Examples for secondary school students - page 104 of 232
Number of problems found: 4622
- Parallel and orthogonal
I need math help in this problem: a=(-5, 5 3) b=(-2,-4,-5) (they are vectors) Decompose the vector b into b=v+w where v is parallel to a and w is orthogonal to a, find v and w - Bisectors
As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE. - The product
The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number? - Pool
How many hectoliters of water is in a cuboid pool (a = 25m, b = 8m) if the area of the wetted walls is 279.2 m²? - Book reading comparison
Peter and Eve read the same book. Petra read 14 pages a day, so she read it a day before Eva, who read 12 pages a day. How many pages did the book have? - Vertical prism
The base of the vertical prism is a rhombus with diagonals of 24 cm and 10 cm. Suppose the shell area is 52% of the total surface area of the prism. Calculate its surface. - Regular hexagonal pyramid
Calculate the height of a regular hexagonal pyramid with a base edge of 5 cm and a wall height of w = 20cm. Sketch a picture. - Parametric form
Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. - Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the base plane is α = 60°. - System equation solving Solve the system: 15x + 30y = -20 0.3x-0.2y = 0.4
- Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'. - Triangle angle ratio
Calculate the magnitude of the interior angles of the triangle ABC if alpha = two-fifths beta and alpha = one-quarter gamma. - Pairs of socks
Ferdinand has twelve pairs of socks, and one sock is leaky. What is the probability of putting on a leaky sock? - Uboid volume
Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm² - Equation of the circle
Find the equation of the circle with center (3,7) and circumference of 8π units. - Integer sum difference
The sum of two integers is three, and their difference is 7. Determine the unknown numbers. - Hexagonal pyramid surface
A regular hexagonal pyramid has a base inscribed in a circle with a radius of 8 cm and a height of 20 cm. Please sketch the picture. Please calculate the surface of a regular hexagonal pyramid. - Pyramid volume calculation
Please calculate the volume of a quadrilateral pyramid when a = 5cm and the wall height is w = 12cm. - Dog goose puzzle
Dogs and geese ran around the backyard. Together, they had 12 heads and 30 legs. How many geese ran around the backyard, and how many dogs? - Crayon basket calculation
Vendelín has 4/5 the number of colored pencils. But if Maruška took 1/2 of it, there would be 20 crayons left. How many crayons were still in the penalty before Vendelín's collection?
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