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Sisilia S.

Computer Science Student at Northwestern University

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Python Programming

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Question:

Write a short program that assigns a student their letter grade on a test with 50 problems, where the number of problems answered correctly divided by 50 is their percent grade. Assume that number_correct is a predefined int variable that stores how many problems the student answered correctly on the test.

Sisilia S.

Answer:

percent = number_correct / 50 letter_grade = " " if (percent >= 90): letter_grade = "A" else if (percent >= 80): letter_grade = "B" else if (percent >= 70): letter_grade = "C" else if (percent >= 60) letter_grade = "D" else: letter_grade = "F" print(letter_grade)

Calculus

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Question:

Find the volume of a solid created by rotating the region bounded by $$y = x^2$$ and $$y = 4$$.

Sisilia S.

Answer:

The first step is to find the area of one ring around the region, and the equation for the area around a circle is $$A = \pi r^2$$. In this problem, the radius is equal to the distance between $$y = x^2$$ and $$y = 4$$, so $$r = 4 - x^2$$. Then, plugging that into the area equation, you get $$A = \pi (4 - x^2)^2$$. Then, you take the integral of that from 0 to 2, which looks like $$V = \int_{0}^{2} \pi (4 - x^2)^2$$, which gives you $$V = \frac{256}{15}\pi$$.

Physics

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Question:

A child is pulling on a $$25 kg$$ wagon by its handle handle at an angle of $$50^\circ$$ from the horizontal with a force of $$40 N$$. What is the normal force on the wagon?

Sisilia S.

Answer:

Start out with what you know. You know the mass of the wagon is $$25 kg$$, so you can find the gravitational force on the wagon using that. Gravitational force is $$F_g = m\cdot g$$, where $$F_g$$ is the gravitational force, $$m$$ is the mass of the object, and $$g$$ is the gravitational constant, which you can just round to $$10 m/s^2$$. So for this problem, it will be $$F_g = 25 kg\cdot 10 m/s^2$$ to get the gravitational force, which will be $$250 N$$. Then, you need to find the y-component of the force the child is exerting on the wagon. Let's say the force by the child is $$F$$. The resultant force from the child is $$40 N$$, but you'll have to break that up into components. Since we only need the y-component, we can set up this equation: $$\sin(50^\circ) = \frac{40 N}{F_y}$$. When this is rearranged to solve for $$F_y$$, you'll get this equation: $$F_y = 40 N \cdot \sin(50^\circ)$$. If you calculate that out, you will get $$F_y = 30.641 N$$. Finally, to find the normal force, subtract $$F_y$$ from $$F_g$$, and that gets you $$F_n = 219.359 N$$.

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