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Hamza M.

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Pre-Calculus

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Question:

There are two students, Student A writes 2 essays each hour. Student B writes 3 essays each hour. If they worked together without interfering each other, how long does it take to finish 1 essay?

Hamza M.

Answer:

Use the formula W=(rA+rB)t where rA and rB are the rates of doing work (essays per hour) for students A and B respectively. rA=2 essays per hour, rB=3 essays per hour, and W=1 essay. Substitute in formula and solve for t. t=1/5 hours.

Calculus

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Question:

If r = cos (xy) + 3xy – 2x2 – 3x – 2y, find ∂F/∂x and ∂F/∂y.

Hamza M.

Answer:

r=cos(xy)+3xy−2x2−3x−2y The partial derivative of r with respect to x is ∂F∂x=−ysin(xy)+3y−4x−3 also The partial derivative of r with respect to y is ∂F∂y=−xsin(xy)+3x−2

Physics

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Question:

Q1:in the reaction : (At#: 95, M#241) Am =(At#: 953 M#237) Np+X What is X ? Q2: A spaceship of alien sports enthusiasts passes by the Earth at a speed of 0.8c, watching the final minute of a basketball game as they zoom by. Though the clock on Earth measures a minute left of play, how long do the aliens think the game lasts?

Hamza M.

Answer:

A1: Both atomic number and mass number are conserved in nuclear reactions. Since the mass number is 241 and the atomic number is 95 on the left side of the equation, the mass number must add up to 241 and the atomic number to 95 on the right side. Since the mass number of the Np atom is 237 and its atomic number is 93, the X atom must have a mass number of 4 and an atomic number of 2, which is the case with an alpha particle. A2: Because the Earth is moving at such a high speed relative to the alien spaceship, time appears to move slower on Earth from the aliens’ vantage point. To be precise, a minute of Earth time seems to last so by using time dilation formula : t'=100s

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