Quadratic equation - examples

  1. Curve and line
    parabol 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?
  2. Find two
    eq222_7 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.
  3. Bamboo
    Bambus 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?
  4. Pravoúhly trojúhelník
    tr_2 Určete obsah pravoúhlého trojúhelníku, jehož délky stran tvoří po sobě jdoucí členy aritmetické posloupnosti a poloměr kružnice opsané tomuto trojúhelníku je 5 cm.
  5. Trapezoid MO
    right_trapezium 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.
  6. Pool
    pool 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?
  7. Root
    root_quadrat The root of the equation ? is: ?
  8. Cuboid
    cuboid Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm3. Calculate the length of the other edges.
  9. Cuboid
    cuboid_1 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.
  10. Right triangle Alef
    r_triangle The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs.
  11. MO SK/CZ Z9–I–3
    ball_floating_water 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.
  12. Right
    r_triangle_1 Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
  13. Right triangle
    righttriangle 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.
  14. Tangents
    tangents 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.
  15. R triangle
    right_triangle_1 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.
  16. Rhombus and inscribed
    rhombus_2 Rhombus has side a = 72 cm, the radius of the inscribed circle is r = 10 cm. Calculate the length of its two diagonals.
  17. Rectangle SS
    rectangle Perimeter of a rectangle is 190 m and its diagonal is 84.72 m. Determine the dimensions of the rectangle.
  18. Trolleybus
    trolejbus_ba_1 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.
  19. 2nd class variations
    cards From how many elements you can create 6480 variations of the second class?
  20. Euclid1
    pravitko Right triangle has hypotenuse c = 15 cm. How large sections cuts height hc=7 cm on the hypotenuse c?

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