# Examples for 9th grade - page 67

- Metal alloy

What is the ratio of metals in the alloy that is in the 50 tonnes of steel to 30 kg nickel? - Diamond

Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal. - Scouts

Scouts purchased for camp cans two types total cost 1460 CZK. First cans were for CZK 32 and second for 25 CZK. How many cans purchased each type? - Max - cone

From the iron bar (shape = prism) with dimensions 8.4 cm, 5.7 cm, 10.7 cm must be produced the greatest cone. a) Calculate cone volume. b) Calculate the waste. - Sphere

Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere. - 3d vector component

The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3? - Triangle midpoints

Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC. - 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 - 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?

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