Badalyan Posted May 15, 2015 Report Share Posted May 15, 2015 (edited) Wait, you had to find the cross product, and that would be the direction vector for the new line. But what did you guys use for the position vector though since the lines did not intersect? I thought that was quite confusing haha. Also, all the people in my class got different percentages for the Area with the goat question lol. I got something round 31 percent. What did you get? Hi, I gave the TZ2 exam... Anyone else saw a conflict in the last question in the paper? First part was prove these two lines are skewed...And then later on in the question it asked for the point of intersection. Isn't skewed by definition non-intersecting?What happened?Was that a trick question? Or have I totally misinterpreted the question. Oh no.. They asked to find a line perpendicular to the given lines and its point of intersection with each of the lines... Edited May 15, 2015 by Badalyan Reply Link to post Share on other sites More sharing options...
kmcgowan2000 Posted May 16, 2015 Report Share Posted May 16, 2015 (edited) Wait, you had to find the cross product, and that would be the direction vector for the new line. But what did you guys use for the position vector though since the lines did not intersect? I thought that was quite confusing haha. Also, all the people in my class got different percentages for the Area with the goat question lol. I got something round 31 percent. What did you get? Hi, I gave the TZ2 exam... Anyone else saw a conflict in the last question in the paper? First part was prove these two lines are skewed...And then later on in the question it asked for the point of intersection. Isn't skewed by definition non-intersecting?What happened?Was that a trick question? Or have I totally misinterpreted the question. Oh no.. They asked to find a line perpendicular to the given lines and its point of intersection with each of the lines... As vish97 said, you had to find the equation of the line perpendicular to the two skew lines. The direction vector is indeed the cross product, but the position vector was a little trickier to figure out. I can't remember the actual vectors used, but let's say the two skew lines are l1 = (a,b,c) + λ(d,e,f) and l2 = (l,m,n) + μ(p,q,r). This is the common perpendicular:l3 = (x,y,z) + α(u,v,w) You know that the common perpendicular intersects with both of the skew lines, so:(l+μp,m+μq,n+μr) = (a+λd,b+λe,c+λf) + α(u,v,w) Essentially, this is saying:point on l2 = point on l1 + direction vector of l3 You already know the values of the following variables: a,b,c,d,e,f,l,m,n,p,q,r,u,v,w. This leaves you to find the values of μ, λ, and α. Because you have this three-dimensional vector equation, you have a system of three simultaneous equations to solve to get the values of three variables, which should be fairly straightforward. Edited May 16, 2015 by kmcgowan2000 Reply Link to post Share on other sites More sharing options...
freshfaced333 Posted May 16, 2015 Report Share Posted May 16, 2015 for tz1 I could not figure out the stupid helicopter question.. I think I got all my numbers wrong I took ages to plug in numbers for the continuous dist question as well and I'm scared that I might have made stupid mistakes. I'm so mad that I didn't think of graphing that really ugly function which asks for the normal equation to the tangent > Reply Link to post Share on other sites More sharing options...
kw0573 Posted May 16, 2015 Report Share Posted May 16, 2015 TZ1For helicopter question Luckily my school is doing Calculus for paper 3 so I used differential equations to solve for t in terms of v (the question was hinting at a similar route). Didn't realise the question said hence. Paper 2 also had a lot of conversions between radians and degrees ("Wait why is my graph of sinx / 4 not visible from 0 to pi? oh my calculator's in degrees") Reply Link to post Share on other sites More sharing options...
vish97 Posted May 16, 2015 Author Report Share Posted May 16, 2015 Wait, you had to find the cross product, and that would be the direction vector for the new line. But what did you guys use for the position vector though since the lines did not intersect? I thought that was quite confusing haha. Also, all the people in my class got different percentages for the Area with the goat question lol. I got something round 31 percent. What did you get? I got a 41%.. But the answers 44% I made a stupid calculator error while entering the inputs and ended up with the wrong answer Hopefully I won't lose too many marks.. 1 Reply Link to post Share on other sites More sharing options...
sam1996 Posted May 16, 2015 Report Share Posted May 16, 2015 (edited) This one went very well for me, unfortunately paper 1 will most likely prevent me from getting a 7. Just to frustrate some of you (I made this mistake), in TZ2 the particle returned to it's starting position when the graph returned to s=3 not s=0 as it started at s=3. Silly mistake but pretty easy to make Edited May 16, 2015 by sam1996 1 Reply Link to post Share on other sites More sharing options...
Cris_101 Posted May 16, 2015 Report Share Posted May 16, 2015 This one went very well for me, unfortunately paper 1 will most likely prevent me from getting a 7. Just to frustrate some of you (I made this mistake), in TZ2 the particle returned to it's starting position when the graph returned to s=3 not s=0 as it started at s=3. Silly mistake but pretty easy to makeUghhhh, you managed to frustrate me hahaha. I hadn't thought about that, I made the same mistake Reply Link to post Share on other sites More sharing options...
sam1996 Posted May 16, 2015 Report Share Posted May 16, 2015 This one went very well for me, unfortunately paper 1 will most likely prevent me from getting a 7. Just to frustrate some of you (I made this mistake), in TZ2 the particle returned to it's starting position when the graph returned to s=3 not s=0 as it started at s=3. Silly mistake but pretty easy to makeUghhhh, you managed to frustrate me hahaha. I hadn't thought about that, I made the same mistakeA lot of us will have made that mistake most of my friends did, and they're good mathematicians ...some of them also tried to convince me one of the turnip questions involved conditional probability but I couldn't recall it well enough, didn't use conditional probability though. Ideas, anyone? Reply Link to post Share on other sites More sharing options...
vish97 Posted May 16, 2015 Author Report Share Posted May 16, 2015 This one went very well for me, unfortunately paper 1 will most likely prevent me from getting a 7. Just to frustrate some of you (I made this mistake), in TZ2 the particle returned to it's starting position when the graph returned to s=3 not s=0 as it started at s=3. Silly mistake but pretty easy to makeOMG Yeahh I actually don't remember what did though... xP Reply Link to post Share on other sites More sharing options...
Hassan76 Posted May 16, 2015 Report Share Posted May 16, 2015 Wait, you had to find the cross product, and that would be the direction vector for the new line. But what did you guys use for the position vector though since the lines did not intersect? I thought that was quite confusing haha. Also, all the people in my class got different percentages for the Area with the goat question lol. I got something round 31 percent. What did you get? I got a 41%.. But the answers 44% I made a stupid calculator error while entering the inputs and ended up with the wrong answer Hopefully I won't lose too many marks..How should I calculate the area ? Reply Link to post Share on other sites More sharing options...
sam1996 Posted May 16, 2015 Report Share Posted May 16, 2015 (edited) Wait, you had to find the cross product, and that would be the direction vector for the new line. But what did you guys use for the position vector though since the lines did not intersect? I thought that was quite confusing haha. Also, all the people in my class got different percentages for the Area with the goat question lol. I got something round 31 percent. What did you get? I got a 41%.. But the answers 44% I made a stupid calculator error while entering the inputs and ended up with the wrong answer Hopefully I won't lose too many marks..How should I calculate the area ?Wait, you had to find the cross product, and that would be the direction vector for the new line. But what did you guys use for the position vector though since the lines did not intersect? I thought that was quite confusing haha. Also, all the people in my class got different percentages for the Area with the goat question lol. I got something round 31 percent. What did you get? I got a 41%.. But the answers 44% I made a stupid calculator error while entering the inputs and ended up with the wrong answer Hopefully I won't lose too many marks..How should I calculate the area ?You drew the 4 by 10 rectangle and the goat was on a 5m rope attached to the corner. The goat could cover an area up to the arc of a circle with radius 5m and centre one of the vertices of the rectangle. Then you could split the area into a sector and a triangle and you could use the triangle to work out the angle of the sector, easy from there. Edited May 16, 2015 by sam1996 1 Reply Link to post Share on other sites More sharing options...
Hassan76 Posted May 16, 2015 Report Share Posted May 16, 2015 Thanks Reply Link to post Share on other sites More sharing options...
kallum Posted May 16, 2015 Report Share Posted May 16, 2015 tz2, how was it that you guys calculated the percentage area of the field the goat could graze? Reply Link to post Share on other sites More sharing options...
Eid Jazairi Posted May 17, 2015 Report Share Posted May 17, 2015 Once you find the total area he can graze on (like what sam1996 said). Then you divide total area he can graze on by size of the field, multiply by 100 and BAM you got the percentage Reply Link to post Share on other sites More sharing options...
gruff1234 Posted May 17, 2015 Report Share Posted May 17, 2015 tz2, how was it that you guys calculated the percentage area of the field the goat could graze? You had to calculate two areas. One was the area of the sector that is created when the goat pivots across the field, and one was the triangle below that area. I got 44% as well. How did you guys do on paper 1 with the geometric sequence created by the products of the roots or whatever it was? Reply Link to post Share on other sites More sharing options...
kallum Posted May 17, 2015 Report Share Posted May 17, 2015 tz2, how was it that you guys calculated the percentage area of the field the goat could graze? You had to calculate two areas. One was the area of the sector that is created when the goat pivots across the field, and one was the triangle below that area. I got 44% as well. How did you guys do on paper 1 with the geometric sequence created by the products of the roots or whatever it was? the sector created by the goats pivot went outside of the area of the field, is the "triangle below that area" an approximation of the extra area the sector created by the goat and your taking that away from the sector? Reply Link to post Share on other sites More sharing options...
Ragamuffin Posted May 17, 2015 Report Share Posted May 17, 2015 tz2, how was it that you guys calculated the percentage area of the field the goat could graze? You had to calculate two areas. One was the area of the sector that is created when the goat pivots across the field, and one was the triangle below that area. I got 44% as well. How did you guys do on paper 1 with the geometric sequence created by the products of the roots or whatever it was? the sector created by the goats pivot went outside of the area of the field, is the "triangle below that area" an approximation of the extra area the sector created by the goat and your taking that away from the sector? Not sure what you mean by "triangle below that area", but you're right that if you draw a sector created by the goat's pivot, you'd eventually go outside of the field. That's why when you draw the sector, you stop once you reach the other side of the field. You'll find that you now have a sector of radius 5m, and a right-angled triangle with height 4m and hypotenuse 5m. Calculate the area of the sector, and the right-angled triangle, and you're good. Reply Link to post Share on other sites More sharing options...
Megamind Posted May 17, 2015 Report Share Posted May 17, 2015 tz2, how was it that you guys calculated the percentage area of the field the goat could graze? You had to calculate two areas. One was the area of the sector that is created when the goat pivots across the field, and one was the triangle below that area. I got 44% as well. How did you guys do on paper 1 with the geometric sequence created by the products of the roots or whatever it was? the sector created by the goats pivot went outside of the area of the field, is the "triangle below that area" an approximation of the extra area the sector created by the goat and your taking that away from the sector? Not sure what you mean by "triangle below that area", but you're right that if you draw a sector created by the goat's pivot, you'd eventually go outside of the field. That's why when you draw the sector, you stop once you reach the other side of the field. You'll find that you now have a sector of radius 5m, and a right-angled triangle with height 4m and hypotenuse 5m. Calculate the area of the sector, and the right-angled triangle, and you're good. The triangle is a very close appromixation to the area of the land that Gruff cannot graze on. You end up with a sector that's 5 m radius, and you take out the area of the whole sector (pi*r*r/4). From this you subtract the area of the triangle with a base of (the extension - i.e. 1 m) and the height (3 m) using 0.5*b*h. The right angle triangle has neither height of 4 m or hypotenuse of 5 m, according to my calculations at least :/ If you want to be really precise, you're correct, the area that gruff cannot graze on is not exactly a triangle but it isn't a sector either. Its more of a quarter of an elliptical orbit, the calculations of which are beyond HL math. Hence, you have to use the triangle method. I got 44% too. Reply Link to post Share on other sites More sharing options...
Ragamuffin Posted May 17, 2015 Report Share Posted May 17, 2015 tz2, how was it that you guys calculated the percentage area of the field the goat could graze? You had to calculate two areas. One was the area of the sector that is created when the goat pivots across the field, and one was the triangle below that area. I got 44% as well. How did you guys do on paper 1 with the geometric sequence created by the products of the roots or whatever it was? the sector created by the goats pivot went outside of the area of the field, is the "triangle below that area" an approximation of the extra area the sector created by the goat and your taking that away from the sector? Not sure what you mean by "triangle below that area", but you're right that if you draw a sector created by the goat's pivot, you'd eventually go outside of the field. That's why when you draw the sector, you stop once you reach the other side of the field. You'll find that you now have a sector of radius 5m, and a right-angled triangle with height 4m and hypotenuse 5m. Calculate the area of the sector, and the right-angled triangle, and you're good. The triangle is a very close appromixation to the area of the land that Gruff cannot graze on. You end up with a sector that's 5 m radius, and you take out the area of the whole sector (pi*r*r/4). From this you subtract the area of the triangle with a base of (the extension - i.e. 1 m) and the height (3 m) using 0.5*b*h. The right angle triangle has neither height of 4 m or hypotenuse of 5 m, according to my calculations at least :/ If you want to be really precise, you're correct, the area that gruff cannot graze on is not exactly a triangle but it isn't a sector either. Its more of a quarter of an elliptical orbit, the calculations of which are beyond HL math. Hence, you have to use the triangle method. I got 44% too. Thanks for the input, Megamind. I'm not sure but according to your calculations, perhaps we used different approaches? I didn't focus on finding the "extra area" Gruff cannot graze, but seeing both of us got correct answers we both should be fine Reply Link to post Share on other sites More sharing options...
Megamind Posted May 17, 2015 Report Share Posted May 17, 2015 tz2, how was it that you guys calculated the percentage area of the field the goat could graze? You had to calculate two areas. One was the area of the sector that is created when the goat pivots across the field, and one was the triangle below that area. I got 44% as well. How did you guys do on paper 1 with the geometric sequence created by the products of the roots or whatever it was? the sector created by the goats pivot went outside of the area of the field, is the "triangle below that area" an approximation of the extra area the sector created by the goat and your taking that away from the sector? Not sure what you mean by "triangle below that area", but you're right that if you draw a sector created by the goat's pivot, you'd eventually go outside of the field. That's why when you draw the sector, you stop once you reach the other side of the field. You'll find that you now have a sector of radius 5m, and a right-angled triangle with height 4m and hypotenuse 5m. Calculate the area of the sector, and the right-angled triangle, and you're good. The triangle is a very close appromixation to the area of the land that Gruff cannot graze on. You end up with a sector that's 5 m radius, and you take out the area of the whole sector (pi*r*r/4). From this you subtract the area of the triangle with a base of (the extension - i.e. 1 m) and the height (3 m) using 0.5*b*h. The right angle triangle has neither height of 4 m or hypotenuse of 5 m, according to my calculations at least :/ If you want to be really precise, you're correct, the area that gruff cannot graze on is not exactly a triangle but it isn't a sector either. Its more of a quarter of an elliptical orbit, the calculations of which are beyond HL math. Hence, you have to use the triangle method. I got 44% too. Thanks for the input, Megamind. I'm not sure but according to your calculations, perhaps we used different approaches? I didn't focus on finding the "extra area" Gruff cannot graze, but seeing both of us got correct answers we both should be fine Oh alright, sorry, I thought we had the same approaches that's why I found the dimensions different from mine. But same answer in Math HL, Yay! Reply Link to post Share on other sites More sharing options...
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