# Examples for secondary school students - page 73

- 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? - 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? - Distance problem 2

A=(x,2x) B=(2x,1) Distance AB=√2, find value of x - 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 - 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. - 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 - 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. - Distance problem

A=(x, x) B=(1,4) Distance AB=√5, find x; - 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 - The pool

The pool contains 220 m^{3}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? - 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? - 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? - 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 - 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. - Hyperbola equation

Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10] - 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? - 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! - Radioactive material

A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years? - Two cubes

The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm^{2}. Calculate the edge length of both cubes. - Rectangular garden 2

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 m^{2}. Calculate the size of the garden.

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