# Tutor profile: Marcillene D.

## Questions

### Subject: Physics (Newtonian Mechanics)

If John, who's mass is 40 kg, sits 2 meters away from the fulcrum on a see-saw, and Geoffrey, who's mass is 50 kg, wants to sit on the other end of the see-saw, how far from the fulcrum does Geoffrey need to sit for the two of them to be suspended in rotational equilibrium? P.S. I am considering rotational motion to be an application of Newton's 3 laws.

If the two are in rotational equilibrium, then their torques must be equal and opposite; cancel out. To find John's torque, you find his force of gravity, Fg = m x g where g = 9.8 m/s^2. Since his mass is 40 kg, his force of gravity is 392 N. Since he is 2 m from the fulcrum, that is his radius, r. To find his torque, you use the equation T = F x r; T = 392 x 2; T = 784 Nxm. Next you need to find Geoffrey's force of gravity; Fg = 50 x 9.8; Fg = 490 N. To be in rotational equilibrium, John's and Geoffrey's torques must be equal; therefore, 784 = 490 x r; to get r all by itself, you divide both sides by 490, and you're left with r = 1.6 m. This is how far Geoffrey must sit from the fulcrum.

### Subject: Writing

Identify the type of figurative language used in the following sentences: 1. I ran for a thousand hours. 2. Gabriela is as beautiful as the ocean. 3. That man is a mountain. 4. "POP!" My rubber band snapped. 5. Angrily, aggressively, Arnold anchored his boat, Alexandria.

1. Hyperbole 2. Simile 3. Metaphor 4. Onomatopoeia 5. Alliteration

### Subject: Algebra

Factor the following polynomial and find the zeroes: 3(x^2) + 12x - 12

First, see if there is a GCF (greatest common factor): can you find a number that evenly divides into each coefficient? Yes: 3. Divide it out of the equation like this: 3 [(x^2) + 4x + 4]. Now you can factor the polynomial within the brackets. To do this, first apply the big X method. Put the coefficient of the last term on the top of a big X and the coefficient of the first term on the bottom of the big X. Then find two numbers that multiply together to equal the top of the big X and add together to equal the bottom of the big X. These two numbers are 2 and 2. Therefore, (x + 2) and (x + 2) are both factors of the polynomial. The fully factored polynomial would be: 3(x + 2){x + 2). To find zeroes, set each factor equal to zero: x + 2 = 0, x + 2 = 0, and 3 = 0. The first and second factors are solved like this: x + 2 = 0; if you subtract 2 from both sides, you get x = -2. The third factor is an untrue statement so the only zeroes are x = 2 and x = 2.

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