# Examples for secondary school students - page 45

- Log

Calculate value of expression log |3 +7i +5i^{2}| . - Debt

Joe and Caryl have a debt of $100,500. Joe makes $90,000 per year, and Caryl makes $35,000 per year. How much should both pay to zero out the debt fairly, based on their salaries? - The city

At the end of 2010 the city had 155000 residents. The population increased by 2.1% each year. What is the population at the end of 2013? - Water reservoir

The cuboid reservoir contains 1900 hectoliters of water and the water height is 2.5 m. Determine the dimensions of the bottom where one dimension is 3.2 m longer than the second one. - Diamond

Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm - Bearing

A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point. - Class - boys and girls

In the class are 60% boys and 40% girls. Long hair has 10% boys and 80% girls. a) What is the probability that a randomly chosen person has long hair? b) The selected person has long hair. What is the probability that it is a girl? - Car and cyclist

Cyclist started from town at speed 18 km/h. After 1 hour 30 min started the car from town and caught up with the cyclist in 50 minutes. How fast was a car? - Quadrilateral 2

Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles. - Enterprise

The value of annual production enterprise is 7.1 million USD. The average annual growth rate is 1.5%. What will be value of production at the end of the fifth year? - Scalar dot product

Calculate u.v if |u| = 5, |v| = 2 and when angle between the vectors u, v is: a) 60° b) 45° c) 120° - Medians and sides

Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6). - Wavelength

Calculate the wavelength of the tone frequency 11 kHz if the sound travels at speeds of 343 m/s. - Interesting property

Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle? - Bank

Paul put 10000 in the bank for 6 years. Calculate how much you will have in the bank if he not pick earned interest or change deposit conditions. The annual interest rate is 3.5%, and the tax on interest is 10%. - Confectionery

The village markets have 5 kinds of sweets, one weighs 31 grams. How many different ways a customer can buy 1.519 kg sweets. - Gain

Find the gain whenever the output power is 21x the input power. - Triangle KLM

In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm - Average mark

Calculate average mark in English, if a student got a couple of 3's, 20% less 2 than 3, and 50% more 1's than the 2's. - 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?

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