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Question 183 ptAtechaician uearing cucular mctal bend on hit ATE moict his hend into urifcrm magectic ficld o{ msgnitude ] S T i ! tme 01032 L Ibe dunaa o{ the bend...

Question

Question 183 ptAtechaician uearing cucular mctal bend on hit ATE moict his hend into urifcrm magectic ficld o{ msgnitude ] S T i ! tme 01032 L Ibe dunaa o{ the bend # 6 } cm end tht field # 25 4 rglc of 42* With the plane ofthe metal band while the Iand # in the feld, fiad tte marmniude ntte eml induced [4 tbe band 0.0434V00052 !1,0839 V00109 UKeda ofte abott

Question 18 3 pt Atechaician uearing cucular mctal bend on hit ATE moict his hend into urifcrm magectic ficld o{ msgnitude ] S T i ! tme 01032 L Ibe dunaa o{ the bend # 6 } cm end tht field # 25 4 rglc of 42* With the plane ofthe metal band while the Iand # in the feld, fiad tte marmniude ntte eml induced [4 tbe band 0.0434V 00052 ! 1,0839 V 00109 U Keda ofte abott



Answers

$21-23$ Use Theorem 10 to tind the curvature.
$$
\mathbf{r}(t)=\sqrt{6} t^{2} \mathbf{i}+2 t \mathbf{j}+2 t^{3} \mathbf{k}
$$

Okay sorry we're trying to find the culture of the curve. L. T. Equals T. T. Square and gt. So the we need to find We need to find the curvature using therm 10 um and 1310 says that curvature can be found by the formula length of the cross product of our prime and double prime Olivia length of our prime to the side. Okay so let's calculate our primary duty which is equal to 12 T. E. T. And then uh double prime of T equals zero two E. T. So let's calculate the cross product of these. These two our prime T cross audible priority equals I J. K. And then we have 12 T. E. T 02 E. T. Which he calls 2- three times e. T minus to E. T. I minus E. T. J plus two K. And then I'm going to simplify the X entry a bit more. Get t minus one, I minus E. T. J. Plus two K. Okay so now we have uh we have the cross product we need to take the link of it. Ah Double property equals CES 482 T t minus one squat Plus 8 to T. Plus four. And then to find the numerator or the copper or the curvature we'll take the norm of our priority which he calls one plus 40 square plus. Eat to T. Which means that our priority normal priority To the 3rd equals one plus 40 square plus eat to T. Two three of the two. Okay so let's plug in these expressions into the function. I do the formula of the curvature and then we get square root for E. T. Times T -1 squad plus eat to T plus four. Are you there one plus 40 square plus eat to T. Two. 3/2.

For this question were asked to determine the magnetic field appoint pee er in the figure 60 worth point P is halfway between the two corners and we can use this to determine the results of the problem for 40 and 41.1. So if you don't no, those results aren't familiar. You can work those out or go back and view the videos on those because I'm gonna be utilizing them here So the total field be is gonna be equal to be one plus B two plus B three the contribution of these three different points. So we simply have to use those results from these previous questions to find these answers. So be one here is gonna be in Munich. Magnetic permeability of free space times the current I divided by four pi times the area a race you'd be the distance a from the figure over too. This gets multiplied by the sine of the angle theta plus, um two divided by over two times Route five. We can simplify this a little bit on. What we find is this is equal to mu, not times I divided by two Hi. A multiplied by two divided by the square root of five. Be too we find is equal to, um you not times I divided by four pi. This time it's just times a knot over too. Um, this is multiplied by the first value is over too divided by over two times Route five. And then this gets added to the second value, which is the exact same. It's over too divided by over two times 35 Simplifying this a little bit. We find that this comes out to equal We have, you know, I over to I a come and then everything in the parentheses e simplifies down to one over Route five. Almost done. We just have to find the three. Now be three is the easiest one from the results of the previous question here that it referenced. This is just me. You know, I divided by two p a times to over revive. So since B is equal to be one plus b two plus b three, we find that B is equal to you, not I, because each one has you not I, over to pay. So that constant is the same in all of them. So we have that multiplied by? Well, let's see. Be three. Has two of her. Room five B one has to over route five and be too at one over Route five. So add those all together, you end up with five over five, but five over Route five is equal to the square to five. So that is our solution. But direction matters, right? So what is the direction using the right hand rule? Uh, for all of these, they aren't together. They all add in the same direction. So using the right hand rule, the direction is into the page. Point your fingers, uh, or curl your fingers in the direction of the current and your thumb points in the direction of the magnetic field so we can say into the page.

Okay. So we're trying to find the curvature of the curve. O. T equals zero T. to the 5th. T. Squad. Using the theory in 2010. So thorium tenses curvature. Copper is equal to the length. Probably cross product of our priority. Our priority and double primary T to link of the prime of T to the third. Okay. So let's calculate the curvature using this formula that we need priority. Which is equal to zero three T. Squad to T. And then double prime or T is equal to zero 60 and two. Okay, so now I'm going to calculate the cross product of these functions. Mm I j. Okay. And zero three T square to T. Zero 60 and two. Which is equal to 60 squad minus 12 T. Squad I minus zero jay plus zero. Okay. Which is equal to negative sixties one. I Okay so that means the length of the cross product is equal to six T squat. Yeah. Now for the denominator we have the we need to calculate the length of our priority which is equal to square it nine T. to the 4th plus four T square. She is equal to T. Times Square it 90 square plus four. By factoring out T squared inside the squared. So that means the denominator of the culture is equal to T. to the 3rd times 90 squared plus four two, And now we have all we need. So I'm just gonna substitute the expressions. Found that both which is 60 square for the numerator. And then this for the denominator T. to the 3rd times 90 square plus four two, She is equal to 6 to Tee Times 90 square plus four two,

Yeah. Right. This is an english grammar section. Question of the A. C. T. Practice test for. So we have problem 14. Um for potential answer choices F. G. H I. J. And as a sentence to mentions um this is asked about like the whole general passage. So the writer specifically wants to put new information to the essay and the information is described in the sentence. It's outlined in the in the question. So we're being asked in this um where the new material should be most logically placed or what what paragraph specifically. So this is about organization. So what the question we have to ask ourselves is what could have been destroyed by the explosion in the Parthenon? Well we have a one potential reason or we can write this down what could have yeah, been destroyed. Yeah. Bye. The explosions in the Parthenon. Well it could have been a so this would be the answer to be carvings. It's looking at context. So the fact that there are some of them, some of the carvings were destroyed during war is a good reason that they can no longer be found in the Parthenon, which is what paragraph four talks about. paragraph four talks about carvings, um, and what that they can no longer be found. So the new material belongs in that paragraph. Answer choice jay is correct.


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