# Quadratic equation - examples

- Evaluation of expressions

If a^{2}-3a+1=0, find (i)a^{2}+1/a^{2}(ii) a^{3}+1/a^{3} - Expression with powers

If x-1/x=5, find the value of x^{4}+1/x^{4} - Speed of car

The car went to a city that was 240 km away. If his speed increased by 8 km/h, it would reach the finish one hour earlier. Determine its original speed. - Find radius

Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r - Diamond diagonals

Calculate the diamonds' diagonals lengths if the diamond area is 156 cm square and the side length is 13 cm. - A bridge

A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H - Trapezoid MO

The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Pool

If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately? - Root

The root of the equation ? is: ? - Cuboid

Cuboid with edge a=23 cm and body diagonal u=41 cm has volume V=13248 cm^{3.}Calculate the length of the other edges. - Cuboid

The cuboid has a surface area 1771 cm^{2,}the length of its edges are in the ratio 5:2:4. Calculate the volume of the cuboid. - Right triangle Alef

The area of a right triangle is 294 cm^{2,}the hypotenuse is 35 cm long. Determine the lengths of the legs. - MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball. - Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ? - Right triangle

Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle. - R triangle

Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg. - 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. - Rhombus and inscribed

Rhombus has side a = 42 cm, the radius of the inscribed circle is r = 18 cm. Calculate the length of its two diagonals. - Rectangle SS

Perimeter of a rectangle is 296 km and its diagonal is 104.74 km. Determine the dimensions of the rectangle. - 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.

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