# Examples for 9th grade - page 66

- 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. - Square ABCD

Construct a square ABCD with cente S [3,2] and the side a = 4 cm. Point A lies on the x-axis. Construct square image in the displacement given by oriented segment SS'; S` [-1 - 4]. - 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. - Diagonals in the diamond

The length of one diagonal in diamond is 25 cm greater than the length of the second diagonal and diamond area is 20 m^{2.}Determine the sizes of the diagonals. - 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. - 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? - Chord - TS

The radius of circle k measures 85 cm. Arc GH = 81 cm. What is TS? - Rotary cone

The volume of the rotation of the cone is 104 cm^{3}and angle between the side of the cone and base angle is 80°. Calculate lateral surface area of this cone. - 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. - Forces

In point X acts three orthogonal forces: F_{1}= 13 N, F_{2}= 8 N and F_{3}= 15 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - Sphere slices

Calculate volume and surface of a sphere, if the radii of parallel cuts r_{1}=37 cm, r_{2}=40 cm and its distance v=20 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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