Examples for secondary school students - page 232 of 237

Number of problems found: 4732

Pumps
A tank is filled by two pumps working together in 23 minutes. The first pump alone fills the tank 37 minutes faster than the second pump alone. How long does it take the first pump to fill the tank on its own?
Diofant 2
Is equation 1140x +876y = 48 solvable on the set of integers Z?
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}

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