Examples for secondary school students - page 21
- Fire tank
Whole fire tank was discharged once in 5 days by first out by second in $n days. Once firefighters pumped out 6/13 of water out from the tank and then let the water flow out both drain. How long take empty the tank?
- Triangle SAA
The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
- Chord AB
What is the length of the chord AB if its distance from the center S of the circle k(S, 92 cm) is 10 cm?
- Chemical parison
The blown parison (with shape of a sphere) have a volume 1.5 liters. What is its surface?
- Circle arc
Calculate the area of the circular arc in m2 where the diameter is 290 dm and a central angle is 135°. Result round to three decimal places.
- 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
- 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?
- Isosceles trapezoid
The lengths of the bases of the isosceles trapezoid are in the ratio 5:3, the arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.
- 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.
If ?, then n is:
- Linear independence
Determine if vectors u=(-4; -5) and v=(20; 25) are linear Linear dependent.
In the arithmetic sequence is given: Sn=2304, d=2, an=95 Calculate a1 and n.
- Goniometric form
Determine goniometric form of a complex number ?.
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.
- Metal alloy
What is the ratio of metals in the alloy that is in the 50 tonnes of steel to 30 kg nickel?
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?
Calculate what member of the sequence specified by ? has value 86.
- Three digits number
How many are three-digit integers such that in they no digit repeats?
Calculate height and volume of a regular tetrahedron whose edge has a length 18 cm.
- 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.