Search & Filtering
1. Determine whether the lines given by the equations below are parallel, perpendicular, or neither. Also, find a rigorous algebraic solution for each problem.
a. {3y+4x=12 \brace -6y=8x+1}
b. {3y+x=12 \brace -y=8x+1}
c. {4x-7y=10 \brace 7x+4y=1}
2. A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by h(t)=-4.9t^2+24t+8 . What is the height of the building? What is the maximum height reached by the ball? How long does it take to reach maximum height? Also, find a rigorous algebraic solution for the problem.
3. A farmer finds that if she plants 75 trees per acre, each tree will yield 20 bushels of fruit. She estimates that for each additional tree planted per acre, the yield of each tree will decrease by 3 bushels. How many trees should she plant per acre to maximize her harvest? Also, find a rigorous algebraic solution for the problem.
If a stock price goes from $10 to $12 from January 1st to January 31, from $12 to $9 from February 1st to February 28th, and from $9 to $15 from March 1st to March 31th is the price change from $10 to $15 a straight line?
It is clear that in each of the three time intervals mentioned there was a complex daily variation of prices as in an electrocardiogram. But what would be a simplified solution for a first naive view of the situation? Would a simple function hold up? What is the simplest function to represent this situation? Does your naïve initial and simplified model allow you to predict the behavior of the stock in the next month?
How can I use three “pieces” of lines to describe the price movements from the beginning of January to the end of March? Show the graph for the price movement.
Go to www.desmos.com/calculator, and write your equations following the example
y = x + 2 {0 < x < 2}
y = –x + 6 {2 < x < 5}
y = 2x – 9 {5 < x < 8}
24 pairwise different positive integer numbers are written on the board. Their mean value is equal to 38. Let M be the smallest of these numbers. Find the largest possible value of M.
classify the following as an english noun or sentence, mathematical expression or sentence
a.) m+3m=5
b.) 6/7
c.) 2+3+1=7
d.) Iu - vI
e.) x^2 = a-1
1). Determine whether set S given below is a basis for ℝ 3 . If not, explain why.
S = {(1,0,0),(0,1,0),(0,0,0)}
2). Find the rank of matrix D given below.
D = [0 3 9 0]
[-2 -1 1 -1]
[0 -1 -3 1]
Find the eigenvalues and corresponding eigenvectors of matrix G given below.
G= [2 -3]
[4 -5]
The left and right page numbers of an open book are two consecutive integers whose sum is 265. Find these page numbers.
what is a function?
The first 1st,5th and 10th term of a linear sequence are geometric progression. If the 2nd and 8th term of the linear sequence is 30, find the non-zero common difference of the linear sequence
How do standard algorithms differ from student-invented strategies? Explain the benefits
of invented strategies over standard algorithms (give at least two valid points).
