Find z-transformation of following u[k] function: u[k]=5 * \delta[k-5]+1[k-2], k=[0, \infty]

3. Jeanne makes jewelry and has an idea for a new pair of earrings. She wants to make a sketchof her design, but only has a marker, a pencil, two pieces of paper, and a coffee mug. Use theseitems to construct the shape of the earring Jeanne is envisioning. Step 1: Jeanne traced her coffee mug on her piece of paper. How might she use paper-folding to find the center of the circle? (2 points) Step 2: Show how a second circle should be drawn in order to continue the construction.What can you say about the radii? Explain your work. (4 points) Step 3: Describe the final steps in constructing the shape of the earring. Include a drawing.(2 points)

In order to prepare a piece of ground for building a brick patio, a rectangle measuring 8 feet by 10 feet must be marked off. Then the dirt within the rectangle must be dug out to a depth of 6 inches. Finally, the resulting space must be filled with sand. (b) Sand costs $4 per cubic foot. What is the total cost of the sand needed to fill this space, including a $35 delivery charge? (a) What is the volume of sand needed, in cubic feet, to fill the space?

The angle of depression to a disabled ship from an approaching helicopter is 55°. If the helicopter is 500 m above the level of the water, what is the horizontal distance from the helicopter to the ship? Provide a diagram to support your answer. [4]

9. Two ladders AB and PQ are resting against opposite walls of an alley. The ladders AB and PQ are 2 m and 6 m above the ground respectively and T is the point where the 2 ladders meet. (i) Given that ATBP is similar to ATAQ, find an expression, in terms of y, for the length of PA. (ii) Given that APTM is similar to APQA, find the length of TM. B 2 m P ym T M xm- Q 6 m A

1.) Which shape seems to maximize the area of the protected region? 2.) Write down a generalization about the relationship between the area of a rectangle and its perimeter, when the perimeter remains constant. 3.) Perform similar calculations, but this time, use a constant area of 36 km?. Set up a table similar to the one above and calculate the perimeter of each configuration. 4.) Describe the rectangle that has the largest perimeter. Describe the rectangle that has the lowest perimeter. 5.) Write down a generalization about the relationship between the area of a rectangle and its perimeter, when the area remains constant. 6.) Give a real-life example of when you would use these generalizations, like the scenario given at the beginning of this investigation.

Which objects experience a larger gravitational force: two 100 kg point masses a distance of 100 km apart, or two 500 kg point masses a distance of 500 km apart? the 100 kg and 500 kg masses feel the same magnitude gravitational force the 500 kg masses the 100 kg masses

We want to put into the same orbit a 5,000 kg new communication satellite and a 1 kg microsatellite. Which initial velocity should we give to each object? The lightest satellite needs a larger initial velocity The initial velocity for both satellites is the same O The heaviest satellite needs a larger initial velocity

4. A telecommunications satellite is orbiting Earth. Students at two Ontario schools, that are 500 km apart, noticethat the flight path passes directly over their schools. At an instant when the satellite is between the twoschools, the students note that the simultaneous angles of elevation are 58° and 77°. How far above Earth is thesatellite, to the nearest kilometer? Provide a diagram to solve this problem. [4] 4. A telecommunications satellite is orbiting Earth. Students at two Ontario schools, that are 500 km apart, noticethat the flight path passes directly over their schools. At an instant when the satellite is between the twoschools, the students note that the simultaneous angles of elevation are 58° and 77°. How far above Earth is thesatellite, to the nearest kilometer? Provide a diagram to solve this problem. [4]

The diagram shows a rhombus ABCD in which the point A is (-1, 2), the point C is (5, 4)and the point B lies on the y-axis. Find(i) the equation of the perpendicular bisector of AC,[3] (ii) the coordinates of B and D,(iii) the area of the rhombus.

You have been hired to design the water arc of a coin fountain. The pool of the fountain is 20 feet wide, and the water arc is to be greater than 6 feet tall, but less than 50 feet. You will need to determine the locations of the launch point and landing points and the maximum height of the arc.Also, you will need to write an equation that describes the water arc in terms of its height in relation to the horizontal distance along the pool. 1. Place the side view of your fountain in a first quadrant graph. Have the surface of the pool correspond to the x-axis with the left side at the origin. Show the coordinates of the roots and vertex,and include all pertinent data points from the following questions.