# Examples for secondary school students - page 21

- Snowman 2

On the medal, which has the shape of a circle with a diameter 18 cm is sketched snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over snowman is the same as under it, 3. diameters of all circles express - Circular motion

Mass point moves moves uniformly in a circle with radius r = 3.4 m angular velocity ω = 3.6 rad/s. Calculate the period, frequency, and the centripetal acceleration of this movement. - Forth and back

Car goes from point A to point B at speed 78 km/h and back at 82 km/h. If went there and back at speed 81 km/h journey would take five minutes less. What is the distance between points A and B? - Tetrahedron

Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm. - Exp

If ?, then n is: - Sequence

In the arithmetic sequence is given: S_{n}=2304, d=2, a_{n}=95 Calculate a_{1}and n. - Linear independence

Determine if vectors u=(-4; -5) and v=(20; 25) are linear Linear dependent. - Rectangular trapezoid

The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid. - Goniometric form

Determine goniometric form of a complex number ?. - Metal alloy

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

The package has no more than 67 m of cloth. If we just cut it all on the blouses or all on dresses, no cloth left remain. On the one blouse consumes 3.8 m of cloth and on one dress 1.7 m. Determine the amount of the cloth in the package. - Sequence

Calculate what member of the sequence specified by ? has value 86. - Subway

Subway train went between two stations that gradually accelerated for 26 seconds and reached a speed of 72 km/h. At this rate, went 56 seconds. Then 16 seconds slowed to a stop. What was the distance between the stations? - Three digits number

How many are three-digit integers such that in they no digit repeats? - Components

In the box are 8 white, 4 blue and 2 red components. What is the probability that we pull one white, one blue and one red component without returning? - Pure quadratic equation

Solve pure quadratic equation ?. - Temperature calculus

Calculate percentage of temperature increase if changed from -9°C to 22°C? - Circles 2

Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm. - Price of state

Estimate the cost of the state based on following reason. State price is expressed as a percentage respectively share in the redistribution of national GDP. Employee creates monthly value € 868 (super-gross wage).Then tax him 35.2% employer contributions - Diamond

Determine the side of diamond if its content is S = 353 cm^{2}and one diagonal u_{2}= 45 cm.

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