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Alice P.
Engineering Physics Major at UIUC
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SAT II Mathematics Level 2
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Question:

Sam deposits $300 into a new savings account. He earns 5% interest compounded annually. How many years will it take for the amount in his account to reach$1000?

Alice P.

Every year the money in the account is increased to the amount in the account times 1.05 since the interest is 5%. For $$n$$ years, the amount of money in the account increases to $$300*(1.05)^n$$. Therefore we can find the number of years by solving for $$n$$ in the equation $$1000 = 300*(1.05)^n$$ $$\frac{1000}{300} = 1.05^n$$ $$ln(\frac{10}{3}) = n*ln(1.05)$$ $$n = 24.7$$ years Since it will take more than 24 years to reach \$1000, round 24.7 to 25 years for your final answer.

Python Programming
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Question:

Create a function "factorial" that accepts a positive integer and returns the factorial of the input.

Alice P.

#define the function def factorial(integer): #create a variable as the product sum as we loop through each number #since factorials are multiplications of numbers less than and equal to the number, we will set the initial value of the variable to 1 product = 1 #loop through each integer equal to and less than the input while integer > 0: product *= integer integer -= 1 return product

Physics (Newtonian Mechanics)
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Question:

Two children are sitting on opposite sides of a 2-meter-long see-saw with its mass evenly distributed and its pivot at the center. Child A and child B weigh 35 kg and 30 kg respectively. If the see-saw is perfectly balanced and child A is sitting 0.80 m away from the pivot, how far is child B from child A?

Alice P.

First, identify all torques acting on the system (including the see-saw and the two children). It may help to draw a diagram. We know there are 4 forces, (1) the force exerted on the see-saw by child A, (2) the gravitational force of the see-saw, (3) the force exerted by the pivot to the see-saw at the center, and (4) the force exerted on the see-saw by child B. Since the mass of the see-saw is not given, and both masses of the children are given, we would position the pivot point at the center of the see-saw and calculate the clockwise and counterclockwise torques. The see-saw is in balance, therefore the net torque = 0 N*m, and the magnitude of clockwise torque equal the magnitude of counterclockwise torque. Now, identify the force(s) causing the clockwise and counterclockwise torques. Clockwise torque = mass of child B * distance of child B to pivot = 30 kg * distance of child B to pivot Counterclockwise torque = mass of child A * distance of child B to pivot = 35 kg * 0.80 m clockwise torque = counterclockwise torque, therefore: 30 kg * distance of child B to pivot = 35 kg * 0.80 m Distance of child B to pivot = 0.93 m Distance from child A to child B = A to pivot + pivot to B = 0.80 m + 0.93 m = 1.73 m

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