Examples for secondary school students - page 145 of 230
Number of problems found: 4597
- The sides
The sides of the rectangle are in a ratio of 3:5, and its circumference measures 72 cm. Calculate: a) the size of both sides of the rectangle b) the area of the rectangle c) the length of the diagonals - The cruise ship
The cruise ship speeds 12 km/h at a calm surface. When we sailed 45 km along the river and 45 km back, it took us exactly 8 hours. Which (constant) speed of flow of the river? - Sphere equation
Obtain the equation of a sphere. Its center is on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Kilograms 5738
The painter used 3.5 times more paint to paint the tin roof than the gutters. He used 3.1 kg more paint to paint the gutters than to paint the fence. In total, he used 20 kg of paint. How many kilograms of paint did he use to grease the roof, fence, and g - Digit sum
The digit sum of the two-digit number is nine. When we turn figures and multiply by the original two-digit number, we get 2430. What is the original two-digit number? - Endless lego set
The endless Lego set contains only 6, 9, and 20-kilogram blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And, of course, they wrote down how much the building weighed. - Resistance 5713
The kettle is connected to a voltage of 230 V. Its resistance is 130 ohms. What is the current flowing through the kettle? - Perpendicular 5712
Adam and Boris go from school on two perpendicular paths. Adam's average speed is 6 km/h, and Borisova's is 8 km/h. How far will they be by air for 0.5 hours? - Toboggan run
The length of the toboggan run is 60 m, and the height is 8 m. The boy pulls a sled weighing 15 kg. How hard does the boy pull the sled uphill? - Equation of circle 2
Find the equation of a circle that touches the axis of y at a distance of 4 from the origin and cuts off an intercept of length 6 on the axis x. - Repay, interest, loan
Ramchacha takes a loan amount of 240000 from a bank for constructing a house at a simple interest rate of 12% per annum. After one year of taking the loan, he rents the house at the rate of 5200 per month. Determine the number of years he would take to re - Matrices 5702
How many columns will the matrix K contain, which will be the product of matrices I and J, where matrices I and J are square matrices of the sixth order? - Determinant 5701 The unit matrix has the value of determinant 3. Find out how many elements this matrix contains.
- A steel
A steel hammer with a weight of 0.5 kg hits the nail at a speed of 3 m/s. How deep does the nail penetrate the wood if the hammer acts on the nail with an average force of 50N? - Vanilla ice cream
Alice stopped at an ice cream stand. Today they had pineapple, chocolate, yogurt, punch, vanilla, and apple ice cream on offer. Alice wants to buy two scoops of different ice cream. How many fewer options does Alice have when choosing ice cream if she kno - Traveling 5687
The distance between the two cities is 60 km. It takes a slower vehicle half an hour longer to travel this distance than a faster one traveling at speed 50 percent faster. How fast is each vehicle going? - Two workers
Two workers should fulfill specific tasks together for five days. If the first worker increased their performance twice and the second twice fell, it took them just four days. For how many days would he handle the entire task, the first worker himself? - Three-fourths 5676
The three numbers are in the ratio of 4:7:14. Three-fourths of the smallest number is one greater than one-fifth of the largest number. How many times is the product of these three numbers greater than their sum? - Grandparents 5675
Susan asked her grandmother how many years had passed since her wedding to her grandfather. The grandmother replied that she has been married for 2/3 of her life and that her grandfather, who is 12 years older than her, has been married for 6/11 of his li - Diameter 5668
The span of the arc is 247 cm, and the height of the arc is 21.5 cm. What is the diameter of the circle?
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