes - 20.2 > 0.

Therefore, the inequality is equivalent to - 20.2 > 0 which is false. (Answer)

4 0
3 years ago
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Step-by-step explanation:

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