Examples for secondary school students - page 213 of 231
Number of problems found: 4612
- Geodesist
Triangle-shaped field (triangle ABC) has a side AB = 129 m. path XY is parallel to the side AB, which divides triangle ABC into two parts with the same area. What will be the length of path XY? Help, please, geodesist. - Fraction
Fraction frac(0, overline(38))(0,38) write as fraction a/b, a, b is integers numerator/denominator. - Balls
Ping-pong balls have a diameter of approximately 5.5 cm. It is sold in boxes of 8 pieces: each box has a cuboid shape with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled with balls. - Sale
If the product was twice price cut by 5%, what percentage was the price cut in total? - Without Euclid laws
Right triangle ABC with a right angle at the C has a=5 and hypotenuse c=22. Calculate the height h of this triangle without the use of Euclidean laws. - JUDr. Usury
Judge JUDr. Usury approved the agreement on guilt and punishment were confessed to paying daily interest 0.15%. How big is a yearly interest? The year has 365 days. - Angles in a triangle
The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=100°. What sizes have other angles in a triangle? - Vector
Determine coordinates of the vector u=CD if C[12;-8], D[6,20]. - Pyramid
The pyramid has a base a = 2cm and height in v = 7 cm. a) calculate the angle between plane ABV and the base plane b) Calculate the angle between the edges on the opposite side. - Isosceles III
The base of the isosceles triangle is 18 cm area 250 cm². Calculate the perimeter of this triangle. - Leg and height
Solve right triangle with height v = 7.8 m and shorter cathetus b = 15 m. - XY triangle
Determine the area of a triangle given by line 2x-4y+47=0 and coordinate axes x and y. - Rotary cone
The volume of the rotation of the cone is 733 cm³. The angle between the side of the cone and the base angle is 75°. Calculate the lateral surface area of this cone. - Cut and cone
Calculate the volume of the rotation cone whose lateral surface is a circular arc with radius 15 cm and central angle 63 degrees. - Goniometric form
Determine the goniometric form of a complex number z = √ 110 +4 i. - Sum of series
Determine the 6-th member and the sum of a geometric series: 5-4/1+16/5-64/25+256/125-1024/625+.... - Boat
A force of 240 kg (2400 N) is required to pull a boat up a ramp inclined at 10° with horizontal. How much does the boat weigh? - Dices
We will throw two dice. What is the probability that the ratio between numbers on the first and second dice will be 1:2? - Ace
We pulled out one card from a complete set of playing cards (32 cards). What is the probability of pulling the ace? - MATES
In MATES (Small Television tipping), from 35 random numbers, five winning numbers are drawn. How many possible combinations are there?
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