Examples for secondary school students - page 61 of 237
Number of problems found: 4730
- Ideal gas law
Assuming compression is according to the law pV = constant. Calculate the initial volume of gas at a pressure of 2 bar, which will occupy a volume of 6 cubic meters when compressed to a pressure of 42 bar. - The projectile
The projectile leaves the 10 m long barrel at an instantaneous speed of 500 m/s. What is the acceleration of the projectile's movement in the barrel, and at what time will the projectile pass the barrel if we assume that It evenly accelerated the motion? - Division residue proof
If n is a natural number that gives a division of 2 or 3 when divided by 5, then n gives a residue of 4 when divided by 5. Prove directly - Divisibility indirect proof
Prove indirectly: No odd natural number is divisible by four. - Truth table tautology
Use the truth table to evaluate the truth of the compound statement (a) [P ∧ (Q ∨ R)] ⇔ [(P ∧ Q) ∨ (P ∧ R)] (b) ¬(P ⇒ ¬Q) ⇒ (¬P ∧ Q) and decide each time whether it is a tautology or A contradiction. - Specific series
Write the next three terms of the series formed according to a specific rule: 1, √2, 9, 2, 25, …, …, … - Linear equation system
Write a system of 3 linear equations with 3 variables (x. Y. z), which has all non-zero coefficients and a solution x= 2+t, y=3-2t, z=t, where t€R. The fact that the system has all non-zero coefficients means that all numbers in the extended matrix of the - Serial resistors
In the circuit shown ( two resistors, R1 and R2, serially connected), the total resistance from A to B is 16 ohms. If the voltage between A and B is 10 V, find the resistance R2 and the current through the R1 = 12-ohm resistor. - Given 2
Given g(x)=x²+x+1 where x=t². What is g(t²)? - Triangle construction procedure
Construct a KLM triangle where side k is 6.7 cm, the line to the k side is 4.1 cm, and the LKM angle is 63 degrees. Write the construction procedure. - Telephone calls
The random variable modelling the time between 2 phone calls has an exponential distribution with density f(x) = 10e^(−10x), x > 0. Calculate its distribution function and the probability that the time between calls does not exceed 5 seconds, the time - Seed germination verification
The supplier of spruce seeds for our nursery declares a germination rate of 80% for his goods. Verify this statement based on an experiment in which only 70 seeds germinated out of 100 randomly selected seeds. - Peter and Lucy
In a group of 3 boys and 4 girls, two players are drawn to play a game. Among the girls is Lucy, and among the boys is Petr (both are the only ones with that name). The first one drawn will be the captain, and the second the helmsman. What is the probabil - Circle inscribed
There is a triangle ABC and a circle inscribed in this triangle with a radius of 15. Point T is the point of contact of the inscribed circle with the side BC. What is the area of the triangle ABC if | BT | = 25 a | TC | = 26? - The isosceles
The isosceles trapezoid ABCD has bases of 18 cm and 12 cm. The angle at apex A is 60°. What is the circumference and area of the trapezoid? - Touch circle
Point A has a distance (A, k) = 10 cm from a circle k with radius r = 4 cm and center S. Calculate: a) the distance of point A from the point of contact T if the tangent to the circle is drawn from point A b) the distance of the contact point T from the l - Insert Insert five numbers between 8 and 27 such numbers that, with two given ones, they form the first seven members of the geometric sequence.
- AP - consecutive members
In the arithmetic sequence, a1 = 4.8, d = 0.4. How many consecutive members, starting with the first, need to be added so that the sum is greater than 170? - The perimeter
The perimeter of the triangle is 24, and the sides are integers and form an arithmetic sequence. Specify the side sizes of this triangle. - Car drive distribution
Five men drive to work together; 2 have a Škoda car, and the others have an Opel, Seat, and Hyundai. They always randomly choose which car to drive. Each of the five cars has an equal chance. The random variable X determines how many days the same charact
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