Examples for 9th grade - page 66
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].
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.
- 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 m2. 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 cm3 and angle between the side of the cone and base angle is 80°. Calculate lateral surface area of this cone.
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.
In point X acts three orthogonal forces: F1 = 13 N, F2 = 8 N and F3 = 15 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
- Sphere slices
Calculate volume and surface of a sphere, if the radii of parallel cuts r1=37 cm, r2=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