Units - problems
One brick is 2 kg and half a brick heavy. What is the weight of one brick?
- Right Δ
Right triangle has length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle.
- Motion problem
From Bratislavy to Martina go car at speed 83 km/h. From Martina to Bratislavy go another car at speed 62 km/h. How many minutes before the meeting will be cars 21 km away?
Points A[1,5] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
Annual rainfall in our country are an average of 854 mm. How many m3 of water rains on average per hectare?
- Slope of track
Calculate the average slope of the rail tracks between Prievidza (309 m AMSL) and Bratislava (152 m AMSL), if the track is 158 km long.
If one side of the rectangle is larger 3-times and second 4-times, what percentage increases the area of rectangle?
John paid 1000 Euros in store for purchase. Calculate value added tax (VAT), which paid in purchase, if the VAT rate is 20%.
The cube weighs 18 kg. How weight is cube of the same material, if its dimensions are 3-times smaller?
Determine the dimensions of cuboid a, b, c; if diagonal d=6 dm has angle with edge a α=57° and has angle with edge b β=60°
- 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.
- Cut and cone
Calculate the volume of the rotation cone which lateral surface is circle arc with radius 14 cm and central angle 66 degrees.
- Angle between lines
Calculate the angle between these two lines: ? ?
Arnold had saved up a number of 1-euro coins. He stored coins in a single layer in a square. Left 4 coins. When he make square, which has one more row, missing 35 coins. How many euros he have?
Vojta left the house at three o'clockat 4 km/h. After half hour later went from the same place Filip by bicycle at speed 25 km/h. How long take Tilip to catch up Vojta and how far from the house?
- Built-up area
John build up area 4.3 x 8 = 34.4 m2 with building with a wall thickness 50 cm. How many centimeters would have to subtract from thickness of the walls that built-up area fell by 8%?
- Lead cube
Calculate the edge of the cube made from lead, which weighs 11 kg. The density of lead is 11341 kg/m3.
Truck went for 5 hours and 21 minutes. If truck increase speed by 19 km/h, went same distance in 2.9 hours. Calculate this distance.
If you know that cos(α) = sin (-968°), what is the angle α?
In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN.