Examples for secondary school students - page 54 of 230
Number of problems found: 4584
- Air bubble
The air bubble at the bottom of the lake at a depth of h = 21 m has a radius of r1 = 1 cm at a temperature of t1 = 4°C. The bubble rises slowly to the surface, and its volume increases. Calculate its radius when it reaches the lake's surface, with a tempe - Collected 61474
Three students collected a total of 32 kg of paper. The second student collected three times more paper than the first student, and the third student collected 2 kg more than the first student. How many kilograms of paper did each of them collect? - Lunes of Hippocrates
Calculate the sum of the area of the so-called Hippocratic lunas, which were cut above the legs of a right triangle (a = 6cm, b = 8cm). Instructions: First, calculate the area of the semicircles above all sides of the ABC triangle. Compare the sum of the - Money spending
Albert and Peter have an amount of money. If Albert spent $6 and Peter did not spend any, then the ratio of Albert's money to Peter's money is 1:3 . If Peter spent $6 and Albert did not spend any, the ratio of Albert's money to Peter's money is 3:7.How mu - Construct 61253
Using Euclid's theorem, construct a line of length √15. - Difference 61133
Determine the difference of the arithmetic sequence (an), if given: a1 = 5, an = 23, Sn = 392 - Arithmetic 61123
In the arithmetic sequence (an), determine a1, d if: a6 = -3, a15 = -8 - Raindrops
The car runs on a horizontal track at a constant speed of 20 m2-1. It is raining. Raindrops fall in a vertical direction at a speed of 6 m/s. a) How fast is the speed of the drops relative to the car windows? b) What is the angle of the raindro - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and whose body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - Sphere submerged in the cone
A right circular cone with a top width of 24 cm and an altitude of 8 cm is filled with water. A spherical steel ball with a radius of 3.0cm is submerged in the cone. Find the volume of water below the sphere. - Similar frustums
The upper and lower radii of a frustum of a right circular cone are 8 cm and 32 cm, respectively. If the altitude of the frustum is 10 cm, how far from the bottom base must a cutting plane be made to form two similar frustums? - Cosine
Cosine and sine theorem: Calculate all unknown values (side lengths or angles) from triangle ABC. c = 2.9 cm; β = 28°; γ = 14° α =? °; a =? cm; b =? cm - Cosine
Cosine and sine theorem: Calculate all unknown values (sides and angles) of the triangle ABC. a = 20 cm; b = 15 cm; γ = 90°; c =? cm; α =? °; β =? ° - AP members
Insert as many arithmetic sequence members between numbers 1 and 53 that the sum is 702. - Pentagon
The signboard has the shape of a pentagon ABCDE, in which line BC is perpendicular to line AB, and EA is perpendicular to line AB. Point P is the heel of the vertical starting from point D on line AB. | AP | = | PB |, | BC | = | EA | = 6dm, | PD | = 8.4dm - 11990 perimeter RT
A right triangle has integer side lengths and a perimeter of 11990. In addition, we know that one of its perpendiculars has a prime number length. Find its length. - Double of principal
How long will it take for the principal to double at 12.25% annual interest? - Tickets 7
Tickets to a concert cost $2 for children, $3 for teenagers, and $5 for adults. When 570 people attended the concert, the total ticket receipts were $1950. Compared to the number of children in attendance, three-fourths as many teenagers attended. How man - Octahedron in a cube
What largest octahedron can we place inside a cubical box with sides equal to 72? - Graph move
When y=2x² has moved 2 units to the left and 3 units upward, what is the graph equation?
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