# Examples for secondary school students - page 74

1. Non linear eqs Solve the system of non-linear equations: 3x2-3x-y=-2 -6x2-x-y=-7
2. The length The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle.
3. Evaluation of expressions If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
4. Three workshops There are 2743 people working in three workshops. In the second workshop works 140 people more than in the first and in third works 4.2 times more than the second one. How many people work in each workshop?
5. Account operations My savings of php 90,000 in a bank earns 6% interest in a year. If i will deposit additional php 10,000 at the end of 6 months, how much money will be left if i withdraw php 25,000 after a year?
6. Collision The two bodies, whose initial distance is 240 m, move evenly against each other consistently. The first body has an initial velocity of 4 m/s and an acceleration of 3 m/s2, the second body has an initial speed of 6 m/s and an acceleration of 2 m/s2. Find
7. Alice Alice spent 5/11 of her money on a back pack. She has \$42 dollars left. How much was her back pack?
8. Right isosceles triangle Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?
9. 600 pencils 600 pencils we want to be divided into three groups. The biggest groups have ten pens more than the smallest. How many ways can this be done?
10. Complex number coordinates Which coordinates show the location of -2+3i
11. Minute average In a factory, four workers are assigned to complete an order received for dispatching 1400 boxes of a particular commodity. Worker A takes 4 mins per box, Worker B takes 6 minutes per box, C takes 10 mins per box, D takes 15 mins per box. Find the average.
12. Investment 1000\$ is invested at 10% compound interest. What factor is the capital multiplied by each year? How much will be there after n=12 years?
13. Today in school There are 9 girls and 11 boys in the class today. What is the probability that Suzan will go to the board today?
14. Friction coefficient What is the weight of a car when it moves on a horizontal road at a speed of v = 50 km/h at engine power P = 7 kW? The friction coefficient is 0.07
15. Car crash On the road, with a maximum permitted speed of 60 km/h, there was a car crash. From the length of the vehicle's braking distance, which was 40 m, the police investigated whether the driver did not exceed that speed. What is the conclusion of the police, as
16. Potatoes For three days the store sold 1400 kg of potatoes. The first day they sold 100 kilograms of potatoes less than the second day, the third-day three-fifths of what they sold the first day. How many kgs of potatoes sold every day?
17. Scalar product Calculate the scalar product of two vectors: (2.5) (-1, -4)
18. Centroid - two bodies A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravit
19. Percentage increase Increase number 400 by 3.5%
20. STRESSED word Each letter in STRESSED is printed on identical cards, one letter per card and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled.

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