Examples for secondary school students - page 232 of 237
Number of problems found: 4730
- Diofant equation
In the set of integers (Z), solve the equation: 212x +316y =0 Write result with integer parameter t in Z (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions) - Subsets
How many are all subsets of set C = (97, 67, 66, 18, 59, 64)? - Roots
Find the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: 5x ² +9x + q = 0 - Biquadratic
By introducing a new variable, solve the biquadratic equation: - x 4 +277 x² -15876=0 - Meridian
What is the arc length of the Earth's meridian corresponding to 41° if the radius of the Earth is 6370 km? - Euler problem
Someone buys a number of towels for a total of 720 tolars. If for the same amount of money they could buy 6 more towels, each towel would be 6 tolars cheaper. How many towels were originally bought? - Rectangular field
One dimension of a rectangular field is 168 m greater than the other. When each side is increased by 9 m, the area of the field becomes 2187 m². Find the dimensions of the field. - Root
Use the law of square roots: cbrt (sqrt[2] (sqrt[4] (6))) = sqrt[n] (6) - Quadratic equation Determine the numbers b and c that the numbers x1 = -8 and x2 = -1 were roots of the quadratic equation: -3x ² + b x + c = 0
- Rates
When gas consumption, the consumer may choose one of two rates: rate A - which pays 0.4 € per 1 m³ of gas a flat monthly fee of 4.2 € (regardless of consumption) rate B - which pays 0.351 € per 1 m³ of gas a flat monthly fee of 10.1 € From what monthly co - Trigonometric functions
In a right triangle, it holds that: tg α= frac(4) 2 Find the values of s and k: sin α= (s)/(√ 20) cos α= (k)/(√ 20) - Number
Is number 2.8814789 irrational? - Transforming cuboid
A cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length? - Pipes
A water pipe has a cross-section of 1903 cm². In one hour, 859 m³ of water flows through it. How much water flows through a pipe with a cross-section of 300 cm² in 11 hours, if the water flows at the same speed? - Trigonometry
Is true equality? sin(x +13 π)= sin(x) - Gold wire
A wire of length 1.4 km was drawn from one gram of gold. What is its diameter if the density of gold is ρ = 19.5 g/cm³? - Word
What is the probability that a random word composed of chars S, G, R, S, E, I, N, A, L, P, C, T, M, H, E, E will be the SPHERICALSEGMENT? - Exponential equation
In the set R, solve the equation: 7 -5 +19x=4 3 -20x - Secret number
Find the secret number n, which reversed decreases by 15.4 if the number increases by 15.4. - Rectangle SS
The perimeter of a rectangle is 154 dm and its diagonal is 62.36 dm. Find the dimensions of the rectangle.
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