3×3 Systems Elimination by Addition

1) -5x-2y+20z=-28
2)   2x-5y+15z=-27
3) -2x-2y-5z= -12

Please write out all of the steps so I'll be able to figure out the formulas myself.

In this project we are going to model the Ball Toss with a quadratic function. So at 30 cm intervals, we draw 4 vertical lines extending from the eraser tray to the top of the marker board. We number the lines with their distances from the left most vertical line (which serves as the y-axis).Each of our volunteers selects a line and stand facing it at close proximity to the board. Between the board and the volunteers, I toss the ball to the catcher. Each of the volunteers will mark the height above the eraser tray at which the ball crosses his/her line. We will measure and label the height from the eraser tray to the marks.

We have the following data: M(0,23.5); N(30,37.2); P(60,35.8); Q(90,19.3)

These data represent a set of ordered pairs or a function. Since this function has an infinite number of ordered pairs, we are going to find an equation that defines this function. So we should use an equation in x and y where x represents the first coordinate and y represents the second coordinate. We should create a coordinate plane by drawing a horizontal number line called the x-axis, and a vertical line called the y-axis.

1. In this specific model of ball toss

    a) What does the x-axis represent?

    b) What do the x-coordinates represent?

    C) What do the y-coordinates represent?

2. Display your data in the coordinate plane or plot the points using a graph paper (Consider each    square 10cm).Make sure you label the axis and the points.

3. Draw a smooth curve containing these points.

4. What shape does the graph have?

5. How does this shape open?

6. What kind of function this graph represents?

7. Write the standard form of the equation that represents this function.

8. Use the 3 points M (0, 23.5); N (30, 37.2) and P (60, 35.8) that verify the equation you wrote in question #7

    a) Find the quadratic polynomial that predicts y from x. (Hint: you should resolve a system of linear equation to find the coefficients of the equation). (Round your answers to the nearest ten thousandths). (Remember to show all your work)

b) Is the leading coefficient positive or negative?

    c) Does your answer for question (8b) contradict with your answer for question (5)? (If yes, check your work over before you continue).

9. a) What does the function say the height of the ball was when it was 120cm from the y-axis? (Round your answer to the nearest tenth).

   b) What is the sign of this height?

   c) What is the position of the ball to the eraser tray?

   d) Write this ordered pairs and plot its point T on the graph.

10. a) At what values of x does the function say the ball should have hit the eraser tray? (Round the values of x to the nearest cm)

      b) Display these points I and J on the graph and write their coordinates.

      c) What are these points called?

11. a) At what distances from the y-axis was the ball 28 cm above the eraser tray?(Round your answers to the nearest cm)

     b) Write these ordered pairs and plot their points R and S on the graph.

12. a) At what distance from the y-axis was the ball at its highest point?(Round your answer to the nearest cm).

     b) What was the maximum height of the ball measured, of course, from the eraser tray? (Round your answer to the nearest cm).

     c) What is the name of this highest point of the graph?

     d) Write the coordinate of the highest point V and plot it on the graph.

please answer q2, q3,24,q5,q6 and q11,q12

Radon-222 decays at a continuous rate of 17.3% per day. How much will 170 mg of Radon-222 decay to in 7 days?



NOTE: Round your answer to 4 decimal places.

show your work. Find the sin t and cos t for t =150^o.

You may need to draw the reference angle first, but you only have to enter the sine and cosine values.

The function
D(t) = 43.1224(1.0475)^t. gives the number of master’s degrees, in thousands, conferred on women in the United States t years after 1960. Find the number of master’s degrees earned by women in 1984, in 2002, and in 2010. Then estimate the number of master’s degrees that will be earned by women in 2020.?When will the number of master’s degrees earned by women in the U.S. reach a million?

Sketch a graph of f(x)= -2(x-1)^2(x+1), based on all the data about zeros, long run behavior, etc.

Question from college algerba webworks:

Find the x and y intercept of

9log₆(8-4x)+18

a5b7a3

The total cost of two calculators and four math sets is R440.00, If a calulator cost R40 more than a math set, what is the cost of each?

Three consecutive integers multiply together to give -120

a)Determine a polynomial equation to represent this situation.

b)Using your equation from part (a), determine the three consecutive integers that multiply together to give -120.

Consider the matrix B =         

−1 1 1 2

−1 1 0 3

−2 2 1 −4          

(a) Find ||B||F.

(b) It can be shown (See Saito, Lecture Notes, 5.7) that the 1-norm of a matrix A ∈ Rm×n can be written as ||A||1 = max 1≤j≤n||aj||1 whereaj is the jth column of A. Find||B||1.

(c) Find ||B||2.

(d) It can be shown (See Saito, Lecture Notes, 5.9) that the ∞-norm of a matrix A ∈ Rm×n can be written as kAk∞ = max

A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. The perimeter of the window is 8m. (a)Write the area of A of the window as a function of r. (b) What dimensions (length and breadth of a rectangle, radius of semicircle will produce a window of maximum area? Write these dimensions in terms of pie and simplify as far as possible.

Suppose θ is an acute angle in a right triangle. Given tan(θ)=1/5, evaluate: 1-sin^2(θ)