# Examples for secondary school students - page 25

1. Airplane Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies? The voltage station is every day changing the master password, which consists of three letters. Code generation process does not change and is based on the following procedure: The following letters (A) to (I) correspond to different numbers from 1 to 9. I
3. Bath In the bath is 30 liters of hot water. Then added 36 liters of cold water at temperature of 19 °C decreased temperature of water to 41 °C. What was the initial temperature of the hot water?
4. Diamond Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal.
5. Triangle Calculate the area of ​​the triangle ABC if b = c = 17 cm, R = 19 cm (R is the circumradius).
6. Vector sum The magnitude of the vector u is 12 and the magnitude of the vector v is 8. Angle between vectors is 61°. What is the magnitude of the vector u + v?
7. Resistors Two resistors connected in series give the resulting resistance 216Ω and 48Ω in parallel. Determine the resistance of these resistors.
8. Isosceles triangle The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area.
9. Square If we increase side of the square, increase its area of 63%. What is the percentage we increase side of the square?
10. Examination The class is 21 students. How many ways can choose two to examination?
11. Euclidean distance Calculate the Euclidean distance between shops A, B and C, where: A 45 0.05 B 60 0.05 C 52 0.09 Wherein the first figure is the weight in grams of bread and second figure is price in USD.
12. Greatest angle Calculate the greatest triangle angle with sides 197, 208, 299.
13. Computer revolution When we started playing with computers, the first processor, which I remember was the Intel 8080 from 1974, with the performance of 0.5 MIPS. Calculate how much percent a year rose CPU performance when Intel 486DX from 1992 has 54 MIPS. What
14. Two workers Two workers carry will do certain work for 12 days. After 8 days of working was one removed, and then the other finished the job alone in 10 days. For how many days would do this work alone each worker?
15. Raffle How many raffle tickets must be purchased by Peter in raffle with issued 200 tickets if he wants to be sure win at least 3 price? In the raffle draws 30 prices.
16. Trapezoid IV In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?
17. Vectors Vector a has coordinates (8; 10) and vector b has coordinates (0; 17). If the vector c = b - a, what is the magnitude of the vector c?
18. Invitations For every 5 minutes writes Dana 10 invitations, while Anna 14 invitations. How long will write together 120 invitations?
19. Plot The length of the rectangle is 8 smaller than three times the width. If we increase the width by 5% of the length and the length is reduced by 14% of the width, the circumference of rectangle will be increased by 30 m. What are the dimensions of the rectan
20. Simple interest 2 Find the simple interest if 13905 USD at 4.5% for 6 months.

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