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Connor L.
Physics student
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Physics (Waves and Optics)
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Question:

What is the emission wavelength of a photon created by an electron in an hydrogen atom moving from the fifth excited state to the second excited state and what color in the visible spectrum of light does this correspond to?

Connor L.

We use the Rydberg equation: $$\frac{1}{\lambda} = R_H(\frac{1}{2^2}-\frac{1}{n^2})$$ where $$n=5$$ and $$R_H$$ is the Rydberg constant. We get $$4.341*10^-9 m$$ or $$434.1 nm$$ which corresponds to blue light.

Calculus
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Question:

A rocket ship accelerates at a rate of $$29t \frac{m}{s^2}$$, where $$t$$ is time in seconds. If the was initially at rest and accelerated for 600 seconds directly away from the surface of the earth, what distance did it travel?

Connor L.

By integrating the acceleration twice with respect to time we can find the position equation. $$\int_{0}^{t}29t = 29t^2 + V_0$$, where the constant $$V_0$$ is the initial velocity which the problem stated is equal to zero. Then, $$\int_{0}^{600}29t^2 = \frac{1}{3}29t^3 + X_0$$ evaluated from 0 to 600. Since we can pick our own coordinate system where the surface of the earth is $$x=0$$, we can say $$X_0 = 0$$, or in other worlds the rocket starts on the surface of the earth. Then, $$\frac{1}{3}29*[600-0] = 5800 m$$ is the total distance traveled by the rocket.

Algebra
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Question:

A bakery sells cupcakes for $2 each and apple pies for$8 each. Last week, they sold some number $$c$$ cupcakes and some number $$p$$ pies. Write an equation that that gives the total dollar amount of baked goods sold last week.

Connor L.

We use $2 times the number of cupcakes sold and add$8 to the number of pies sold. $$2*c+8*p$$.

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