# Grade - math word problems

1. Circles
The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
2. Movement
From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling.
3. Climb
Road has climbing 1:27. How big is a angle corresponds to this climbing?
4. Pentagon
Calculate the area of regular pentagon, which diagonal is u=17.
5. Compass
What angle are between directions WSW (WestSouthWest) and SSE (SouthSouthEast) on the compass?
6. Lines
In how many points will intersect 14 different lines, where no two are parallel?
7. Gimli Glider
Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long it takes to plane from engine failure to hit the ground. C
8. Numbers
Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
9. Balance
The rod are 1.9 m long hanging weights 4 kg and 1 kg on ends. Where are centre of rod (distance from weight 4 kg) to be in balance?
10. Log
if ?, what is b?
11. Fall
The body was thrown vertically upward at speed v0 = 79 m/s. Body height versus time describe equation ?. What is the maximum height body reach?
12. Equation
How many real roots has equation ? ?
13. Gear
Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
14. Resistors
Two resistors connected in series give the resulting resistance 216Ω and 48Ω in parallel. Determine the resistance of these resistors.
15. Free fall
Lloyd fall from height 7 m. Calculate the speed he hit the ground when falling with acceleration g = 9.81 m/s2
16. Cubes
Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm2. Determine the length of the edges of this cubes.
17. Statue
On the pedestal high 4 m is statue 2.7 m high. At what distance from the statue must observer stand to see it in maximum viewing angle? Distance from the eye of the observer from the ground is 1.7 m.
18. Cuboid
Determine the dimensions of cuboid a, b, c; if diagonal d=9 dm has angle with edge a α=55° and has angle with edge b β=58°
19. Salary
Calculate equivalent annual salary to hourly salary \$ 19. Assume a 42-hour work week.
20. Rail turn
The curve radius on the railway line is 532 m . Length of rail track on it is 818 m. How many degrees is the angle ASB, if A and B are boundary points and S is center of arc curve.

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