Examples for secondary school students - page 20 of 229
Number of problems found: 4578
- Elevator efficiency
To what height will an elevator motor with a power of 25 kW and an efficiency of 48.6% transport a cabin weighing 445 kg with seven people (the average weight of one person is 64 kg) if it takes 54 seconds? - Standard
What will be the speed of a two-pole synchronous motor connected to a standard network with a frequency of 50Hz? In revolutions per minute. - Crowbar - lever
How much force must we apply to the end of a 2.4 m long crowbar to lift a door weighing 220 kg, if it stands on the crowbar 35 cm from its end, which is resting on the ground? - Weighing 83881
From what height did a body weighing 9.8 kg fall if it hit the surface at a speed of 100 km/h? - Motor efficiency Calculate the power input of a motor operating at an efficiency of 58% that will lift an elevator car (weighing 390 kg) with twenty boxes (each 25 kg) to a height of 85 m in 29 seconds.
- Acceleration - gravity
What is the gravitational constant (acceleration) if a body with a mass of 5.8 kg fell from 68 meters and hit the ground at a speed of 60 km/h? - Borrowed
Mr. Douda borrowed 200,000 SK from the bank at an annual interest rate of 15.4%. He will repay the loan after four years. How many korunas will he have to repay?
- Maths exam
One-third of all high school students passed the math exam. Five of these students failed the math exam. One-quarter of all students in the high school graduating class passed the math exam. Calculate how many students there were in the high school gradua - One-time payment
The price of a refrigerator is 7500 CZK for a one-time payment. If the customer chooses to purchase in installments, he will pay 800 CZK every month for 1 year. Determine by how much percent the customer will pay more for the refrigerator when purchasing - Calculate 5
Calculate the area and perimeter of a trapezoid if side a=10, angle alpha 40 degrees, beta 50 degrees, and side c=3. - Quadratic without formula
A quadratic equation is given: x²-x-2=0 Without solving this equation, construct a quadratic equation whose roots are the square of the roots of the given equation. - Construction 83662
Using Euclid's theorems, construct a triangle ABC with height on side c and size v = √8 cm. Choose the length of the hypotenuse c correctly. Write the construction procedure. - Dimensions - rectangle
One side of the rectangle is 12 cm longer than the other. If we reduce each dimension by a third, the area of the rectangle will be reduced by 60 cm². Determine the dimensions of the rectangle. - Atmospheric pressure
How and by how much hPa will the atmospheric pressure change when we take the cable car from Skalnate Pleso to Lomnický štít? The altitudes of the cable car stations are 1754 m above sea level and 2634 m above sea level. - Grouping - combinatorics
In how many different ways can 24 people be divided into: a) 6 groups of the same size. b) Groups of 5, 6, 7, and 6 people. c) Groups of 4, 5, 7, and 8 people.
- Probability - coin
When tossing a coin 4 times in a row, what is the probability that a sign will come up 3 times? - Heptagon's 83628
Calculate a regular heptagon's perimeter if its shortest diagonal length is u=14.5cm. - The Celebration
Five boys and five girls were nominated for a celebration at a local school. How many ways can the prom king, prom queen, and two other students be chosen from those nominated? (The king must be a boy, and the queen must be a girl) - Harvest 83600
Martin brought twice as much harvest as Tomáš and Filip, 15 kg more than Martin. They got a total of 65 kg of harvest. How much did each person bring? - Intersection 83575
Given a circle with a radius r = 4 cm and a point A for which |AS| applies = 10 cm. Calculate the distance of point A from the intersection of the points of contact of the tangents drawn from point A to the circle.
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