Examples for secondary school students - page 105 of 230
Number of problems found: 4586
- A hammer
A hammer weighing 500 g hits the nail at a speed of 3 m/s. What is the average force acting on the nail, which penetrates the board to a depth of 5 cm? - Energy on impact
A stone weighing 200 g falls in a free fall for 3 s. Find its kinetic energy on impact. - Weighing 12471
Compare the kinetic energy of a man weighing 80 kg who runs at a speed of 2 m/s and missiles weighing 20 g fired at 400 m/s. - Determine 12461
The 150t aircraft takes off at a speed of 288km/h and, after a while, reaches a speed of 900km/h. Determine the change in the kinetic energy of the aircraft. - Truncated cone and sphere
A sphere is inscribed in a truncated cone with base diameters D1=10 cm and D2=20 cm, touching both bases and the surface. What is its diameter? - Rectangle field
The field has the shape of a rectangle, having a length of 119 m and a width of 19 m. How many meters have to be shortened in length and increased in width to maintain its area and circumference by 24 m? - Three parallels
The vertices of an equilateral triangle lie on three different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle. - An animal shelter
An animal shelter costs $5.50 per day to care for each bird and $8.50 per day for each cat. On Wednesday, Nicole noticed the shelter spent $283.00 caring for birds and cats. Nicole found a record showing a total of 40 birds and cats on Wednesday. How many - Land boundary
The land is a right triangle. Its hypotenuse is 30 meters long, and its circumference is 72 meters. What are the sizes of the remaining sides of the land boundary? - Parallels and one secant
There are two different parallel lines, a, b, and line c, that intersect the two parallel lines. Draw a circle that touches all lines at the same time. - Circular railway
The railway connects points A, B, and C in a circular arc, whose distances are | AB | = 30 km, AC = 95 km, and BC | = 70 km. How long will the track be from A to C? - A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in a ratio of 5:3. Find its side lengths. - Square side
If we enlarge the square side a = 5m, its area will increase by 10,25%. How much percent will the side of the square increase? How many percent will it increase the circumference of the square? - Heptagonal pyramid
A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm, and the upper base is 14 cm. The altitude is 30 cm. Determine the weight in kg if the wood density is 10 grams/cm³. - Inequality 12021
Solve on Z - inequality with absolute value: | x-18 | +4> 1 - Cooperative 11981
According to the plan, the cooperative secured 210 tons of silage for the winter. However, it then bought 10 heads of cattle, so it was necessary to reduce the amount of silage by half a ton per head. How many tons of silage did the cooperative initially - Sides of right angled triangle
One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. - Before yesterday
The merchant adds a sale sign in his shop window to the pair of shoes shown in the morning: "Today by p% cheaper than yesterday. " After a while, however, he decided that the sign saying: "Today 62.5% cheaper than the day before yesterday". Determine the - Coordinates of square vertices
I have coordinates of square vertices A / -3; 1/and B/1; 4 /. Find coordinates of vertices C and D, C and D. Thanks, Peter. - A rhombus
A rhombus has sides of the length of 10 cm, and the angle between two adjacent sides is 76 degrees. Find the length of the longer diagonal of the rhombus.
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