# Examples for 9th grade - page 22

- Aircraft

The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements. - Trains for people

It is said that the train is synonymous to delay. Calculate the average speed of travel by train long 19 km, with regular train leave at 5:47 and arrive at 6:13, but train is late and has departure at 9:01 and arrive at 9:25. - Triangle TBC

TBC is isosceles triangle with base TB with base angle 63° and legs length |TC| = |BC| = 25. How long is the base TB? - ISO trapezium

Calculate area of isosceles trapezoid with base 95 long, leg 27 long and with the angle between the base and leg 70 degrees. - Lines

In how many points will intersect 14 different lines, where no two are parallel? - Rhombus base

Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u_{1}= 12 cm and u_{2}= 10 cm. Prism height is twice base edge length. - Apartments

Apartment on the first floor was 10% more expensive than the same apartment on the second floor. The difference was 105 Kc annually. Calculate the annual rent of the apartment in the first floor and from apartment on the second floor. - Pine wood

From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lum - Iron sphere

Iron sphere has weight 100 kg and density ρ = 7600 kg/m^{3}. Calculate the volume, surface and diameter of the sphere. - Map - climb

On the map of High Tatras in scale 1:11000 are cable car stations in the Tatranska Lomnica and in the Skalnate Pleso with distance 354.6 mm. Altitude of this stations are 949 m and 1760 m. What is average angle of climb of this cable car track? - Certificate

There is 31 students in a class. From mathematics was'nt worse mark than 2. Average mark in mathematics was 2. How many students have mark 1 and how many mark 2? - Height

Calculate height of the equilateral triangle if its perimeter is 8? - Sphere - parts

Calculate the area of a spherical cap, which is part of an area with base radius ρ = 9 cm and a height v = 3.1 cm. - Equilateral cylinder

Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm^{3}. Calculate the surface area of the cylinder. - Chord

In a circle with radius r=60 cm is chord 4× longer than its distance from the center. What is the length of the chord? - Perpendicular

Determine the slope of the line perpendicular to the line p: y = -x +4. - Truncated pyramid

How many cubic meters is volume of a regular four-side truncated pyramid with edges one meter and 60 cm and high 250 mm? - Cable car 2

Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car? - Rectangle

The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle. - Salary

Calculate equivalent annual salary to hourly salary $ 19. Assume a 42-hour work week.

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