# Examples for secondary school students - page 46

1. Average age The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, average age was again equal to the number present. How many people were originally to celebrate?
2. Gain Find the gain whenever the output power is 21x the input power.
3. Unions now The plant has 1,250 employees. The Trade Unions (former ROH, OH) is 18% male, 23% female. Plant management reported that in the trade union is 20% of all employees. How many men and women are in plant and how many are men and women in trade unions?
4. Triangle Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 158 b = 185 c = 201
5. The mast A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
6. Medians and sides Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
7. Triangle ABC v2 Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x. What is greater angle? -0.7 radians or -0.7π radians? What will be hexadecimal number 303 as decimal number?
10. Copper wire What is the weight of 1000 m copper wire with a diameter of 5 mm when rezistivity p = 8.8 g / cm3?
11. Angle Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence.
12. V-belt Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
13. Chebyshev formula To estimate the number of primes less than x is used Chebyshev formula: ? Estimate the number of primes less than 30300537.
14. Two masons Two masons built the garage together - it took 18 days. If they worked independently, the other would work 15 days more than the first. For how many days would build the garage each mason himhelp?
15. The farmer The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine th
16. Locomotive Locomotive pulled a train permanent load of 200 kN horizontally along the track of 5km. What work it done?
17. Concentration How many grams of 65% and 50% acid is to be mixed to give 240 g acid with a concentration of 60%? What is the slope of a ladder 6.2 m long and 5.12 m in height. At one college, GPA's are normally distributed with a mean of 3.1 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.7 and 3.5? The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flow