# Examples for secondary school students - page 73

1. Coordinates of midpoint If the midpoint of the segment is (6,3) and the other end is (8,4) what are the coordinate of the other end?
2. Average temperature The average temperature from Monday to Sunday was 40.5 and the average temperature from Monday to Saturday was 42.8. What was the temperature on Sunday?
3. Distance problem 2 A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
4. Symmetry by plane Determine the coordinates of a image of point A (3, -4, -6) at a symmetry that is determined by the plane x-y-4z-13 = 0
5. Construct Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
6. Precious metals In 2006-2009, the value of precious metals changed rapidly. The data in the following table represent the total rate of return (in percentage) for platinum, gold, an silver from 2006 through 2009: Year Platinum Gold Silver 2009 62.7 25.0 56.8 2008 -41.3 4
7. Angle of two lines There is a regular quadrangular pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV.
8. Distance problem A=(x, x) B=(1,4) Distance AB=√5, find x;
9. Young mathematician One young mathematician was bored again. He found that the average age of people in the room where the seminar is equal to its count. Then his 29-year-old brother entered this room. Even then, the average age of all present was the same as the count of peo
10. The pool The pool contains 220 m3 of water. The pool can be emptied either: a) 10 hours of pipe B and 8 hours of pipe A, or b) 10 hours of pipe A and 7 hours of pipe B. How many cubic meters of water will flow in 1 hour from pipe A and how many from pipe B?
11. Circus On the circus performance was 150 people. Men were 10 less than women and children 50 more than adults. How many children were in the circus?
12. Find the 10 Find the value of t if 2tx+5y-6=0 and 5x-4y+8=0 are perpendicular, parallel, what angle does each of the lines make with the x-axis, find the angle between the lines?
13. How many 2 How many three lettered words can be formed from letters A B C D E G H if repeats are: a) not allowed b) allowed
14. Balloon and bridge From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
15. Hyperbola equation Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
16. Curve and line The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
17. A car A car weighing 1.05 tonnes driving at the maximum allowed speed in the village (50 km/h) hit a solid concrete bulkhead. Calculate height it would have to fall on the concrete surface to make the impact intensity the same as in the first case! A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years? The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm2. Calculate the edge length of both cubes. A farmer bought 600 m of wire for the fence. He wants to use it to besiege a rectangular garden with a surface of 16875 m2. Calculate the size of the garden.