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
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.
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 cm2 and 108 cm2. 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.
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?
Rhombus has two diagonals e=11 dm and f=17 dm. Calculate the side angle and height of the rhombus.
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.
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?
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?
Calculate the sides of a right triangle if the length of the medians to the legs are ta = 23 cm and tb=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