# Examples for 9th grade - page 18

- Machine

Price of the new machine is € 56000. Every year is depreciated 16% of residual value. What will be the value of the machine after 5 years? - Euler problem

Someone buys a 720 tolars towels. If it was for the same money of 6 more towels, it would be 6 tolars cheaper each. How many were towels? - Workers

Workers digging a jump pit in the school yard. Pit has a cuboid shape with a length 20 m, a width 20 dm and depth 36 cm. They excavate 0.4 cubic meters of soil an hour. How much time (hours and minutes) is need to the excavate this pit? - Sphere growth

How many times grow volume of sphere if radius rises 3×? - Dog

Man goes with a dog on a long walk 18 km from the house. Man is walking at speed 5.3 km/h and a dog that constantly running between house and man at 17.1 km/h. How many kilometers will run the dog when they reach their destination? - Similarity n-gon

11-gones ABCDEFGHIJK and A'B'C'D'E'F'G'H'I'J'K' are similar. The area of 11-gon ABCDEFGHIJK is S_{1}=254 cm^{2}and the diagonal length HG is 20 cm. Calculate area of the 11-gon A'B'C'D'E'F'G'H'I'J'K' if H'G' = 36 cm. - Triangle and its heights

Calculate the length of the sides of the triangle ABC, if v_{a}=13 cm, v_{b}=17 cm and side b is 5 cm shorter than side a. - Rectangle

Area of rectangle is 1430. Its length is 29 larger than the width. What are the dimensions of the rectangle? - Bits, bytes

Calculate how many different numbers can be encoded in 16-bit binary word? - Height difference

What height difference overcome if we pass road 1 km long with a pitch21 per mille? - Electronics: Resistors in parallel

From relation for calculating the resistance of parallel combination of resistors: ? Calculate the R, if R_{1}= 8kΩ a R_{2}= 18kΩ - Oil rig

Oil drilling rig is 23 meters height and fix the ropes which ends are 8 meters away from the foot of the tower. How long are these ropes? - Glass of juice

Glass of juice shaped cylinder 16 cm height and base diameter of 10 cm is filled with juice so that the level is 3 cm below the rim of the glass. Determine the maximum angle of the cup can be tilted and juice don't overflow. - Party

At party overyone clink with everyone. Together, they clink 406 times. How many people were at the party? - Boat

A force of 226 kg (2260 N) is required to pull a boat up a ramp inclined at 10° with horizontal. How much does the boat weight? - Water inlets

Inlet valve with a flow rate of 12 liters per second is filled tank for 72 minutes. How long take to fill full tank if we open one more such valve half an hour after? - Axial section

Axial section of the cylinder has a diagonal 18 cm. The size of the shell and the base surface are in the ratio 2:3. Calculate the volume and surface area of this cylinder. - Horizon

The top of a lighthouse is 12 m above the sea. How far away is an object which is just “on the horizon”? [Assume the earth is a sphere of radius 6378.1 km.] - Triangle KLB

It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area o - Circles

Area of circle inscribed in a square is 6. What is the area of a circle circumscribed around a square?

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