# Examples for 9th grade - page 10

- Diofant 2

Is equation ? solvable on the set of integers Z? - Shelf

How many ways are there to arrange 9 books on a shelf? - Cuboid

Determine the dimensions of cuboid a, b, c; if diagonal d=6 dm has angle with edge a α=57° and has angle with edge b β=60° - Clocks

How long path will walk the end of the clock's minute-hand long 24 cm for 110 minutes? How long will walk in the same time hour-hand? - Madams

During the spring cleaning ladies going to wash windows. Mother takes wash all the windows 5 hours, the grandmother 3 times longer and Paula wash all windows in 5 hours. How many hours will spend washing the windows this "women's team" if working togethe - Building

How high is the building that throws horizontal shadow 58.5 m long at angle 36°36'? - Triangle ABC

Right triangle ABC with right angle at the C, |BC|=20, |AB|=35. Calculate the height of the triangle h_{AB}to the side AB. - Square diagonal

Calculate the length of diagonal of the square with side a = 18 cm. - Cubes

Cube, which consists of 27 small cubes with edge 3 dm has volume: - Map

On the tourist map at a scale of 1 : 100000 is distance between two points along a straight road 5.4 cm. How long travels this distance on a bike at 23 km/h? Time express in minutes. - Diofant equation

In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions) - Freedom

In the city are 2/6 of women married for 4/4 men. What proportion of the townspeople is free (not married)? Express as a decimal number. - Center

Calculate the coordinates of the center of gravity T [x, y] of triangle ABC; A[27,-11] B[2,-30] C[11,12]. - Phone numbers

How many 9-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated? - Seedcake

Seedcake costs 50 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros? - Estate

Semicircle estate must be fence. The straight section has 44 meters long fence. How many meters of fence should buy? - Euclid1

Right triangle has hypotenuse c = 15 cm. How large sections cuts height h_{c}=7 cm on the hypotenuse c? - Speed of Slovakian trains

Rudolf decided to take the train from the station 'Nová Baňa' to 'Gelnica'. In the train timetables found train R 371 Horehronec : km0Břeclav os.n.05:268Lanžhot05:3205:3214Brodské05:3705:3818Kúty05:4205:4344Malacky05:5906:0082Bratislava hl.st.06:2606:37 - Wire

One pull of wire is reduced its diameter by 9%. What will be diameter of wire with diameter 9 mm over 8 pulls? - Stairway

What angle rising stairway if step height in 17 cm and width 24 cm?

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