• What is this question asking? Critical points of multi variable functions?

    I'm just struggling with understanding what the question is asking? O.o I know about critical points existing when the gradient (all derivatives are zero) is 0. I just don't understand what the question even wants lol.
    I'm just struggling with understanding what the question is asking? O.o I know about critical points existing when the gradient (all derivatives are zero) is 0. I just don't understand what the question even wants lol.
    2 answers · Mathematics · 3 days ago
  • Finding tangent line to surface at point?

    I know directional derivatives, equations of lines the direction vector of lines, the dot product, etc, stuff related to tangent lines. But I'm having trouble understanding the following description. 1) Why is the line through (xₒ, yₒ, f(xₒ, yₒ)) and also parallel to <1, 0, fₓ(xₒ, yₒ)> is the tangent line to the x axis at (xₒ, yₒ)? 2)... show more
    I know directional derivatives, equations of lines the direction vector of lines, the dot product, etc, stuff related to tangent lines. But I'm having trouble understanding the following description. 1) Why is the line through (xₒ, yₒ, f(xₒ, yₒ)) and also parallel to <1, 0, fₓ(xₒ, yₒ)> is the tangent line to the x axis at (xₒ, yₒ)? 2) What would the direction of the tangent line be? <1, 0, fₓ(xₒ, yₒ)>?
    Mathematics · 3 days ago
  • Polar coordinates, interval of integration?

    1) Why is the interval of integration for dθ from just 0 to π? It interval kinda looks like it's from -π/4 to π/4. So I can see the "duration" of the integral is π radians also. So... 2) Why does it not matter where we start our integration? What am I missing?
    1) Why is the interval of integration for dθ from just 0 to π? It interval kinda looks like it's from -π/4 to π/4. So I can see the "duration" of the integral is π radians also. So... 2) Why does it not matter where we start our integration? What am I missing?
    2 answers · Mathematics · 4 days ago
  • Implicit differentiation?

    1) z = x⁴e³ʸ, find dz. dz by definition is dz = fₓdx + fᵧdy dz = 4x³e³ʸ dx + 3x⁴e³ʸ dy. Now the next one is really confusing me. 2) eᶻ + yz = x + y, find dz. Let's try to take the derivative with respect to x first, dz/dx dz/dx(eᶻ + yz) = d/dz(x + y) What happens to dz/dx(eᶻ), since we have a z? Why don't I treat eᶻ as a constant, I'm... show more
    1) z = x⁴e³ʸ, find dz. dz by definition is dz = fₓdx + fᵧdy dz = 4x³e³ʸ dx + 3x⁴e³ʸ dy. Now the next one is really confusing me. 2) eᶻ + yz = x + y, find dz. Let's try to take the derivative with respect to x first, dz/dx dz/dx(eᶻ + yz) = d/dz(x + y) What happens to dz/dx(eᶻ), since we have a z? Why don't I treat eᶻ as a constant, I'm doing d/dx, so should everything but x be treated as a constant? dz/dx(yz) = 0z + ydz/dx? or = 0z + 0y = 0?
    Mathematics · 5 days ago
  • Direction derivative definition? Orthogonal to level surface?

    1) Why is the definition saying the function w is on an open ball? 2) Why is the gradient orthogonal to the level surface? I know the gradient is maximum rate of change automatically. "Level surface = c at (xo,yo,zo)" is confusing me. 3) Why are definitions so confusing o.O
    1) Why is the definition saying the function w is on an open ball? 2) Why is the gradient orthogonal to the level surface? I know the gradient is maximum rate of change automatically. "Level surface = c at (xo,yo,zo)" is confusing me. 3) Why are definitions so confusing o.O
    Mathematics · 5 days ago
  • Explain multivariable differentiability definition?

    For z = f(x, y), the total differential of z is dz = fₓdx + fᵧdy, by definition. So I understand the above sort of. At least I can read it. I cannot understand the next definition for multivariable differentiability o.O I don't think any can! It looks like gibberish to me!
    For z = f(x, y), the total differential of z is dz = fₓdx + fᵧdy, by definition. So I understand the above sort of. At least I can read it. I cannot understand the next definition for multivariable differentiability o.O I don't think any can! It looks like gibberish to me!
    1 answer · Mathematics · 5 days ago
  • Magnitude of magnetic field from current carrying wire?

    For point 1, the magnetic field due to the horizontal wire and diagonal wire add up. The answer I get is C. (μ₀×I) / (πd) This is correct. 1) For point 2, I'm not sure how to find the magnitude of the magnetic field due to the diagonal wire? The answer is F apparently. 2) Why did we not have to account for the angle for point 1, but now it... show more
    For point 1, the magnetic field due to the horizontal wire and diagonal wire add up. The answer I get is C. (μ₀×I) / (πd) This is correct. 1) For point 2, I'm not sure how to find the magnitude of the magnetic field due to the diagonal wire? The answer is F apparently. 2) Why did we not have to account for the angle for point 1, but now it matters for point 2? Because the horizontal wire is in between?
    1 answer · Physics · 1 week ago
  • What is ionizing radiation?

    Nuclear radiation energy is much larger than visible light energies. So instead of just being absorbed and increasing an objects temperature, nuclear radiation ionizes matter and breaks molecular bonds. Explanation was because: "These energies are much larger than ionization energies of atoms and molecules". "The ionization energies... show more
    Nuclear radiation energy is much larger than visible light energies. So instead of just being absorbed and increasing an objects temperature, nuclear radiation ionizes matter and breaks molecular bonds. Explanation was because: "These energies are much larger than ionization energies of atoms and molecules". "The ionization energies of an atom is about 10 eV, while alpha or beta particles are around 1 MeV". How does an atom's ionization energy and ionizing radiation fight? Atom ionization energy is energy needed to rid of an electron. Nuclear radiation just damages everything. I don't see how they connect?
    1 answer · Physics · 1 week ago
  • Why is induced electric field non-conservative?

    To paraphrase my textbook: Usually a 'Coulomb electric field' starts at a positive charge and ends at a negative charge. A 'Non-Coulomb electric field' such as an induced electric field caused by changing magnetic field is non-conservative. I'm not sure what or why this is? The explanation was: "There's never any... show more
    To paraphrase my textbook: Usually a 'Coulomb electric field' starts at a positive charge and ends at a negative charge. A 'Non-Coulomb electric field' such as an induced electric field caused by changing magnetic field is non-conservative. I'm not sure what or why this is? The explanation was: "There's never any negative work to balance positive work so net work done in a closed path is not zero". I still don't understand :(
    3 answers · Physics · 2 weeks ago
  • Induced current direction, eddy currents?

    We have an electric rail car. To brake, we flick on a magnetic field (x) in the page. Thus this increase into the page must be opposed by an induced magnetic field out of the page (.) which mean induced current is counter clockwise I believe. Which image best represents this? I picked C but that's incorrect. The hint was then: consider both... show more
    We have an electric rail car. To brake, we flick on a magnetic field (x) in the page. Thus this increase into the page must be opposed by an induced magnetic field out of the page (.) which mean induced current is counter clockwise I believe. Which image best represents this? I picked C but that's incorrect. The hint was then: consider both leading and trailing edges.
    1 answer · Physics · 2 weeks ago
  • Direction of conducting loop, if we increase magnetic field strength?

    A stationary loop has a magnetic field through it. We increase the magnetic field strength into the page (X). What happens to the loop? The answer: The loop is pushed to the right, out of the magnetic field. Why? I can see the the magnetic force up and down cancel out. Don't the magnetic forces left and right also cancel out then?
    A stationary loop has a magnetic field through it. We increase the magnetic field strength into the page (X). What happens to the loop? The answer: The loop is pushed to the right, out of the magnetic field. Why? I can see the the magnetic force up and down cancel out. Don't the magnetic forces left and right also cancel out then?
    1 answer · Physics · 2 weeks ago
  • Same direction/like current carrying wires attract?

    I know opposite magnetic fields attract. So the top pair of wires with current both coming out of the page, there is an attractive force exerted between them. However I'm getting confused with magnetic force. By the right hand rule: Top left wire: Your thumb is coming out of the page: current Your index finger points up in direction of B:... show more
    I know opposite magnetic fields attract. So the top pair of wires with current both coming out of the page, there is an attractive force exerted between them. However I'm getting confused with magnetic force. By the right hand rule: Top left wire: Your thumb is coming out of the page: current Your index finger points up in direction of B: magnetic field. Then your middle finger is pointing left: magnetic force Top right wire: Your thumb is coming out of the page: current Your index finger points down in direction of B: magnetic field. Then your middle finger is pointing right: magnetic force So the two magnetic forces are away from each other aren't they??
    1 answer · Physics · 2 weeks ago
  • Find the current induced in loop moving through magnetic field?

    Find the maximum induced current? Voltage = the negative change in magnetic flux over change in time: V = -dΦ / dt magnetic flux = magnetic field multiplied by area Φ = BA. Then: V = -dBA / dt Our magnetic field, B, is constant. Then: V = -BdA / dt Maximum current occurs when the diamond is halfway in. The trouble I have is expressing this area in... show more
    Find the maximum induced current? Voltage = the negative change in magnetic flux over change in time: V = -dΦ / dt magnetic flux = magnetic field multiplied by area Φ = BA. Then: V = -dBA / dt Our magnetic field, B, is constant. Then: V = -BdA / dt Maximum current occurs when the diamond is halfway in. The trouble I have is expressing this area in terms of L and x. Then the position derivative dx/dt is just velocity. The answer is: V = -BLv = -(0.80)(0.1414m)(10m/s) = 1.13V. Then I = V/R = 1.13V / 0.10Ω = 11.3A. 1) How do we go from V = -BdA / dt to V = -BLv ?? I'm having trouble seeing how dA / dt becomes Lv.
    1 answer · Physics · 3 weeks ago
  • How do you find the limits of integration? Triple Integral?

    Find the limits of integration for ∫∫∫ dx dz dy for region bounded by: In the first octant paraboloid y = x² + 5z² y = 4 y = 10 1) How do you generally approach these problems? I had always drawn out double integrals, but with triple integrals its not so convenient. I don't have any system or method now. So far I have ∫[4,10]∫[0,?]∫[0,?] dx dz dy
    Find the limits of integration for ∫∫∫ dx dz dy for region bounded by: In the first octant paraboloid y = x² + 5z² y = 4 y = 10 1) How do you generally approach these problems? I had always drawn out double integrals, but with triple integrals its not so convenient. I don't have any system or method now. So far I have ∫[4,10]∫[0,?]∫[0,?] dx dz dy
    3 answers · Mathematics · 3 weeks ago
  • Faraday's Law, Find Induced Current?

    A square loop moves through a magnetic field as in the picture. 1) What is the maximum current induced in the loop? Man I really cannot solve this for the life of me :( Relevant equations: Voltage = change in magnetic flux / change in time V = -dΦ / dt = -dBAcosθ / dt I barely even understand the equation :(
    A square loop moves through a magnetic field as in the picture. 1) What is the maximum current induced in the loop? Man I really cannot solve this for the life of me :( Relevant equations: Voltage = change in magnetic flux / change in time V = -dΦ / dt = -dBAcosθ / dt I barely even understand the equation :(
    2 answers · Physics · 3 weeks ago
  • Calculate the magnetic flux through loop, around solenoid?

    A 1.8cm diameter solenoid passing through the center of 7.0cm diameter loop. The magnetic field inside the solenoid is 0.16T. When the flux through the loop and the solenoid's area vector are parallel (Top) I calculated magnetic flux Φ = 4.1E-5, which was correct. 1) What is being represented in the image?? A loop is puncturing the side of a... show more
    A 1.8cm diameter solenoid passing through the center of 7.0cm diameter loop. The magnetic field inside the solenoid is 0.16T. When the flux through the loop and the solenoid's area vector are parallel (Top) I calculated magnetic flux Φ = 4.1E-5, which was correct. 1) What is being represented in the image?? A loop is puncturing the side of a solenoid?? I don't really understand the picture lol 2) What is the magnetic flux through the loop when tilted 60 degrees?
    1 answer · Physics · 3 weeks ago
  • What is the ratio of the resistors?

    I have two resistors R₁ and R₂. R₂ > R₁. The resistors are connected to a voltage source V₀ When the resistors are connected in series the current is Iₛ When in parallel, the current Iₚ from the source is equal to 10Iₛ 1) Why do we only consider the smaller root to the quadratic equation ? I got to: The voltage can be expressed in two ways... show more
    I have two resistors R₁ and R₂. R₂ > R₁. The resistors are connected to a voltage source V₀ When the resistors are connected in series the current is Iₛ When in parallel, the current Iₚ from the source is equal to 10Iₛ 1) Why do we only consider the smaller root to the quadratic equation ? I got to: The voltage can be expressed in two ways V₀ = Iₛ (R₁ + R₂) V₀ = Iₚ (R₁R₂ / (R₁ + R₂)) Substituting in R₁ = rR₂, and solving the above for r: R₂² (8r - r² - 1) = 0 We use the quadratic formula to solve for r And r = 7.873 or 0.127. ∴ r = 0.127. The answer is r = 0.127. But why not 7.871?
    1 answer · Physics · 3 weeks ago
  • Which magnet is more representative of Earth’s magnetic field?

    Which magnet is more representative of Earth’s magnetic field? So the answer is ∴A, but could I get an explanation? My homework just tells me I was incorrect for choosing B :( I know the north pole generally is considered up in the arctic. The south pole is down in the antarctic. And opposite magnetic poles attract. So the south end of a magnet... show more
    Which magnet is more representative of Earth’s magnetic field? So the answer is ∴A, but could I get an explanation? My homework just tells me I was incorrect for choosing B :( I know the north pole generally is considered up in the arctic. The south pole is down in the antarctic. And opposite magnetic poles attract. So the south end of a magnet would point up as in magnet A. But don't compasses have it the other way, B?
    4 answers · Physics · 3 weeks ago
  • How many stereocenters does this molecule have? Check my work?

    Am I correct with the location of the stereocenters?
    Am I correct with the location of the stereocenters?
    1 answer · Chemistry · 4 weeks ago
  • Name this organic chemistry molecule? Is it cis or trans?

    1) How would you go through the steps to name this? 2) Is this a trans (E) molecule or cis (Z) molecule? My work (you can ignore this stuff) Butene: 4 carbon main/root chain. Also a double bond. 2-Butene: The shortest number of carbons to the double bond. 3-Methyl-2-Butene: There's a methyl CH3 group at carbon 3. 4-Carboxy-3-Methyl-2-Butane:... show more
    1) How would you go through the steps to name this? 2) Is this a trans (E) molecule or cis (Z) molecule? My work (you can ignore this stuff) Butene: 4 carbon main/root chain. Also a double bond. 2-Butene: The shortest number of carbons to the double bond. 3-Methyl-2-Butene: There's a methyl CH3 group at carbon 3. 4-Carboxy-3-Methyl-2-Butane: Carboxylic acid COOH is at carbon 1) 4-Carboxy-3-Methyl-2-Butane ? R1 is the top left functional group. R2 is the bottom left. C vs H. ---> C has larger atomic number ---> R1 has higher priority. R3 is top right. R4 is bottom right. C vs C. ---> tie HHH vs. OOO ---> O has larger atomic number ---> R4 has priority. We have a trans (Z) molecule, so the full name is 2) (Z) 4-Carboxy-3-Methyl-2-Butane ?
    2 answers · Chemistry · 4 weeks ago