Examples for secondary school students - page 28
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
How many different circles is determined by 9 points at the plane, if 6 of them lie in a straight line?
- Electrics - conductor
The wire is 106 meters long at 0 °C and at every temperature increase of 1 °C the length increases by 0.15 mm per 1 m length of wire. Determine a function which represents the overall length of the wire as a function of temperature. What is the length of t
- Triangular pyramid
Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm
- Euclid 5
Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
Cycling race was run at an average speed of 45 km/h. One cyclist lost with defect 8 minutes. How long and how far he must go at speed 51 km/h to catch peleton again?
For linear function f(x) = ax + b is f(14)=179; f(15)=154. Calculate m, if f(m) = 2019 .
Can the expression ? be factored into rational factors?
- Inclined plane
On the inclined plane with an angle of inclination of 30 ° we will put body (fixed point) with mass 2 kg. Determine the acceleration of the body motion on an inclined plane.
- Tin with oil
Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm2. Calculate how many liters of oil is in the tin.
- Car rent
Rental cars are paid a fixed daily fee plus 16 cents for each kilometer traveled. Samuel want to rent a car for a day and worked out that will pay 175 euros. When paying he got a 20% discount on the daily fee, the cost per kilometer is unchanged. Samuel th
- Bus stop
Determine at what time the bus leaves from the bus stop outside the village, if you know that when you leave home at 8:00 and go at speed 3 km/h, you come to a stop 9 minutes after the departure of the bus, and when you go speed at 4 km/h, you come to the
- Variations 3rd class
From how many elements we can create 13,800 variations 3rd class without repeating?
- Chord - TS
The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
- Rotary cylinder
The rotating cylinder has a surface area 69.08 cm2. The area of the shell is 62.8 cm 2. What is the diameter of the cylinder?
- The hall
The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m2. What were the original dimensions of the hall?
Exists a function whose derivation is the same function?
- Rectangle - sides
What is the perimeter of a rectangle with area 266 cm2 if length of the shorter side is 5 cm shorter than the length of the longer side?
The new copier copying a folder of papers 5 min. faster than the old. The operator used new, but out of toner and exchange took 5 min. In that time copied on the old. The whole work has been done for 9 min. How long would the work done only by old copier?
- Eight blocks
Dana had the task to save the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be four