(b) Show that the three bisectors of the an- gles of a triangle are concurrent, that is,they all pass through some point P.

During four years of college, Nolan MacGregor's student loans are $4000, $3500, $4400, and $5000 for freshman year through senior year, respectively. Each loan amount gathers interest of 1.9%, compounded quarterly, while Nolan is in school and 3%, compounded quarterly, during a 6-month grace period after graduation.

(a) What is the loan balance after the grace period? Assume the freshman year loan earns 1.9% interest for 3/4 year during the first year, then for 3 full years until graduation. Make similar assumptions for the loans for the other years. (Round your answer to the nearest cent.) the answer is not 17.66 or 17.67 or 21828.40

(b) After the grace period, the loan is amortized over the next 10 years at 3%, compounded quarterly. Find the quarterly payment. (Round your answer to the nearest cent.)
$ the answer is not 21421.39 or 1,054

(c) If Nolan decides to pay an additional $70 per payment, how many payments will amortize the debt? (Round your answer up to the next whole number.)
the answer is 35 quarters

(d) How much will Nolan save by paying the extra $70 with the number of payments from part (c)? (Round your answer to the nearest cent.)
$ the answer isnt 784.84 or 1124 or 5270

Can i please have a quick explanation on Markov Chain in linear algebra.

Thanks

Applied Math

Let T be the operator on P₂ defined by the equation T(f)=f+(1+x)f'

(a) Show T i linear operator from P₂ into P₂!

(b) Give matrix reppressentaion in base vectorss B={1,x,x²}!

(c) Give a diagonal matrix representing T

(d) Give a diagonal matrix representing T

Where P₂ is ppolynomials with degree less then or equal to 2 and f' is the derivative of polynomial f.

A small business owner contributes $2000 at the end of each quarter to a retirement account that earns 4% compounded quarterly.

(a) How long will it be until the account is worth $150,000? (Round your answer UP to the nearest quarter.)
quarters the asnwer is not 56
(b) Suppose when the account reaches $150,000, the business owner increases the contributions to $8000 at the end of each quarter. What will the total value of the account be after 15 more years? (Round your answer to the nearest dollar.)
$ the answer is not 907891

In hyperbolic geometry, suppose ABCD is a quadrilateral with right angles at C and D such that AD = BC. Show that AB > CD. Hint: Use Proposition 24 of Euclid.

Let 3x3 matrix A = -3 0 -4

                              0 5 0

                             -4 0 3

a) Find the eigenvalues of A and list their multiplicities.

b) Find a basis, Bi, for each eigenspace, E(i).

c) If possible, diagonalise matrix A. (i.e find matrices P and D such that Pinv AP = D is diagonal).

solve the following

1. solve the following inequality for X
2x^2 +5x <3

2. without solving the equation 2x^2 +5x =3, how would I know that it has two rational solutions.

3. 3^2(x+1) - 8.3^x+1 = 1

4. log (x+1) + log x =1

4.1. show that the above equation will have a irrational root if the base is changed to 2, and a rational root if the base is changed to 4

5. the sum of squares of two consecutive even intigers is 1 252. find the intigers

6. suppose x, 2x+1 and 3x+2 are consecutive terms in a geometric sequence. calculate x and hence find the other two terms. how can you be sure the answer is correct?

7. The sizes of angles of a triangle is in proportion 1:2:3. find the size of each angle.

Assume that you have a balance of $9000 on your MasterCard and that you make no more charges. Assume that MasterCard charges 12% APR and that each month you make only the minimum payment of 5% of the balance.

Find how many months it will take to bring the remaining balance down to $400. (Round your answer to the nearest whole number.)

A plane delivers two types of cargo between two destinations. Each crate of cargo I is 7 cubic feet in volume and 131 pounds in weight, and earns $20 in revenue. Each crate of cargo II is 7 cubic feet in volume and 262 pounds in weight, and earns $25 in revenue. The plane has available at most 525 cubic feet and 12,576 pounds for the crates. Finally, at least twice the number of crates of I as II must be shipped. Find the number of crates of each cargo to ship in order to maximize revenue. Find the maximum revenue.

crates of cargo 1

crates of cargo 2

maximum revenue $

2. National Business Machines manufactures x model A fax machines and y model B fax machines. Each model A costs $100 to make, and each model B costs $150. The profits are $45 for each model A and $30 for each model B fax machine. If the total number of fax machines demanded per month does not exceed 2500 and the company has earmarked no more than $600,000/month for manufacturing costs, how many units of each model should National make each month to maximize its monthly profit?

What is the optimal profit?

On May 12, 2008, a certain country had a 7.8 magnitude earthquake. What was the intensity of that earthquake? (Round your answer to two decimal places.)

The amount of outstanding consumer debt? (in trillions of? dollars) is approximated by g(t)= 0.365362 * 1.068022^t, where t=0

corresponds to 1980. Find the year in which consumer debt is

(a) $2 trillion

(b) $9 trillion

(a) The consumer debt will reach???$2 trillion in the latepart of year:

?(b) The consumer debt will reach???$9 trillion in late part of the year:

(3) Write elimination matrix representing each step in elimination process. ( not augmented matrix)

(a)

2x + y − z = 3

x + 3y − z = 6

3x − y + 7z = 8

b)

x+y−z−t=0

x + y + 2z − t = 3

2x + 2y + z + 3t = 13

x + 2y + 5z − 7t = 3

This exercise is designed to be solved using technology such as calculators or computer spreadsheets.

You borrow $18,000 with a term of four years at an APR of 8%. Make an amortization table. How much equity have you built up halfway through the term? (Round your answer to two decimal places.)