# Examples for 8th grade - page 75

- Concentric circles

In the circle with diameter 17 cm is constructed chord 12 cm long. Calculate the radius of a concentric circle that touches this chord. - Circle and hexagon

Calculate the radius of a circle whose circumference is 6.8 cm longer than the circumference of the inscribed regular hexagon. - Train from Prague

First train from Prague started at 8:00 hour at 40 kilometers per hour. Train from Ostrava started at 9:20 at 80 km per hour. In how many hours and how far from cities with trains meet if the distance of cities is 400 km. - Otto and Joachim

Otto and Joachim go through the woods. After some time Otto tire and make 15 minutes stop. Joachim meanwhile continues at 5 km/h. Otto when he set off again, first running speed of 7 km/h, but it keep only 30 sec and 1 minute must continue at 3 km/h. This. - Enterprise and wages

The enterprise operates a total 159 workers and their average salary is M dollars. If the company has hire an additional 21 employees whose average wage would be the S dollars, would reduce the overall average salary in the company of 2%. Calculate the v - Loan

Apply for a $ 20000 loan, the loan repayment period is 19 years, the interest rate 2.3%. How much should I pay for every month (or every year if paid yearly). Example is for practise geometric progression and/or periodic payment for an annuity. - Angle

A straight line p given by the equation ?. Calculate the size of angle in degrees between line p and y-axis. - Triangular prism

Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 50 degrees, |AB| = 5 cm. Calculate the volume of the prism. - Mystery of stereometrie

Two regular tetrahedrons have surfaces 48 cm^{2}and 108 cm^{2.}In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places. - Cone and the ratio

Rotational cone has a height 28 cm and the ratio of the base surface to lateral surface is 4: 7. Calculate a surface of the base and the lateral surface. - Wheel

How many times turns the wheel of a passenger car in one second if car run at speed 89 km/h. Wheel diameter is d = 62 cm. - Cars 2

Opava is 360 km distance from Prešov. At 12:00 hour two cars started against each other from this cities at average speeds 84 km/h and 106 km/h. At what hour its will meet and what distance its travel if car started from Prešov is faster? - Diagonals

Rhombus has two diagonals e=11 dm and f=17 dm. Calculate the side angle and height of the rhombus. - Retail

At what price bought retail 1 kg goods from wholesale, if lost in the distribution is 3.9% of weight of the goods and retail still have a profit of 13.2%? Goods are sold at retail for 17 euro per kg. - Angles

The outer angle of the triangle ABC at the vertex A is 121°5'59″. The outer angle at the vertex B is 137°18'. What size is the internal angle at the vertex C? - Reflector

Circular reflector throws light cone with a vertex angle 60° and is on 22 m height tower. The axis of the light beam has with the axis of the tower angle 24°. What is the maximum length of the illuminated horizontal plane? - Medians

Calculate the sides of a right triangle if the length of the medians to the legs are t_{a}= 23 cm and t_{b}=14 cm. - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 236 dm. - 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

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