# Square root + quadratic equation - examples

1. Find parameters Find parameters of the circle in the plane - coordinates of center and radius: ?
2. Pool If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately?
3. Rectangular cuboid The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
4. Cuboid Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
5. Rhombus and inscribed circle It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
6. Tangents To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre.
7. Trolleybus Trolleybus line No. 207 measured 20 km. If the trolleybus go faster by 9 km/h, the way there and back would is shorter by 20 minutes. Calculate the trolleybus speed and how much time it takes a return trip.
8. Tank In the middle of a cylindrical tank with a bottom diameter 251 cm is standing rod which is 13 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank?
9. Biquadratic By introducing a new variable solve biquadratic equation: ?
10. Pure quadratic equation Solve pure quadratic equation ?.
11. Quadratic equation Solve quadratic equation: 2x2-58x+396=0
12. Square If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm2. Determine the side length of the original square.
13. Factors Can the expression ? be factored into rational factors?
14. 3d vector component The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
15. Apples A 2 kg of apples cost a certain sum of money. This sum is equal to the amount of kilograms for which we pay 72 CZK. How much is 1 kg of apples?
16. Product The product of two consecutive odd numbers is 8463. What are this numbers?
17. Trapezoid 15 Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
18. Trapezium The length of the base and the height size of the base of the trapezium is at ratio 5:3:2, the content area of the trapezium is 128 cm2. Calculate the length of the base and the height of the trapezoid.
19. Diagonal of the rectangle Calculate the diagonal of the rectangle which area is 54 centimeters square and the circuit is equal to 30 cm.
20. Unknown number 7 Calculate unknown number whose 12th power when divided by the 9th power get a number 27 times greater than the unknown number. Determine the unknown number.

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