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'= =9 & 4" B ~NormalDody Tertist #atdiapDraw a ll ofthe structura sonersor_tromerspwini: gcomcttk Komcr nonoTne ottrmany olher po'cibl...

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'= =9 & 4" B ~NormalDody Tertist #atdiapDraw a ll ofthe structura sonersor_tromerspwini: gcomcttk Komcr nonoTne ottrmany olher po'cibl

' = =9 & 4" B ~ Normal Dody Tert ist #atdiap Draw a ll ofthe structura sonersor _tromer spwini: gcomcttk Komcr nono Tne ottr many olher po'cibl



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The points on the curve $9 y^{2}=x^{3}$, where the normal to the curve makes equal intercepts with the axes are (A) $\left(4, \pm \frac{8}{3}\right)$ (B) $\left(4, \frac{-8}{3}\right)$ (C) $\left(4, \pm \frac{3}{8}\right)$ (D) $\left(\pm 4, \frac{3}{8}\right)$

Today we are subtracting fractions with unlike denominators specifically involving polynomial denominators. So these are the two fractions we are doing in this problem here. I want to start by finding a common denominator. I'm gonna do that by factoring I notice this polynomial right here can be factored, it's a difference of two squares. I'm gonna do that first d -9 but deep past nine. Now I see that in order for them to share a common denominator, this you know what? We can save some space in order to share a common denominator. Um this fraction on the right here only is missing AD -9. So I'm gonna multiply both the top and bottom By D -9 and distribute the two Which gives me two d -18 over are now common denominator of D plus rd minus nine E plus nine. Now we can simply subtract the numerator. Mhm. For d minus two D. Is to the minus -18 is plus 18. That's going to be over, okay. T minus nine T plus nine. And I see up here I can take it two out of two D n 18. So I'm going to do to D plus nine Over at AD -9 D plus nine. Which will then make these D plus nines cancel and give me two over d minus nine as my final answer.

Hello. We have fallen number 145 christian says that X coordinate of a point on the curve. Okay, copies given normal at which cuts off in equal triceps on the axis. So whenever any line cuts equal intercept. So it's slope must be plus minus one. Okay, now, so this is the slope of normal. Okay. Ah no curb is nine wives quite equal to x cubed nine wide square equal to X. Q. So we have to first find the slope of the tangent. So 18 YY. is equal to three X. Esquire. Which means why does equal to access square by six? What? And if that point is excellent common violin on this. So this point has to be Uh huh excellent comma if you plug in excellent here so it will be excellent. Raised to the power three by two by the by. Oh I understand that is three. Okay, No, at this point we need to find the slope of tangent. Okay, slow about and then we have all the fallout slope of normal will be equal to let us say I am and will be equal to minus six Y by access. Choir and slope of normal at this point that is excellent comma Excellent. Raised about three x 2 by three Will be equal to -6 in two X- one day to about three x 2 to fight by three and two. Excellent. Square So too is -2 and it will be divided by excellent raise to the power one x 2. This is the Slope of normally so we have to find the equation why minus why when why won't it expanded to about three x 2. Excellent. It's about three x 2, divide by three equal to minus two by Excellent. Is department by two x minus x one. Okay this is the equation normal. If we try to solve he tried to solve it, it will become by multiplying with Excellent. Is department by two. Expended Department by two Y minus. Excellent, squired by three equal to -2 x Plus two X 1. Okay so two x. Yeah. Towards Excellence Square batteries. So this will be Letters from listeners multiply with three. three. Excellent days to the parliament by two Excellent Square equal to -6 x Plus 661 this away here. So six X. Place three x 1 days with power one x 2 Y. Equal to two works. One place. Yeah. Excellent. Square by three. Okay. They fortified both sides by this thing. two. Excellent Plus Excellent Square by three. Excellent square battery. We have already multiplied. So it will be only excellent square. Sorry for this. Excellent sweat. Hm Let's multiply both sides. Mhm. Let us divide both sides by this. So this will become six by two. Excellent players. Excellent Squire. Uh huh. three x 1 day tripper. one x 2 developed by to work someplace Excellent Square equal to one. So if you compare with The intercept from Xviii Plus Y would be equal to one. We'll be getting here equal to two x 1 plus. Excellent squired by six. Be equal to two. Excellent place. Extra square by three. X 1 raised fallen by two. And equating because they're both has to be called so two. Excellent place. Excellent squired by six. Equal to two. Excellent place. Excellent Squire by three. Access to go and buy two. Okay so this is to X. Department by two equal to two. So X will be equal to four. This is excellent. No. Yeah. Okay. Excellent. Equal to four. Yeah. And if you plug in an ordinary question, why one will be Not really really question. We should plug in here. X one days with our three by two or three X one raised the power three by 24 days to the power three by two by three. So eight by thing. Okay. So what we needed to find one equals they've got an X coordinate. So X coordinate is simply false. This thing we need to find out an option number. B is the correct option. Thank you.

Hello. We have fallen number 145 christian says that X coordinate of a point on the curve. Okay, copies given normal at which cuts off in equal triceps on the axis. So whenever any line cuts equal intercept. So it's slope must be plus minus one. Okay, now, so this is the slope of normal. Okay. Ah no curb is nine wives quite equal to X cubed nine wide square equal to X. Q. So we have to first find the slope of the tangent. So 18 Y Y. Is equal to three X. Esquire. Which means why does equal to access square by six? What? And if that point is excellent common violin on this. So this point has to be Uh huh excellent comma if you plug in excellent here so it will be excellent. Raised to the power three by two by the by. Oh I understand that is three. Okay, No, at this point we need to find the slope of tangent. Okay, slow about and then we have all the fallout slope of normal will be equal to let us say I am and will be equal to minus six Y by access. Choir and slope of normal at this point that is excellent comma excellent. Raised about three by two by three will be equal to minus six in two X one day to about three by two to fight by three and two. Excellent. Square So too is minus two and it will be divided by excellent raise to the power one by two. This is the slope of normally so we have to find the equation why minus why when why won't it expanded to about three by two. Excellent. It's about three by two, divide by three equal to minus two by Excellent. Is department by two x minus x one. Okay this is the equation normal. If we try to solve he tried to solve it, it will become by multiplying with Excellent. Is department by two. Expended Department by two Y minus. Excellent, squired by three equal to minus two X plus two X one. Okay so two X. Yeah. Towards Excellence Square batteries. So this will be letters from listeners multiply with three. Three. Excellent days to the parliament by two minus Excellent Square equal to minus six X plus 6 +61 this away here. So six X. Place three X one days with power one by two Y. Equal to two works. One place. Yeah. Excellent. Square by three. Okay. They fortified both sides by this thing. Two. Excellent plus Excellent square by three. Excellent square battery. We have already multiplied. So it will be only excellent square. Sorry for this. Excellent sweat. Hm Let's multiply both sides. Mhm. Let us divide both sides by this. So this will become six by two. Excellent players. Excellent Squire. Uh huh. Three X one day tripper. One by two developed by to work someplace excellent square equal to one. So if you compare with the intercept from XviII plus y would be equal to one. We'll be getting here equal to two X one plus. Excellent squired by six. Be equal to two. Excellent place. Extra square by three. X one raised fallen by two. And equating because they're both has to be called so two. Excellent place. Excellent squired by six. Equal to two. Excellent place. Excellent Squire by three. Access to go and buy two. Okay so this is to x rays department by two equal to two. So X will be equal to four. This is excellent. No. Yeah. Okay. Excellent. Equal to four. Yeah. And if you plug in an ordinary question, why one will be Not really really question. We should plug in here. X one days with our three by two or three X one raised the power three by 24 days to the power three by two by three. So eight by thing. Okay. So what we needed to find one equals they've got an X coordinate. So X coordinate is simply false. This thing we need to find out an option number. B is the correct option. Thank you.

Okay, Um, front. The first population. We have a one. You go to 40 and p one prime. You go, Teoh narrow. But tonight, so you can calculate the cute one Prime. It should be 10.1, and we multiply it. Mom on one times, be one prime. It goes Teoh 36 and a long times. Q one primary goes you for the Sioux Of others are the estimated value for oh, uh, times P one and and one times cure because the true about a p one or q uh, are unknown. So inches used the observed value to estimate that true value for the second population. And tol goes to Pepsi and again be to prime opposed to There were quite a night so cute to prime you cooked to their what one and we have and two times p two prying, which is 45 and two times Q two. Crime is five here. We can tell, um, this example is actually violating the gut lining for the approximately normal cause. Um, or according to the gut line, all this quantities should be greater than five. But here Subaru's are not greater than five


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