Examples of Q&A in the following topics:
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- The reaction quotient is a measure of the relative amounts of reactants and products during a chemical reaction at a given point in time.
- The reaction quotient, Q, is a measure of the relative amounts of reactants and products during a chemical reaction at a given point in time.
- This expression shows that Q will eventually become equal to Keq, given an infinite amount of time.
- The ball in the initial state is indicative a reaction in which Q < K; in order to reach equilibrium conditions, the reaction proceeds forward.
- Calculate the reaction quotient, Q, and use it to predict whether a reaction will proceed in the forward or reverse direction
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- The electric potential of a point charge Q is given by $V=\frac{kQ}{r}$.
- Another way of saying this is that because PE is dependent on q, the q in the above equation will cancel out, so V is not dependent on q.
- The electric potential due to a point charge is, thus, a case we need to consider.
- Using calculus to find the work needed to move a test charge q from a large distance away to a distance of r from a point charge Q, and noting the connection between work and potential (W=–qΔV), it can be shown that the electric potential V of a point charge is
- The electric potential is a scalar while the electric field is a vector.
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- For the following data, plot the theoretically expected z score as a function of the actual z score (a Q-Q plot).
- For the data in problem 2, describe how the data differ from a normal distribution.
- For the "SAT and College GPA" case study data, create a contour plot looking at College GPA as a function of Math SAT and High School GPA.
- Naturally, you should use a computer to do this.
- Naturally, you should use a computer to do this.
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- Describe the shape of a q-q plot when the distributional assumption is met.
- Here we define the qth quantile of a batch of n numbers as a number ξqsuch that a fraction q x n of the sample is less than ξq, while a fraction (1 - q) x n of the sample is greater than ξq.
- As before, a normal q-q plot can indicate departures from normality.
- (Right) q-q plot of a sample of 100 uniform points
- Figure 6. q-q plots of a sample of 10 and 1000 uniform points
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- A particle of mass $m$, charge $q$, moves in a plane perpendicular to a uniform, static, magnetic field $B$.
- If at time $t=0$ the particle has a total energy $\displaystyle t = \frac{ r_i^3 m^2 c^3}{4 e^4 } = \frac{1}{4 c} r_i \left ( \frac{r_i}{r_0} \right )^2$, show that it will have energy $E=\gamma m c^2 < E_0$ at a time ${\bf F} = -\hat{\bf r} \frac{q^2}{r^2}$, where$t \approx \frac{3 m^3 c^5}{2 q^4 B^2} \left ( \frac{1}{\gamma} - \frac{1}{\gamma_0} \right ).$
- A particle of mass $m$ and charge $q$ moves in a circle due to a force ${\bf F} = -\hat{\bf r} \frac{q^2}{r^2}$.
- What is the time if $\displaystyle P = \frac{2 q^2 \dot{u}^2}{3 c^3} = \frac{2 q^2 }{3 c^3} \left ( \frac{q^2}{r^2 m} \right )^2$ A (for an hydrogen)?
- There is a natural limit to the luminosity a gravitationally bound object can emit.
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- Average Fixed Cost (AFC) is the FC divided by the output or TP, Q, (remember Q=TP).
- AFC is fixed cost per Q.
- It is the variable cost per Q.
- AC = TC/Q.
- Marginal cost (MC) is the change in TC or VC "caused" by a change in Q (or TP).
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- Define a matrix $Q$ such that
- The matrix appearing in Equation 4.6.3 is the complex conjugate of $Q$ ; i.e., $Q^*$ .
- The matrix $Q$ is almost orthogonal.
- We have said that a matrix $A$ is orthogonal if $A A^T = A^T A = I$, where $I$ is the N-dimensional identity matrix.
- Once again, orthogonality saves us from having to solve a linear system of equations: since $Q^* = Q^{-1}$ , we have
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- To address the electrostatic forces among electrically charged particles, first consider two particles with electric charges q and Q , separated in empty space by a distance r.
- (The electric force vector has both a magnitude and a direction. ) We can express the location of charge q as rq, and the location of charge Q as rQ.
- Electric Force on a Field Charge Due to Fixed Source Charges
- Suppose there is more than one point source charges providing forces on a field charge. diagrams a fairly simple example with three source charges (shown in green and indexed by subscripts) and one field charge (in red, designated q).
- In a simple example, the vector notation of Coulomb's Law can be used when there are two point charges and only one of which is a source charge.
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- In this formula, p(q) is the price level at quantity q.
- The cost to the firm at quantity q is equal to c(q).
- As a result, the first-order condition for maximizing profits at quantity q is represented by:
- Consider the example of a monopoly firm that can produce widgets at a cost given by the following function:
- This occurs because marginal revenue is the demand, p(q), plus a negative number.
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- As an exercise, show that $A I_n = I_n A = A$ for any $n\times x$ matrix $A$ .
- A matrix $Q \in \mathbf{R}^{{n \times n}}$ is said to be orthogonal if $Q^TQ = I_n$ .
- In this case, each column of $Q$$\mathbf{q}_i \cdot \mathbf{q}_i = 1$ is an orthonormal vector: $\mathbf{q}_i \cdot \mathbf{q}_i = 1$ .
- Now convince yourself that $Q^TQ = I_n$ implies that $QQ^T = I_n$ as well.
- In which case the rows of $Q$ must be orthonormal vectors too.