# Examples for secondary school students - page 70

1. Axial cut of a rectangle Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
2. Rectangle - area, perimeter The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
3. Find two Find two consecutive natural numbers whose product is 1 larger than their sum. Searched numbers expressed by a fraction whose numerator is the difference between these numbers and the denominator is their sum.
4. Integer Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6.
5. Points collinear Show that the point A(-1,3), B(3,2), C(11,0) are col-linear.
6. Standard deviation Find standard deviation for dataset (grouped data): Age (years) No. Of Persons 0-10 15 10-20 15 20-30 23 30-40 22 40-50 25 50-60 10 60-70 5 70-80 10
7. Depth angle From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
8. Inverted nine In the hotel,, Inverted nine" each hotel room number is divisible by 6. How many rooms we can count with three-digit number registered by digits 1,8,7,4,9?
9. Resistance A resistor having an electrical resistance of 1.5 k ohms passes an electrical current of 0.1 A. Calculate what voltage is between the terminals of the resistor.
10. Reciprocal equation 2 Solve this equation: x + 5/x - 6 = 4/11
11. Company and employees There are 370 employees in the company - women are 15% less than men. How many men work in the company?
12. Three shooters Three shooters shoot, each one time, on the same target. The first hit the target with a probability of 0.7; second with a probability of 0.8 and a third with a probability of 0.9. What is the probability to hit the target: a) just once b) at least once c
13. Practice How many ways can you place 20 pupils in a row when starting on practice?
14. Pavement Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
15. A candle A candle shop sells scented candles for \$16 each and unscented candles for \$10 each. The shop sells 28 candles today and makes \$400. a. Write a system of linear equations that represents the situation. b. Solve the system to answer the questions: How m
16. Spherical cap Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.
17. Cancel fractions Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)!
18. 2 pipes 2 pipes can fill a tank in 35 minutes. The larger pipe alone can fill the tank in 24 minutes less time than the smaller pipe. How long does each pipie take to fill the tank alone?
19. Driver The driver of the car at a speed of 100 km/h faced the obstacle and began to brake with a slowing of 5 m/s². What is the path to stopping the car when the driver has registered the obstacle with a delay of 0.7 s?
20. Associative law multiplication In a warehouse, you obtain a 20% discount but you must pay a 15% sales tax. Which would you prefer to have calculated first: discount or tax? Explain. (result write as: 1 = first discount, 2 = first tax, 3 = no matter what first)

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