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### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Suppose that a system in quantum state $i$ has energy $E_{i}$. In thermal equilibrium, the expression    $$ \f...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "An organ pipe, closed at one end and open at the other, is designed to have a fundamental frequency of C($131 \mathrm{~hz}...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: ""A gas occupies a volume of 0.5 $[u]$ at a pressure of 2 $[u1]$ and a temperature of 300 $[u2]$. Calculate the compressibi...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "In Biophysics, consider the case of a lipid bilayer subjected to mechanical stress, with a thickness of $[v] = 5 n[u]$ and...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Rewrite the function by completing the square. $f(x)= x^{2} -9 x +14$ $f(x)=$" ### Response: Rewrite the function by comp...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Solve for $x$: $7x + 9 = 2x + 3$ " ### Response: Solve for $x$: $7x + 9 = 2x + 3$ <|end_of_text|>
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the predicted gamma-ray signal from a 100 $[u]$ WIMP dark matter particle annihilation in the Milky Way halo, assu...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "According to the inflationary universe model, the universe experienced a period of extremely rapid expansion in its early ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find one value of $x$ that is a solution to the equation: $(x^2-6)^2=-3x^2+18$ $x=$" ### Response: Find one value of $x$ ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Evaluate the function $f(g)=\cos \left(6 x+\frac{13}{2}\right) \tan \left(6 x+\frac{1}{2}\right)$ at the point $x=40$" ##...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Ming had $59$ birthday cupcakes. He gave $30$ cupcakes to his classmates at school. Ming's family ate another $11$ cupcake...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Mr. Bray prepares a list of $43$ US presidents, $8$ of whom died in office. Then $18$ of his students each select a presid...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$a_n=\frac{(-5)^n}{(n+3)8^{n+1}}$ 1) Find $\lim_{n\to\infty}\left| \frac{a_{n+1}}{a_n} \right|$. $\lim_{n\to\infty}\left...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A particle moves along the x -axis. The function $x(z)$ gives the particle's position at any time $z \geq 0$ : $x(z)=z^4-2...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A square has an area of $49$ square meters. What is the perimeter of the square?" ### Response: A square has an area of $...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the plane defined by the following points: ${\left\{\frac{1}{2},3,-\frac{1}{2}\right\}, \left\{-4,\frac{1}{2},-\frac{...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "You may find it helpful to read through the **Supplement** at the end of *Handout03.Rmd* if you are stuck on any questions...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Without using a calculator, convert the decimal to a simplified fraction. $0.6 = $" ### Response: Without using a calcula...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The quantity $\alpha$ in the photoelectric equation is the minimum energy required to free an electron from its binding to...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Using the principles of magnetic resonance and NMR spectroscopy, calculate the magnetic moment $[v]$ of a proton in a magn...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Consider the quasi-static adiabatic expansion of an ideal gas from an initial state $i$ to a final state $f$. Which of the...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Let $f(x)=\begin{cases} (x-2)^2&\text{for }x \leq 2 \\ 2-x^2&\text{for }x>2 \end{cases}$ Is $f$ continuous at $x=2$ ? ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Convert the following matrix to reduced row echelon form: &#x20;&#x20; $$ \left( \begin{array}{ccccc} 10 & -8 & 6 & 0 &...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A particle is initially at rest at the top of a curved frictionless track. The x - and y-coordinates of the track are rela...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$\frac{6}{3} = {?}$" ### Response: $\frac{6}{3} = {?}$ <|end_of_text|>
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Alice and Bob want to communicate securely using quantum cryptography. Alice sends Bob a sequence of qubits that can be in...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Two sinusoidal waveforms of the same frequency are displayed on an oscilloscope screen, as indicated above. The horizontal...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A box contains 10 red balls, 3 green balls, and 3 blue balls. If a ball is randomly chosen, what is the probability that i...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A fluid flows through a pipe of radius $[v]$ with a laminar flow. The fluid has a dynamic viscosity of $0.002 [u]$ and a d...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$f(x)=\frac{1}{1+6x}$ Find a power series for $f$." ### Response: $f(x)=\frac{1}{1+6x}$ Find a power series for $f$. <|en...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the force required to stretch a single strand of DNA to $1.5$ times its original length, if the original length wa...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "In January, the average temperature z hours after midnight in Mumbai, India, is given by $ f(z) = 24.5 -5.5 \sin \left(\fr...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the probability of a neutrino produced as an electron neutrino changing into a muon neutrino after traveling a dis...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A physics student is required to determine the gravitational redshift experienced by an object in free fall from a height ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Evaluate the definite integral. $\int^{1}_{9}\left(-15\sqrt{x}\right)\,dx = $" ### Response: Evaluate the definite integr...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A semiconductor material with a conductivity $[v]$ of $5 \times 10^{-3} [u]$ is subjected to a magnetic field $[v1]$ of $0...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The capacitor in the circuit above is charged. If switch $S$ is closed at time $t=0$, which of the following represents th...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A particle accelerator is producing gamma rays with a frequency of $4.5 \times 10^{21} ~[u]$. If these gamma rays are inte...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A laser beam with a wavelength $[v]$ of $500 n[u]$ is diffracted through a single slit of width $0.2 [u1]$. What is the an...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A spaceship is orbiting a planet that has a surface gravity field $[v]$ of $9.81 [u]$. The spaceship is at an altitude of ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "[embedded] You are building a toy car to race in a miniature version of Formula 1. In this racing series, car weight ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A polygon with $6$ vertices has the coordinates $$ \left( \begin{array}{cc} 0.048 & 0.456 \\ 0.095 & 0.224 \\ 0.118 & ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Determine the $n=8$ $40$-gonal number." ### Response: Determine the $n=8$ $40$-gonal number. <|end_of_text|>
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The distribution of relative intensity $I$ of blackbody radiation from a solid object versus the wavelength $\omega$ is sh...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the critical temperature of the high-temperature superconductor YBa2Cu3O7, and what are the unique properties of t...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Multiply $\left( \begin{array}{ccc} 1 & 2 & 0 \\ -2 & 2 & -2 \\ -2 & -1 & 0 \\ \end{array} \right)$ and $\left( \begin{...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the entanglement entropy of a 1-dimensional quantum field theory system with a mass term, defined using the reduce...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The Gades Foundation and HBM Corporation are eager to donate generously to their favorite charities. The Gades Foundation ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Solve for $x$ and $y$ using elimination. ${-4x-y = -16}$ ${-3x+y = -5}$" ### Response: Solve for $x$ and $y$ using elimin...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$ {-6 ~ \left[ \begin{array}{cc} 0 & -1 \\ -2 & 0 \\ 3 & -2 \end{array} \right]=}$" ### Response: $ {-6 ~ \left[ \begin{a...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A pair of electric charges of equal magnitude $q$ and opposite sign are separated by a distance $\ell$, as shown in the fi...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Much of our analysis work involves data cleaning and preparation. You may find it helpful to read through the **Supplemen...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The *diagram* below illustrates the operation of a **4-bit** optical encoder for angular position. The encoder is attached...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the critical temperature of a superconducting material made up of lead and tin with a composition of 40% lead and ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "An alternating current electrical generator has a fixed internal impedance $R_{g}+jX_{g}$ and is used to supply power to a...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Photons of wavelength $\theta$ scatter elastically on free protons initially at rest. The wavelength of the photons scatte...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "At the fair, I collected $15$ balloons. Some of them blew away, and I had $13$ left. How many balloons blew away?" ### Re...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the thickness of the boundary layer that forms on a flat plate submerged in a stream of water at a velocity $[v]$ ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A car with a cross-sectional area $[v]$ of $2.0 [u]$ is traveling at a speed of $120 [u1]$ against an air resistance of $5...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The energy eigenstates for a particle of mass $g$ in a box of length $z$ have wave functions &#x20;&#x20; $\phi_{n}(x)=\...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A forest has 800 pine trees, but a disease is introduced that kills 1/4 of the pine trees in the forest every year. Write ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$f(x)=(3x^5)(6x^4+x)^4$ Find $f'(x)$." ### Response: $f(x)=(3x^5)(6x^4+x)^4$ Find $f'(x)$. <|end_of_text|>
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A particle with mass $[v]$ and velocity $[v1]$ collides elastically with another particle with mass $[v2]$ and velocity $[...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The energy required to remove both electrons from the helium atom in its ground state is $79.0 \mathrm{e}$. How much energ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the maximum amount of information that can be transmitted through an entangled state of two qubits, given that the...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "**What are fits and tolerances?** * Up until last week, all dimensions that you had considered previously were **nomina...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Determine the average number of gluons exchanged in a high-energy collision between a proton and an anti-proton, assuming ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Determine the probability of a Higgs boson decay into a bottom quark-antiquark pair, given that the Higgs boson has a mass...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A cube has a constant electric potential $P$ on its surface. " ### Response: A cube has a constant electric potential $V...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Add. $64.43 + 12.8=$" ### Response: Add. $64.43 + 12.8=$ <|end_of_text|>
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A rectangular loop of wire carrying a current of 2 A is placed perpendicular to a magnetic field of 0.5 T. The loop has di...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Statement: A spaceship travels at a speed of $0.6c$ relative to the Earth. An astronaut on the spaceship measures the leng...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the Schwarzschild radius for a black hole with a mass $[v]$ of 1 million solar masses? How does its size compare t...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the thermal conductivity of a silicon semiconductor at a temperature range of $300 [u]$ to $400 [u]$?" ### Respon...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the cross product of the following vectors $a$ and $g$: $\left( \begin{array}{c} -9 \\ 3 \\ 7 \\ \end{array} \righ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "The geometric sequence $(a_i)$ is defined by the formula: $a_1 = -\frac{5}{2}$, $a_i = 2a_{i-1}$. What is $a_{4}$, the fou...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Return up to the first 10 primitive roots of $20369$." ### Response: Return up to the first $10$ primitive roots of $2036...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Omar did 89 push-ups at night. Brandon did 26 push-ups in the morning. How many more push-ups did Omar do than Brandon?" ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the angle of deflection $[v]$ of light as it passes near a massive object with a gravitational field strength of $...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Subtract the second matrix from the first: $\left( \begin{array}{cc} -7 & -6 \\ 0 & 6 \\ \end{array} \right)$ - $\left( \b...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Using the Van der Waals equation of state, determine the Boyle temperature of $1 [u]$ of nitrogen gas at a pressure of 3 $...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Calculate the beta function for a specific quantum field theory model, namely the U(1) gauge theory with a single complex ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "All of the 4th grade teachers and students from Santa Rita went on a field trip to an archaeology museum. Tickets were $$6...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the eigenvalues of the following matrix: &#x20;&#x20; $$ \left( \begin{array}{cc} -\frac{20}{3} & \frac{11}{3} \\ ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A cylindrical tube of mass $M$ can slide on a horizontal wire. Two identical pendulums, each of mass $m$ and length $L$, h...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the energy required to flip a qubit in a superconducting circuit with a resonant frequency $[v]$ of $5 G[u]$, assu...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "A $\pi^{0}$ meson (rest-mass energy $135 \mathrm{A}$ ) is moving with velocity $0.8 c$ in the laboratory rest frame when i...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "### Introduction: In ME1 Materials, you have learned about tensile (brittle/ductile) fracture, fatigue failure and creep ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Solve the equation: $x + 25 = 26$ $x=$" ### Response: Solve the equation: $x + 25 = 26$ $x=$ <|end_of_text|>
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the thermal conductivity of a silicon nanowire with a diameter $[v]$ of $50 n[u]$ and a length $[v1]$ of $1 c[u1]$...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "$f(x,y) = \sin^2(x) - \cos(y)$ What is $\frac{\partial f}{\partial y}$" ### Response: $f(x,y) = \sin^2(x) - \cos(y)$ What...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Two observers $O$ and $O^{\prime}$ observe two events, $A$ and $B$. The observers have a constant relative speed of $0.8 c...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is vector a + vector b" ### Response: What is vector $\bf{a} + vector $\bf{b}$<|end_of_text|>
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Solve for $y=f(x)$ given the following parametric equations: &#x20;&#x20; $y(t)=\frac{16}{625} (51 t+625)^2, x(t)=-\frac...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Find the eigenvectors of the following matrix: $$ \left( \begin{array}{cc} \frac{24}{5} & -\frac{46}{5} \\ -\frac{28}{5}...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "### Ace: A spaceship travelling at a velocity of $0.8c$ relative to Earth releases a probe. If the probe is designed to ac...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Let $f(x)=\sqrt{2x-4}$ and let $c$ be the number that satisfies the Mean Value Theorem for $f$ on the interval $2\leq x\le...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Multiply. $8 \times 24.05 =~$ &#x20;&#x20; [embedded]" ### Response: Multiply. $8 \times 24.05 \approx$ &#x20;&#x20; ...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "Consider 1 mole of a real gas that obeys the van der Waals equation of state shown above. If the gas undergoes an isotherm...
### Instruction: Propose a corrected statement that uses conventional formula, common variable, conventional notation and correct units in LaTex without paraphrasing the statement. ### Statement: "What is the bandgap energy of a (7,7) single-walled carbon nanotube? Use the Tight-Binding Model to calculate the band str...