Grade - examples - page 206

  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. Iron density
    pipe1_2 Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3.
  3. Volume of ball
    ball1_5 Find the volume of a volleyball that has a radius of 4 1/2 decimeters. Use 22/7 for π
  4. Train speed
    trains_9 Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of the train (in km/hr), supposing that sound travels at 340 m/s is:
  5. Construct
    inscircle_triangle Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
  6. Area of a triangle
    triangle1_2 What is the area of a triangle that has the base 4 1/4 and the height of 3 3/3?
  7. The length
    rectangle_14 The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle.
  8. Winery
    wines_2 The wine processing plant sold 8/15 of its total wine production to the domestic market, 2/7 to the foreign the rest of the wine. How many percents are still in stock?
  9. Circus
    cirkus On the circus performance was 150 people. Men were 10 less than women and children 50 more than adults. How many children were in the circus?
  10. Equations - simple
    linearna_1 Solve system of linear equations: x-2y=6 3x+2y=4
  11. Evaluation of expressions
    eq222_10 If a2-3a+1=0, find (i)a2+1/a2 (ii) a3+1/a3
  12. Together
    work_1 If 8 men, 10 women, 16 children collects ₹1024 in 4 days, how many days will be required for 6 men, 5 women and 4 boys to collect ₹768? (₹ is Indian Rupee)
  13. 12 apples
    apples_11 12 apples and 2 loaves of bread cost 5.76 and 6 apples and 3 loaves of bread cost 7.68. How much is a loaf of bread?
  14. Radioactive material
    radium A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years?
  15. Alice
    usd_10 Alice spent 5/11 of her money on a back pack. She has $42 dollars left. How much was her back pack?
  16. Supplementary angles
    susedne_huly One of the supplementary angles is larger by 33° than the second one. Calculate the angles size.
  17. Discount sale
    penize_49 At Christmas Sale after a 20% discount cosmetic package was priced at a price of 5 euros and 60 cents; later it went to 3 euros and 80 cents. How much percentage is the total discount?
  18. Account operations
    penize_49 My savings of php 90,000 in a bank earns 6% interest in a year. If i will deposit additional php 10,000 at the end of 6 months, how much money will be left if i withdraw php 25,000 after a year?
  19. Simplify 3
    fractal_14 Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution.
  20. Reducing scale
    map_mo I am sizing some landscaping and I measured everything for a 20 to 1 scale. I realized when I was done that it was at 30 to 1. How can I convert what I already have to 30 to 1. (Example, grass area is 22,871.6' at 20 to 1, how do you figure it out to be 30

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