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1. Coplanar vectors and linear dependance

how do i prove vectors u v w are coplanar if and only if they are linearly dependent ? i have no idea where to start.
2. Resource on induction

In your first post. I should check my posts more carefully. The principle is that the general equation of a series is correct if it works for a number n and is n+1 i got k^2+k+2k+2=k^2+k+2k+2 by subbing in k=n into n(n+1)/2 and then taking that and subbing that into the sequence of k+1=n and...
3. Resource on induction

im starting to get the hang of that now. however i have problems when trying to get the General formula of the series from the formula of the sequence. a example is that im asked to prove ((n^3)-n) is divisible by 6 for all n belongs to N by induction.
4. Resource on induction

The principle is that if a series it is true for any number n it is ALSO true for the number that follows n. i solved the question above and got that k^2+3k+2==k^2+3k+2 therefore i proved this series. however the sequence is not always that easy as it it just equals n how do i find the nth term...
5. Resource on induction

i am totally lost on this subject. like i have NO CLUE what its about or what to do or how to prove things. Can anyone recommend a good site or online resource about this induction stuff?
6. Combinations: C(28,2n)/C(24,2n-4)=225/11 Solve for n

i am given C(28,2n)/C(24,2n-4)=225/11 where C are combonations. i am supposed to solve for n. after subbing in n and k and simplifying i get (11*28!)/2n!=(225*24!)/(2n-4)! (i am pretty sure this is correct). i do not seem to be able to continue after that. how do i solve for n?
7. Perpendicular Lines in 3 Space

its aliright but i still have one more question. i do not understand how you got this: \vec a_1 -\vec a_2+ \vec b_1 t_1-\vec b_2 t_2
8. Perpendicular Lines in 3 Space

okay if i do a cross product of the b vectors i will get a line that is perpendicular to both of the line but only at the origin. the line does not have to necessarily come across the origin right? so this would be the like B value of my 3rd line right? now then they want me to put the line so...
9. Perpendicular Lines in 3 Space

i know how to get values of vector b but i don't understand how to do the calculations. i dont know how to find the a line that intersects 2 other lines and at a 90 degree angle...
10. Perpendicular Lines in 3 Space

i am given parametric equations of 2 lines L1 and L2 and i am asked to find the vector, parametric and symmetric equation of a line that intersects these 2 lines at 90 degrees so a line that is perpendicular to those 2 lines. how do i go about this? at first i tried converting the parametric...
11. Coplanar vectors problem

But i cant solve it there are too many variables. i subbed in the values for W vectors and then i expanded it so now i have like C(1)V(1)+C(1)V(2) etc.. then i added up all the V(1) vectors and ended with sumthing like V(1)[C(1)+C(2)]=0 then that led me to [C(1)+C(2)]=0 cause C would be the...
12. Coplanar vectors problem

The numbers in brackets are supposed to be in subscript so V(2) would be V subscript 2 and the number in front is just multiply, all the variables are vectors so they have a arrow on top. Determine if, W(1) = 2V(1) + 3V(2) , W(2) = V(2) + 2V(3) and W(3) = -V(1) - 3V(3) are coplanar i dont...
13. 3 Space Parallelogram

Thanks HallsofIvy for correcting me. But i dont understand if im given 3 vertices i would only know 2 vectors that form the parallelepiped and one vector that is a diagonal of the parallelepiped.
14. 3 Space Parallelogram

i am given the (x,y,z) coordinates of 3 sides of a parallelogram how do i go about finding the 4 coordinate. do i find the distance between points using the same way to find vectors then try to find direction angles or something like that? because there is no slope or anything to compare too...
15. Help simplifying derivitive

okay so how does this prove y' = y/x?
16. Help simplifying derivitive

okay im supposed to prove the derivitive of: sqrt x/y + sqrt y/x is equal to y/x okay im stuck where i have finally isolated y' i dont know how to reduce it further im stuck with this at the moment (see attachment) can you please tell me the process you went through to simplify it?
17. Absolute values of variables

so basically|x| means the answer is like always positive so therefor there will be a possibility of where the x is negative or -x and positvie just x right? so |x| is like F(x) rite? and if you sub x-7 for f(x) you would get like in order for x to be the positive value it would have to be...
18. Absolute values of variables

so if |x|=(x,if x>=0, and -x, if x<0) then what would be like |x-7| be equal too and how do you do this i do not understand why |x|equals (x,if x>=0, and -x, if x<0) could you explain it to me?
19. Intersection points of the graph its solutions?

i still dont understand i can find the points where f(t) and g(t) intersect by graphing (how do i do this by graphing?) but what do you mean by having same points as zeros?
20. Intersection points of the graph its solutions?

The graphs of f(theta) = 2sin(theta) - 1 , and g(theta) = 3cos(theta)+2 are given. What equation would have the intersection points of the graph its solutions? ummm..... what does this mean? and how do i solve it?
21. Parabola Problem

Given {x | -50 < x < 50}, {y | 0 < y < 20} vertex at (0,20) it is a parabola find the equation in (x-h)^2=4p(y-k) its pretty easy except how do i find p?
22. Hyperbola equations

nope it does say that the graph is supposed to be a curved arch that will have horizontal span of 100m and a maximum height of 20m.
23. Hyperbola equations

Using a domain of {x | -50 < x < 50} and a range of {y | 0 < y < 20}, determine the following types of equations that you could use to model the curved arch. The equation of a hyperbola in the form , where b = 10. The lower arm of the hyperbola would represent the arch...
24. Locus question

thanks i am asked to draw a diagram that represent the locus in each of the following situations also i am asked "what is the locus of each?" a) Going down on a elevator b)sitting in a seat on a ferris wheel as it rotates c)all the points that are 2cm from a parabola d)all the point that...
25. Locus question

is the locus of points equidistant from the two given points on the same line as the perpendicular bisector of the 2 points?
26. How do you solve for n in this question 34=r^n

how do you solve for n in this question 34=r^n i know what the r value is man i should know this
27. Interest on principal over 5 years

yes that is what got from the question as well that means that there are 5 payments of 6000 to the school. the hockey star pay gives only 1 one payment. so that means what i did for a) was correct right? my problem is i dont know how to sub that into the equation of Sn

30. Pendulum- Maximum displacement?

what is the maximum displacement of a pendulum i dont know what it is. is it the distance from the central point to the end of the arm? and how do i solve it if i am given a periodic Sin function?