# Examples for 9th grade - page 4

- Movement

From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 18 km/h, the second at average speed 24 km/h. Determine the distance between them after 30 minutes cycling. - Gimli Glider

Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 2080 feet and maintain constant speed 196 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate - Short cut

Imagine that you are going to the friend. That path has a length 330 meters. Then turn doprava and go another 840 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field? - Scale

Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 13200 cm^{2.}What scale is the city plan? - River

From the observatory 18 m high and 26 m from the river bank, river width appears in the visual angle φ = 14°30'. Calculate width of the river. - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2.}Calculate the volume of a cone. - Cube diagonal

Determine length of the cube diagonal with edge 55 dm. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm^{2.} - Transforming cuboid

Cuboid with dimensions 5 cm, 14 and 17 cm is converted into a cube with the same volume. What is its edge length? - Regular 5-gon

Calculate area of the regular pentagon with side 11 cm. - Rhombus

Calculate the perimeter and area of rhombus whose diagonals are 26 cm and 42 cm long. - Logs

Trunk diameter is 79 cm. Is it possible to inscribe a square prism with side 75 cm? - Right triangle Alef

The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs. - Sphere

Surface of the sphere is 2260 cm^{2,}weight is 52.2 kg. What is its density? - Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - No. of divisors

How many different divisors has number ?? - Rectangle

In rectangle with sides 10 and 9 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle? - Rhombus ABCD

Rhombus ABCD, |AC| = 42 cm, |BD| = 96 cm. Calculate the perimeter of the rhombus ABCD. - Diagonal

Calculate the length of the diagonal of the rectangle ABCD with sides a = 6 cm, b = 7 cm. - 7 heroes

5 heroes galloping on 5 horses behind. How many ways can sort them behind?

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