# Examples for 9th grade - page 59

- Variations

Determine the number of items when the count of variations of fourth class without repeating is 50 times larger than the count of variations of third class without repetition. - Vector - basic operations

There are given points A [13; 11] B [23; -4] C [9; -1] and D [-11; 25] a. Determine the coordinates of the vectors u=AB v=CD s=DB b. Calculate the sum of the vectors u + v c. Calculate difference of vectors u-v d. Determine the coordinates of the vector w - Triangle

Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 177 b = 124 c = 63 - Cuboid - edges

The sum of all edges cuboid are 11 meters. However, the width is twice shorter than the length and height is seven times longer than the width. Determine the dimensions of the cuboid. - Float boya

A 0.5 meter spherical float is used as a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and salt water weighs 1027 kg/m - Product - quadratic equation

Product of two numbers is 900. If we increase lowest number by 2 then product will increase by 150. Determine both numbers. - Diagonal - simple

Calculate the length of the diagonal of a rectangle with dimensions 5 cm and 12 cm. - Suzan

My daughter reaches X years in X squared, said Suzan father in 2013 during the celebration of her birthday. When will given fact become reality and how many years at that time will have Suzan? - Basic form

Expressed the ratios of values in the basic form: 0,5 t : 1,2 kg 200 l : 0,15 m^{3}12 t : 3600 kg 500 kg : 2,5 t 0,9 kg : 500 g 3,6 m : 240 cm 1200 mm : 2,4 m 300 l : 0,3 m^{3}6 min 30 s : 900 s - Sugar cubes

The glass has 600 ml of tea, which represents 80% of the volume of the glass. If you put twenty regular sugar cubes of 2 cm in the tea, how many ml of tea are poured? - Prism bases

Volume perpendicular quadrilateral prism is 360 cm^{3.}The edges of the base and height of the prism are in the ratio 5:4:2 Determine the area of the base and walls of the prism. - Three friends

The three friends spent 600 KC in a teahouse. Thomas paid twice as much as Paul. Paul a half less than Zdeněk. How many each paid? - Football league

In the 4th football league plays each of the 16 participants with each opponent twice. For every victory gets 3 points, 1 point for a draw, a defeat none. After the competition was team with 56 points and 8 defeats at 6th place. How many times have won? - Two masons

Two masons built the garage together - it took 18 days. If they worked independently, the other would work 15 days more than the first. For how many days would build the garage each mason himhelp? - Cone area and side

Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side. - Jane

Jane buy gift together for 464 Sk. For tie paid 4.5 times less than in the shirt, but 56 Sk more than for socks. How much she paid for each item in gift? - Truncated cone

A truncated cone has a base radius 40 cm and 10 cm and a height of 25 cm. Calculate its surface area and volume. - 3 years savings

Simple interest - Tereza has deposited CZK 100,000 in the bank with an annual interest rate of 1.5%. Interest is added each year and left aside. How many CZK crowns will has total after 3 years? - The farmer

The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 54, 71 and 44 meters. Find a suitable way to determine the. - Trapezium

The length of the base and the height size of the base of the trapezium is at ratio 5:3:2, the content area of the trapezium is 128 cm^{2.}Calculate the length of the base and the height of the trapezoid.

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