# Grade - examples - page 71

- Concentric circles

In the circle with diameter 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord. - Stairs

Between adjacent levels are 15 stairs. If step will be 1.2 cm lower there would be 16 stairs. What is the stair height? - Combinatorics

The city has 7 fountains. Works only 6. How many options are there that can squirt ? - Prism

The volume of tetrahedral prism is 2.43 m^{3}. Base of prism is a parallelogram in which a side 2,5dm and height ha = 18cm. Calculate the height of the prism. - Diagonal 20

Diagonal pathway for the rectangular town plaza whose length is 20 m longer than the width. if the pathway is 20 m shorter than twice the width. How long should the pathway be? - Sequence 2

Write the first 5 members of an arithmetic sequence a_{11}=-14, d=-1 - Bank deposit

Ms Jana after the withdraw amount of 2,500 euros after year saving in bank. What was her deposit if the interest rate was 2.5% p.a.. - Rectangle vs square

One side of the rectangle is 1 cm shorter than the side of the square, the second side is 3 cm longer than the side of the square. Square and rectangle have the same content. Calculate the length of the sides of a square and a rectangle. - RT leg and perimeter

Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269. - Percentage of waste

In a square plate with side 75 cm we cut 4 same circles. Calculate the percentage of waste. - Cars motion

From point A car start at the speed of 90 km/h. Against it departs from the point B at the same time another car at 60 km/h. For how long and where they met if the distance between A and B is 180 km? - News

From 28 students buy magazine 10 The economist students, 10 Pravda students and 18 students don't buy any of these magazines. How many students buy both magazines? - Wood

Wood contains 12% water. 1 m^{3}of wood weighs 650 kg. How many liters of water it contains? - Inflow - outflow

The tank will fill by inflow for 145 minutes and empties by outflow for 188 minutes. How long take to fill tank if it is also opened the inflow and outflow? - Angle in RT

Determine the size of the smallest internal angle of a right triangle whose sides constitutes sizes consecutive members of arithmetic progressions. - The cylindrical container

The container has a cylindrical shape the base diameter 0.8 meters has a content area of the base is equal to the content area of the shell. How many full liters of water can be poured maximally into the container? - Slope

Calculate the slope of a line that intersects points (-84,41) and (-76,-32). - Vertices of RT

Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle. - Bulbs

In the box are 6 bulbs with power 75 W, 14 bulbs with power 40 W and 15 with 60 W. Calculate probability that a randomly selected bulb is: - Max - cone

From the iron bar (shape = prism) with dimensions 6.2 cm, 10 cm, 6.2 cm must be produced the greatest cone. a) Calculate cone volume. b) Calculate the waste.

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