Solve the following problems. Take all final answers to two decimal places. (a) A rectangular sheet of metal is twice as long as it is wide. Squares 3 cm by 3 cm, are cut from each comer and the ends are turned up to form a container having a volume of 695 cm. Find the dimensions. (b) A missile is fired vertically upward such that its distance s(in m) above the ground is given by the equation below where t is the time in seconds. Find when the missile will hit the ground, the maximum height and the time it takes to reach 275 m. - -4.9.1 + 120t+ 65 S= (c) Find the dimensions of a rectangular field having a perimeter of 724 m and an area of 32,400 square meters. Find the diagonal and two angles. (d) The length of a rectangle is five times its width. If the width is increased by one cm and the length decreased by four cm, the new area will be 399 cm. Find the dimensions of the original rectangle. (e) Find the equation. Find the vertex and x and y intercepts y = ax + bx+c (1,9) (-1,3) (2,18) (f) The hypotenuse of a right angled triangle is 34.0 m. Find the lengths of the remaining two sides if one of these sides is 14.0 m longer than the other side. A rectangular name plate for a machine has an area of 44 square cm and a perimeter of 27 cm. Calculate the dimensions. (h) A rectangular solar panel is 20 cm by 30 cm. By adding the same amount to each dimension the area is doubled? How much is added? i) In remodeling a house an architect finds that by adding the same amount to each dimension of a 4.5 by 6.0 m rectangular room the area would be increased by 13 square meters. How much must be added to each dimension? j) The width of a rectangular TV is 10.5 m more than the height. If the diagonal is 68.6 cm find the dimensions of the screen k) Two circular oil spills in Sydney harbour are tangent to each other. If the distance between the centers is 825 m and they cover a combined area of 1107841.809 square m, find the radius of each? 1) Find the dimensions of the rectangle if the area is 5292 square cm and the diagonal is 105 cm. m) The pressure and volume of a gas are related by the equation below. If the volume is increased by 2, the pressure is diminished by 2. Find the pressure and volume. p= 100 V n) A rectangular photograph has an area of 1728 square cm. If the diagonal is 60 find the length and width and angles of the diagonal.