Quadratic equation - examples
- Curve and line
The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C?
- Find two
Find two consecutive natural numbers whose product is 1 larger than their sum. Searched numbers expressed by a fraction whose numerator is the difference between these numbers and the denominator is their sum.
Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken?
- Pravoúhly trojúhelník
Určete obsah pravoúhlého trojúhelníku, jehož délky stran tvoří po sobě jdoucí členy aritmetické posloupnosti a poloměr kružnice opsané tomuto trojúhelníku je 5 cm.
- 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.
If water flows into the pool by two inlets, fill the whole for 12 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately?
The root of the equation ? is: ?
Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm3. Calculate the length of the other edges.
The cuboid has a surface area 3380 cm2, the length of its edges are in the ratio 4:3:1. Calculate the volume of the cuboid.
- Right triangle Alef
The perimeter of a right triangle is 132 cm, the hypotenuse is 55 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.
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 = 5:8. Hypotenuse has a length of 16 dm. Calculate the perimeter and area of the triangle.
To circle with a radius of 98 dm from the point A guided two tangents. The distance of both points of contact is 155 dm. Calculate the distance from point A and circle centre.
- R triangle
Calculate the area of a right triangle whose longer leg is 9 mm shorter than the hypotenuse and 4 mm longer than the shorter leg.
- Rhombus and inscribed
Rhombus has side a = 72 cm, the radius of the inscribed circle is r = 10 cm. Calculate the length of its two diagonals.
- Rectangle SS
Perimeter of a rectangle is 190 m and its diagonal is 84.72 m. Determine the dimensions of the rectangle.
Trolleybus line No. 207 measured 26 km. If the trolleybus go faster by 7 km/h, the way there and back would is shorter by 12 minutes. Calculate the trolleybus speed and how much time it takes a return trip.
- 2nd class variations
From how many elements you can create 6480 variations of the second class?
Right triangle has hypotenuse c = 15 cm. How large sections cuts height hc=7 cm on the hypotenuse c?
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