Examples for secondary school students - page 220 of 230
Number of problems found: 4586
- Rhombus
It is given a rhombus with a side length of a = 20 cm. Touchpoints of the inscribed circle divided its sides into sections a1 = 13 cm and a2 = 7 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Circle
From the equation of a circle: -x² -y² +16x -4y -59 = 0 Calculate the coordinates of the center of the circle S[x0, y0] and the radius of the circle r. - Freedom
In the city are 3/9 of women married for 3/6 men. What proportion of the townspeople is free (not married)? Express as a decimal number. - Pine
How much of a mixed forest ranger wants to cut down if their head said: "We only cut down pine trees, which in our mixed forest 98%. After cut, pine trees constitute 94% of all trees left." - Cube in a sphere
The cube is inscribed in a sphere with a volume 8101 cm³. Determine the length of the edges of a cube. - Trapezoid MO
The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Beer
After three 10° beers consumed in a short time, there is 5.2 g of alcohol in 5 kg adult human blood. How much is it per mille? - Ravens
The tale of the Seven Ravens was seven brothers, each of whom was born exactly 4 years after the previous one when the eldest of the brothers was 4-times older than the youngest, mother all curse. How old were seven Ravens brothers when their mother curse - Area of RT
Calculate the right triangle area in which the hypotenuse has length 14 and one hypotenuse segment has length 5. - Derivation
Does there exist a function whose derivation is the same function? - Radians
Convert 90° to radians. Write the result as a multiple of the number π. - Discount
The ladies' sweater was twice discounted. First, it will be calculated by 8%, then by 8% of the new price. Its final price was 66 €. Determine the sweater's original price. - Permill
How many permills is 1141 from 98313? - Cotangent
If the angle α is acute, and cotan α = 1/3. Determine the value of sin α, cos α, and tan α. - Hypotenuse and height
In a right triangle is length of the hypotenuse c = 195 cm and height hc = 70 cm. Determine the length of both triangle legs. - Laws
From which law directly follows the validity of Pythagoras' theorem in the right triangle? ... - Cuboid
Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm³. Calculate the length of the other edges. - Described
Calculate the perimeter of the circle described by a triangle with sides 82, 495, 438. - Proof PT
Can you easily prove Pythagoras' theorem using Euclidean theorems? If so, do it. - Newton's task
Grass grows in the meadow equally fast and evenly. It is known that 35 cows graze meadow for 27 days and 39 cows by 24 days. How many cows graze the meadow for 6 days?
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