# Algebra - math word problems

1. Reciprocal It is true (prove it) that if a> b> 0: ?
2. Arc and segment Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 11 and corresponding angle is ?.
3. Roots Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
4. Diofant 2 Is equation ? solvable on the set of integers Z?
5. Pumps The tank is filled with two pumps in 16 minutes. The first pump is filled in 30 minutes earlier than two one. How many minutes is filled with the first pump? By introducing a new variable solve biquadratic equation: ?
7. Determine the number Determine the number x that ?.
8. Subsets How many are all subsets of set ?? Determine the numbers b, c that the numbers x1 = -1 and x2 = 3 were roots of quadratic equation: ?
10. Diofant equation In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
11. 3-bracket 2 May be the smallest angle in the triangle greater than 40°?
12. 3-bracket May be the largest angle in the triangle less than 20°?
13. 3-bracket 3 Two angles in a triangle are 90° and 60°. Has triangle at least two equal sides?
14. Rectangular field One dimension of the rectangular field is 56 m greater than second dimension. If each side of the rectangle increases by 10 m, increases the surface field is 1480 m2 . Determine dimencions of the field.
15. Euler problem Someone buys a 180 tolars towels. If it was for the same money of 3 more towels, it would be 3 tolars cheaper each. How many were towels?
16. Number Is number 5.146852 irrational?
17. Special cube Calculate the edge of cube, if its surface and its volume is numerically equal number.
18. 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 3.9 € (regardless of consumption) rate B - which pays 0.359 € per 1 m3 of gas a flat monthly fee of 12.5 € From what month
19. Exponential equation In the set R solve the equation: ?
20. Proof I When added to the product of two consecutive integers larger one, we get square larger one. Is this true or not?

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