Basic functions - problems

  1. Exponential warm
    teplomer_6 Suppose that a body with temperature T1 is placed in surroundings with temperature T0 different from that of T1. The body will either cool or warm to temperature T(t) after time t, in minutes, where T(t)=T0 + (T1-T0)e^(-kt) . If jello salad with 30 degre
  2. Dice
    dices2_4 We throw five times the dice. What is the probability that six fits exactly twice?
  3. Rhombus 29
    rhombus3_2 One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus.
  4. Map scale
    mapa_14 The rectangular plot has in a scale of 1: 10000 area 3 cm2 on the map. What content does this plot have on a 1:5000 scale map?
  5. Painters
    malovka2_3 Six of the painters paint 90 m of fence in five hours. For how long would the 4 painters paint a 45 meter fence? How many meters fence painted painters 5 for two hours?
  6. 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?
  7. Cuboid
    kvader11 The sum of the lengths of the three edges of the cuboid that originate from one vertex is 210 cm. Edge length ratio is 7: 5: 3. Calculate the length of the edges.
  8. Playing
    clock-night-schr_6 How long have we trained on the pitch when we know that the warm-up took 10 minutes, we trained passes for one-third of the time and we played football half the time?
  9. Radioactive material
    radium A radioactive material loses 10% of its mass each year. What proportion will be left there after n=10 years?
  10. Investment
    penize_49 1000$ is invested at 10% compound interest. What factor is the capital multiplied by each year? How much will be there after n=12 years?
  11. Percentage 10
    trenky_1 52 shorts and missed 13. Calculate percentage
  12. Line segment
    lines_7 The 4 cm long line segment is enlarged in the ratio of 5/2. How many centimeters will measure the new line segment?
  13. Commission
    sale_2 Daniel works at a nearby electronics store. He makes a commission of 15%, percent on everything he sells. If he sells a laptop for 293.00$ how much money does Daniel make in commission?
  14. Combinations 6
    dices2_3 6 purses 9 flaps 12 straps Every combination must include 1 purse, 1 flap and 1 strap. How many possible combinations?
  15. Test points
    test_2 If you earned 80% of the possible 40 points, how many points did you miss to get 100%?
  16. Equilateral triangle
    vpisany_stvorec A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
  17. 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.
  18. Fruit juice
    cukr_9 Fruit juice contains 37.5% sugar. How many percents of sugar will be in the flavored mineral that we prepare from 100 grams of fruit juice and 1.4 liters of mineral? (1 liter = 1 kg)
  19. Cube edges
    cubes3_3 If the edge length of the cube increases by 50%, how does the volume of this cube increase?
  20. Trapezoid - intersection of diagonals
    intersect_trapezoid_diagonals In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area.

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