Find a transformation from u,v space to x,y,z space that takes the triangle U = [(0,0),(1,0),(0,1)] to the triangle T=[(1,0),-2),(-1,2,0),(1,1,2)]

aortiH 2021-01-02 Answered
Find a transformation from u,v space to x,y,z space that takes the triangle U=[001001] to the triangle
T=[(1,0),2),(1,2,0),(1,1,2)]
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

averes8
Answered 2021-01-03 Author has 92 answers
Step 1
The triangle U=[001001] and the triangle
T=[102120112]
Step 2
Consider T(u,v)=(a1u+b1v+c1,a2u+b2v+c2,a3u+b3v=c3) .Obtain the transformation from u, v to x, y, z as
T(0,0)=(a1(0)+b1(0)+c1,a2(0)+b2(0)+c2,a3(0)+b3(0)+c3)
T(0,0)=(c1,c2,c3)
T(0,0)=(1,0,2)
c1=1,c2=0,c3=2
Step 3
Further evaluate as,
T(1,0)=(a1(1))+b1(0)+c1,a2(1)+b2(0)+c2,a3(1)+b2(0)+c3)
T(0,0)=(a1+c1,a2+c2,a3+c3)
T(0,0)=(1,2,0)
a1=c1=1,a2+c2=2,a3+c3=0
a1=2,a2=2,a3=2
Step 4
Also evaluate,
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2021-08-16
Discrete mathematics
If x1=2,xn=4Xn14nn2.
Find the general term xn.
asked 2021-08-11
Consider the following statement:
” A is a subset of B. Therefore A is a subset of P(B).”
This statement is incorrect as written. Assuming the first sentence is true, what is incorrect about the second sentence? State the second sentence correctly.
asked 2022-06-18
Consider the non-homogeneous linear recurrence relations a n = 2 a n 1 + 2 n find all solutions.
I can show that a n ( h ) characteristic equation r 2 = 0 a n ( h ) = α 2 n .
But I'm stuck on a n ( p ) characteristic equation A 2 n = 2 A 2 n 1 + 2 n
Simplifies to A = 2
A = 2 A + 2
asked 2021-08-21

Discrete math Question.
Suppose your friend makes the following English statement "If XY, but X, then we have Y." Convert it into a statement form. Then show that your friend's statement is valid. Is it true that "XY, but X" is equivalent to Y?

asked 2021-08-15

Maurice and Lester are twins who have just graduated from college. They have both been offered jobs where their take-home pay would be $2500 per month. Their parents have given Maurice and Lester two options for a graduation gift. Option 1: If they choose to pursue a graduate degree, their parents will give each of them a gift of $35,000. However, they must pay for their tuition and living expenses out of the gift. Option 2: If they choose to go directly into the workforce, their parents will give each of them a gift of $5000. Maurice decides to go to graduate school for 2 years. He locks in a tuition rate by paying $11,500 for the 2 years in advance, and he figures that his monthly expenses will be $1000. Lester decides to go straight into the workforce. Lester finds that after paying his rent, utilities, and other living expenses, he will be able to save $200 per month. Their parents deposit the appropriate amount of money in a money market account for each twin. The money market accounts are currently paying a nominal interest rate of 3 percent, compounded monthly. At the end of 2 years, Lester receives a raise and decides to save $250 each month. Maurice receives a $5000 graduation gift from his parents and deposits this amount into his money market account. Maurice goes to work and saves $500 each month. Complete the equations below for the money market account balance for each twin. Let the initial balance u0 be the account balance at the end of 2 years. Write an expression for this month's account balance un in terms of un−1. Recall that the interest rate for the account is 3 percent, compounded monthly. Maurice: u0=$5248.47,un=_____.Lester: u0=_____,un=_____.

asked 2022-06-25
Battleship placement proving that the number of battleships is divisible by 3
We have a grid of 6 columns and x number of rows. All battleships are three units long and can be placed like this: 1 or like this: 2
Where the entire grid is filled with ships with no square units left unfilled, I'm interested in showing that the number of ships positioned as seen in (2) must be divisible by 3; the number of ships placed upright is divisible by 3.
I noticed that the restriction on the number of columns to be 6 means that each column can only have up to two of the ships of type (1), I can show that the number of square units remaining is divisible by 3 but I know that this does not imply the actual number of ships is divisible by 3.
asked 2022-05-17
Existence of a path of length n/2 in every bipartite graph with d ( A , B ) = 1 / 2
Claim: Let G = A B be a balanced bipartite graph with e ( A , B ) n / 2 then G has a path of length n/2.
I know about the erdos-gallai theorem that would net a path of length n/4. By noting that d ( G ) = 2 E ( G ) / V ( G ) n 2 / 4 n
I suspect that the condition of being bipartite forces the ecistence of a longer path, and I am yet unaware of such a result or a counterexample.
Part of my intuition is from the fact that considering a disjoint union of 2 copies of K n / 4 1 , n / 4 which are edge-maximal biparite graphs not containing such a path, we then have these two subgraphs and two yet to be connected vertices on A, also:
2 e ( K n / 4 1 , n / 4 ) = n 2 8 n 2 < n 2 / 8
And adding any edge would form a path of the desired length. Any help on how to go about proving this, or a reference for such a resukt would be greatly appreciated.

New questions

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question